💡 Download the complete guide to AI-generated synthetic data!
Go to the ebook

In this tutorial, you will learn the key concepts behind MOSTLY AI’s synthetic data Quality Assurance (QA) framework. This will enable you to efficiently and reliably assess the quality of your generated synthetic datasets. It will also give you the skills to confidently explain the quality metrics to any interested stakeholders.

Using the code in this tutorial, you will replicate key parts of both the accuracy and privacy metrics that you will find in any MOSTLY AI QA Report. For a full-fledged exploration of the topic including a detailed mathematical explanation, see our peer-reviewed journal paper as well as the accompanying benchmarking study.

The Python code for this tutorial is publicly available and runnable in this Google Colab notebook.

QA reports for synthetic data sets

If you have run any synthetic data generation jobs with MOSTLY AI, chances are high that you’ve already encountered the QA Report. To access it, click on any completed synthesization job and select the “QA Report” tab:

Fig 1 - Click on a completed synthesization job.

Fig 2 - Select the “QA Report” tab.

At the top of the QA Report you will find some summary statistics about the dataset as well as the average metrics for accuracy and privacy of the generated dataset. Further down, you can toggle between the Model QA Report and the Data QA Report. The Model QA reports on the accuracy and privacy of the trained Generative AI model. The Data QA, on the other hand, visualizes the distributions not of the underlying model but of the outputted synthetic dataset. If you generate a synthetic dataset with all the default settings enabled, the Model and Data QA Reports should look the same. 

Exploring either of the QA reports you will discover various performance metrics, such as univariate and bivariate distributions for each of the columns and well as more detailed privacy metrics. You can use these metrics to precisely evaluate the quality of your synthetic dataset.

So how does MOSTLY AI calculate these quality assurance metrics?

In the following sections you will replicate the accuracy and privacy metrics. The code is almost exactly the code that MOSTLY AI runs under the hood to generate the QA Reports – it has been tweaked only slightly to improve legibility and usability. Working through this code will give you a hands-on insight into how MOSTLY AI evaluates synthetic data quality.

Preprocessing the data

The first step in MOSTLY AI’s synthetic data quality evaluation methodology is to take the original dataset and split it in half to yield two subsets: a training dataset and a holdout dataset. We then use only the training samples (so only 50% of the original dataset) to train our synthesizer and generate synthetic data samples. The holdout samples are never exposed to the synthesis process but are kept aside for evaluation.

Fig 3 - The first step is to split the original dataset in two equal parts and train the synthesizer on only one of the halves.

Distance-based quality metrics for synthetic data generation

Both the accuracy and privacy metrics are measured in terms of distance. Remember that we split the original dataset into two subsets: a training and a holdout set. Since these are all samples from the same dataset, these two sets will exhibit the same statistics and the same distributions. However, as the split was made at random we can expect a slight difference in the statistical properties of these two datasets. This difference is normal and is due to sampling variance

The difference (or, to put it mathematically: the distance) between the training and holdout samples will serve us as a reference point: in an ideal scenario, the synthetic data we generate should be no different from the training dataset than the holdout dataset is. Or to put it differently: the distance between the synthetic samples and the training samples should approximate the distance we would expect to occur naturally within the training samples due to sampling variance. 

If the synthetic data is significantly closer to the training data than the holdout data, this means that some information specific to the training data has leaked into the synthetic dataset. If the synthetic data is significantly farther from the training data than the holdout data, this means that we have lost information in terms of accuracy or fidelity.

For more context on this distance-based quality evaluation approach, check out our benchmarking study which dives into more detail.

Fig 4 - A perfect synthetic data generator creates data samples that are just as different from the training data as the holdout data. If this is not the case, we are compromising on either privacy or utility.

Let’s jump into replicating the metrics for both accuracy and privacy 👇

Synthetic data accuracy 

The accuracy of MOSTLY AI’s synthetic datasets is measured as the total variational distance between the empirical marginal distributions. It is calculated by treating all the variables in the dataset as categoricals (by binning any numerical features) and then measuring the sum of all deviations between the empirical marginal distributions.

The code below performs the calculation for all univariate and bivariate distributions and then averages across to determine the simple summary statistics you see in the QA Report.

First things first: let’s access the data. You can fetch both the original and the synthetic datasets directly from the Github repo:

repo = (
tgt = pd.read_parquet(f"{repo}/census-training.parquet")
    f"fetched original data with {tgt.shape[0]:,} records and {tgt.shape[1]} attributes"
syn = pd.read_parquet(f"{repo}/census-synthetic.parquet")
    f"fetched synthetic data with {syn.shape[0]:,} records and {syn.shape[1]} attributes"

fetched original data with 39,074 records and 12 attributes
fetched synthetic data with 39,074 records and 12 attributes

We are working with a version of the UCI Adult Income dataset. This dataset has just over 39K records and 12 columns. Go ahead and sample 5 random records to get a sense of what the data looks like:


Let’s define a helper function to bin the data in order treat any numerical features as categoricals:

def bin_data(dt1, dt2, bins=10):
    dt1 = dt1.copy()
    dt2 = dt2.copy()
    # quantile binning of numerics
    num_cols = dt1.select_dtypes(include="number").columns
    cat_cols = dt1.select_dtypes(
        include=["object", "category", "string", "bool"]
    for col in num_cols:
        # determine breaks based on `dt1`
        breaks = dt1[col].quantile(np.linspace(0, 1, bins + 1)).unique()
        dt1[col] = pd.cut(dt1[col], bins=breaks, include_lowest=True)
        dt2_vals = pd.to_numeric(dt2[col], "coerce")
        dt2_bins = pd.cut(dt2_vals, bins=breaks, include_lowest=True)
        dt2_bins[dt2_vals < min(breaks)] = "_other_"
        dt2_bins[dt2_vals > max(breaks)] = "_other_"
        dt2[col] = dt2_bins
    # top-C binning of categoricals
    for col in cat_cols:
        dt1[col] = dt1[col].astype("str")
        dt2[col] = dt2[col].astype("str")
        # determine top values based on `dt1`
        top_vals = dt1[col].value_counts().head(bins).index.tolist()
            np.setdiff1d(dt1[col].unique().tolist(), top_vals),
            np.setdiff1d(dt2[col].unique().tolist(), top_vals),
    return dt1, dt2

And a second helper function to calculate the univariate and bivariate accuracies:

def calculate_accuracies(dt1_bin, dt2_bin, k=1):
    # build grid of all cross-combinations
    cols = dt1_bin.columns
    interactions = pd.DataFrame(
        np.array(np.meshgrid(cols, cols)).reshape(2, len(cols) ** 2).T
    interactions.columns = ["col1", "col2"]
    if k == 1:
        interactions = interactions.loc[
            (interactions["col1"] == interactions["col2"])
    elif k == 2:
        interactions = interactions.loc[
            (interactions["col1"] < interactions["col2"])
        raise ("k>2 not supported")

    results = []
    for idx in range(interactions.shape[0]):
        row = interactions.iloc[idx]
        val1 = (
            dt1_bin[row.col1].astype(str) + "|" + dt1_bin[row.col2].astype(str)
        val2 = (
            dt2_bin[row.col1].astype(str) + "|" + dt2_bin[row.col2].astype(str)
        # calculate empirical marginal distributions (=relative frequencies)
        freq1 = val1.value_counts(normalize=True, dropna=False).to_frame(
        freq2 = val2.value_counts(normalize=True, dropna=False).to_frame(
        freq = freq1.join(freq2, how="outer").fillna(0.0)
        # calculate Total Variation Distance between relative frequencies
        tvd = np.sum(np.abs(freq["p1"] - freq["p2"])) / 2
        # calculate Accuracy as (100% - TVD)
        acc = 1 - tvd
        out = pd.DataFrame(
                "Column": [row.col1],
                "Column 2": [row.col2],
                "TVD": [tvd],
                "Accuracy": [acc],

    return pd.concat(results)

Then go ahead and bin the data. We restrict ourselves to 100K records for efficiency.

# restrict to max 100k records
tgt = tgt.sample(frac=1).head(n=100_000)
syn = syn.sample(frac=1).head(n=100_000)
# bin data
tgt_bin, syn_bin = bin_data(tgt, syn, bins=10)

Now you can go ahead and calculate the univariate accuracies for all the columns in the dataset:

# calculate univariate accuracies
acc_uni = calculate_accuracies(tgt_bin, syn_bin, k=1)[['Column', 'Accuracy']]

Go ahead and inspect the first 5 columns:


Now let’s calculate the bivariate accuracies as well. This measures how well the relationships between all the sets of two columns are maintained.

# calculate bivariate accuracies
acc_biv = calculate_accuracies(tgt_bin, syn_bin, k=2)[
    ["Column", "Column 2", "Accuracy"]
acc_biv = pd.concat(
        acc_biv.rename(columns={"Column": "Column 2", "Column 2": "Column"}),

The bivariate accuracy that is reported for each column in the MOSTLY AI QA Report is an average over all of the bivariate accuracies for that column with respect to all the other columns in the dataset. Let’s calculate that value for each column and then create an overview table with the univariate and average bivariate accuracies for all columns:

# calculate the average bivariate accuracy
acc_biv_avg = (
    .to_frame("Bivariate Accuracy")
# merge to univariate and avg. bivariate accuracy to single overview table
acc = pd.merge(
    acc_uni.rename(columns={"Accuracy": "Univariate Accuracy"}),
).sort_values("Univariate Accuracy", ascending=False)
# report accuracy as percentage
acc["Univariate Accuracy"] = acc["Univariate Accuracy"].apply(
    lambda x: f"{x:.1%}"
acc["Bivariate Accuracy"] = acc["Bivariate Accuracy"].apply(
    lambda x: f"{x:.1%}"

Finally, let’s calculate the summary statistic values that you normally see at the top of any MOSTLY AI QA Report: the overall accuracy as well as the average univariate and bivariate accuracies. We take the mean of the univariate and bivariate accuracies for all the columns and then take the mean of the result to arrive at the overall accuracy score:

print(f"Avg. Univariate Accuracy: {acc_uni['Accuracy'].mean():.1%}")
print(f"Avg. Bivariate Accuracy:  {acc_biv['Accuracy'].mean():.1%}")
acc_avg = (acc_uni["Accuracy"].mean() + acc_biv["Accuracy"].mean()) / 2
print(f"Avg. Overall Accuracy:    {acc_avg:.1%}")

Avg. Univariate Accuracy: 98.9%
Avg. Bivariate Accuracy:  97.7%
Avg. Overall Accuracy:    98.3%

If you’re curious how this compares to the values in the MOSTLY AI QA Report, go ahead and download the tgt dataset and synthesize it using the default settings. The overall accuracy reported will be close to 98%.

Next, let’s see how MOSTLY AI generates the visualization segments of the accuracy report. The code below defines two helper functions: one for the univariate and one for the bivariate plots. Getting the plots right for all possible edge cases is actually rather complicated, so while the code block below is lengthy, this is in fact the trimmed-down version of what MOSTLY AI uses under the hood. You do not need to worry about the exact details of the implementation here; just getting an overall sense of how it works is enough:

import plotly.graph_objects as go

def plot_univariate(tgt_bin, syn_bin, col, accuracy):
    freq1 = (
        tgt_bin[col].value_counts(normalize=True, dropna=False).to_frame("tgt")
    freq2 = (
        syn_bin[col].value_counts(normalize=True, dropna=False).to_frame("syn")
    freq = freq1.join(freq2, how="outer").fillna(0.0).reset_index()
    freq = freq.sort_values(col)
    freq[col] = freq[col].astype(str)

    layout = go.Layout(
            text=f"<b>{col}</b> <sup>{accuracy:.1%}</sup>", x=0.5, y=0.98
        margin=dict(l=10, r=10, b=10, t=40, pad=5),
        hovermode="x unified",
    fig = go.Figure(layout=layout)
    trn_line = go.Scatter(
    syn_line = go.Scatter(

def plot_bivariate(tgt_bin, syn_bin, col1, col2, accuracy):
    x = (
        pd.concat([tgt_bin[col1], syn_bin[col1]])
    y = (
        pd.concat([tgt_bin[col2], syn_bin[col2]])
    df = pd.merge(x, y, how="cross")
    df = pd.merge(
        pd.concat([tgt_bin[col1], tgt_bin[col2]], axis=1)
    df = pd.merge(
        pd.concat([syn_bin[col1], syn_bin[col2]], axis=1)
    df = df.sort_values([col1, col2], ascending=[True, True]).reset_index(
    df["target"] = df["target"].fillna(0.0)
    df["synthetic"] = df["synthetic"].fillna(0.0)
    # normalize values row-wise (used for visualization)
    df["target_by_row"] = df["target"] / df.groupby(col1)["target"].transform(
    df["synthetic_by_row"] = df["synthetic"] / df.groupby(col1)[
    # normalize values across table (used for accuracy)
    df["target_by_all"] = df["target"] / df["target"].sum()
    df["synthetic_by_all"] = df["synthetic"] / df["synthetic"].sum()
    df["y"] = df[col1].astype("str")
    df["x"] = df[col2].astype("str")

    layout = go.Layout(
            text=f"<b>{col1} ~ {col2}</b> <sup>{accuracy:.1%}</sup>",
        margin=dict(l=10, r=10, b=10, t=40, pad=5),
        # prevent Plotly from trying to convert strings to dates
    fig = go.Figure(layout=layout).set_subplots(
        subplot_titles=("target", "synthetic"),
    # plot content
    hovertemplate = (
        col1[:10] + ": `%{y}`<br />" + col2[:10] + ": `%{x}`<br /><br />"
    hovertemplate += "share target vs. synthetic<br />"
    hovertemplate += "row-wise: %{customdata[0]} vs. %{customdata[1]}<br />"
    hovertemplate += "absolute: %{customdata[2]} vs. %{customdata[3]}<br />"
    customdata = df[
    ].apply(lambda x: x.map("{:.2%}".format))
    heat1 = go.Heatmap(
        colorscale=["white", "#A7A7A7", "#7B7B7B", "#666666"],
    heat2 = go.Heatmap(
        colorscale=["white", "#81EAC3", "#43E0A5", "#24DB96"],
    fig.add_trace(heat1, row=1, col=1)
    fig.add_trace(heat2, row=1, col=2)

Now you can create the plots for the univariate distributions:

for idx, row in acc_uni.sample(n=5, random_state=0).iterrows():
    plot_univariate(tgt_bin, syn_bin, row["Column"], row["Accuracy"])

Fig 5 - Sample of 2 univariate distribution plots.

As well as the bivariate distribution plots:

for idx, row in acc_biv.sample(n=5, random_state=0).iterrows():
        tgt_bin, syn_bin, row["Column"], row["Column 2"], row["Accuracy"]

Fig 6 - Sample of 2 bivariate distribution plots.

Now that you have replicated the accuracy component of the QA Report in sufficient detail, let’s move on to the privacy section.

Synthetic data privacy

Just like accuracy, the privacy metric is also calculated as a distance-based value. To gauge the privacy risk of the generated synthetic data, we calculate the distances between the synthetic samples and their "nearest neighbor" (i.e., their most similar record) from the original dataset. This nearest neighbor could be either in the training split or in the holdout split. We then tally the ratio of synthetic samples that are closer to the holdout and the training set. Ideally, we will see an even split, which would mean that the synthetic samples are not systematically any closer to the original dataset than the original samples are to each other. 

Fig 7 - A perfect synthetic data generator creates synthetic records that are just as different from the training data as from the holdout data.

The code block below uses the scikit-learn library to perform a nearest-neighbor search across the synthetic and original datasets. We then use the results from this search to calculate two different distance metrics: the Distance to the Closest Record (DCR) and the Nearest Neighbor Distance Ratio (NNDR), both at the 5-th percentile.

from sklearn.compose import make_column_transformer
from sklearn.neighbors import NearestNeighbors
from sklearn.preprocessing import OneHotEncoder
from sklearn.impute import SimpleImputer

no_of_records = min(tgt.shape[0] // 2, syn.shape[0], 10_000)
tgt = tgt.sample(n=2 * no_of_records)
trn = tgt.head(no_of_records)
hol = tgt.tail(no_of_records)
syn = syn.sample(n=no_of_records)

string_cols = trn.select_dtypes(exclude=np.number).columns
numeric_cols = trn.select_dtypes(include=np.number).columns
transformer = make_column_transformer(
    (SimpleImputer(missing_values=np.nan, strategy="mean"), numeric_cols),
    (OneHotEncoder(), string_cols),
transformer.fit(pd.concat([trn, hol, syn], axis=0))
trn_hot = transformer.transform(trn)
hol_hot = transformer.transform(hol)
syn_hot = transformer.transform(syn)

# calculcate distances to nearest neighbors
index = NearestNeighbors(
    n_neighbors=2, algorithm="brute", metric="l2", n_jobs=-1
# k-nearest-neighbor search for both training and synthetic data, k=2 to calculate DCR + NNDR
dcrs_hol, _ = index.kneighbors(hol_hot)
dcrs_syn, _ = index.kneighbors(syn_hot)
dcrs_hol = np.square(dcrs_hol)
dcrs_syn = np.square(dcrs_syn)

Now calculate the DCR for both datasets:

dcr_bound = np.maximum(np.quantile(dcrs_hol[:, 0], 0.95), 1e-8)
ndcr_hol = dcrs_hol[:, 0] / dcr_bound
ndcr_syn = dcrs_syn[:, 0] / dcr_bound
    f"Normalized DCR 5-th percentile original  {np.percentile(ndcr_hol, 5):.3f}"
    f"Normalized DCR 5-th percentile synthetic {np.percentile(ndcr_syn, 5):.3f}"

Normalized DCR 5-th percentile original  0.001
Normalized DCR 5-th percentile synthetic 0.009

As well as the NNDR:

    f"NNDR 5-th percentile original  {np.percentile(dcrs_hol[:,0]/dcrs_hol[:,1], 5):.3f}"
    f"NNDR 5-th percentile synthetic {np.percentile(dcrs_syn[:,0]/dcrs_syn[:,1], 5):.3f}"

NNDR 5-th percentile original  0.019
NNDR 5-th percentile synthetic 0.058

For both privacy metrics, the distance value for the synthetic dataset should be similar but not smaller. This gives us confidence that our synthetic record has not learned privacy-revealing information from the training data.

Quality assurance for synthetic data with MOSTLY AI

In this tutorial, you have learned the key concepts behind MOSTLY AI’s Quality Assurance framework. You have gained insight into the preprocessing steps that are required as well as a close look into exactly how the accuracy and privacy metrics are calculated. With these newly acquired skills, you can now confidently and efficiently interpret any MOSTLY AI QA Report and explain it thoroughly to any interested stakeholders.

For a more in-depth exploration of these concepts and the mathematical principles behind them, check out the benchmarking study or the peer-reviewed academic research paper to dive deeper.

You can also check out the other Synthetic Data Tutorials:

Synthetic data holds the promise of addressing the underrepresentation of minority classes in tabular data sets by adding new, diverse, and highly realistic synthetic samples. In this post, we'll benchmark AI-generated synthetic data for upsampling highly unbalanced tabular data sets. Specifically, we compare the performance of predictive models trained on data sets upsampled with synthetic records to that of well-known upsampling methods, such as naive oversampling or SMOTE-NC.

Our experiments are conducted on multiple data sets and different predictive models. We demonstrate that synthetic data can improve predictive accuracy for minority groups as it creates diverse data points that fill gaps in sparse regions in feature space.

Our results highlight the potential of synthetic data upsampling as a viable method for improving predictive accuracy on highly unbalanced data sets. We show that upsampled synthetic training data consistently results in top-performing predictive models, in particular for mixed-type data sets containing a very low number of minority samples, where it outperforms all other upsampling techniques.

The definition of synthetic data

AI-generated synthetic data, which we refer to as synthetic data throughout, is created by training a generative model on the original data set. In the inference phase, the generative model creates statistically representative, synthetic records from scratch.

The use of synthetic data has gained increasing importance in various industries, particularly due to its primary use case of enhancing data privacy. Beyond privacy, synthetic data offers the possibility to modify and tailor data sets to our specific needs. In this research paper, we investigate the potential of synthetic data to improve the performance of machine learning algorithms on data sets with unbalanced class distributions, specifically through the synthetic upsampling of minority classes.

Upsampling for class imbalance

Class imbalance is a common problem in many real-world tabular data sets where the number of samples in one or more classes is significantly lower than the others. Such imbalances can lead to poor prediction performance for the minority classes, often of greatest interest in many applications, such as detecting fraud or extreme insurance claims.

Traditional upsampling methods, such as naive oversampling or SMOTE, have shown some success in mitigating this issue. However, the effectiveness of these methods is often limited, and they may introduce biases in the data, leading to poor model performance. In recent years, synthetic data has emerged as a promising alternative to traditional upsampling methods. By creating highly realistic samples for minority classes, synthetic data can significantly improve the accuracy of predictive models.

While upsampling methods like naive oversampling and SMOTE are effective in addressing unbalanced data sets, they also have their limitations. Naive oversampling mitigates class imbalance effects by simply duplicating minority class examples. Due to this strategy, they bear the risk of overfitting the model to the training data, resulting in poor generalization in the inference phase.

SMOTE, on the other hand, generates new records by interpolating between existing minority-class samples, leading to higher diversity. However, SMOTE’s ability to increase diversity is limited when the absolute number of minority records is very low. This is especially true when generating samples for mixed-type data sets containing categorical columns. For mixed-type data sets, SMOTENC is commonly used as an extension for handling categorical columns.

SMOTE-NC may not work well with non-linear decision boundaries, as it only linearly interpolates between minority records. This can lead to SMOTE-NC examples being generated in an “unfavorable” region of feature space, far from where additional samples would help the predictive model place a decision boundary.

All these limitations highlight the need for exploring alternative upsampling methods, such as synthetic data upsampling, that can overcome these challenges and improve the accuracy of minority group predictions.

The strength of upsampling minority classes with AI-generated synthetic data is that the generative model is not limited to upsampling or interpolating between existing minority classes. Most AI-based generators can create realistic synthetic data examples in any region of feature space and, thus, considerably increase diversity. Because they are not tied to existing minority samples, AI-based generators can also leverage and learn from the properties of (parts of) the majority samples that are transferable to minority examples.

An additional strength of using AI-based upsampling is that it can be easily extended to more complex data structures, such as sequential data, where not only one but many rows in a data set belong to a single data subject. This aspect of synthetic data upsampling is, however, out of the scope of this study.

In this post, we present a comprehensive benchmark study comparing the performance of predictive models trained on unbalanced data upsampled with AI-generated synthetic data, naive upsampling, and SMOTE-NC upsampling. Our experiments are carried out on various data sets and using different predictive models. 

The upsampling experiment

Data upsampling experiment setup

Figure 1: Experimental Setup: (1) We split the original data set into a base data set and a holdout. (2) Strong imbalances are introduced in the base data set by downsampling the minority classes to fractions as low as 0.05% to yield the unbalanced training data. (3) We test different mitigation strategies: balancing through naive upsampling, SMOTE-NC upsampling, and upsampling with AI-generated synthetic records (the hybrid data set). (4) We train LGBM, RandomForest, and XGB classifiers on the balanced and unbalanced training data. (5) We evaluate the properties of the upsampling techniques by measuring the performance of the trained classifier on the holdout set. Steps 1–5 are repeated five times, and we report the mean AUC-ROC as well as the AUC-PR.

For every data set we use in our experiments, we run through the following steps (see Fig. 1):

  1. We split the original data set into a base and a holdout set by using a five-fold stratified sampling approach to ensure that each class is represented proportionally.
  2. All of the original data sets have a binary target column and only a rather moderate imbalance with the fraction of the minority class ranging from 6% to 24% (see table 1 for data set details). We artificially induce different levels of strong imbalances to the base set by randomly down-sampling the minority class, resulting in unbalanced training data sets with minority fractions of 0.05%, 0.1%, 0.2%, 0.5%, 1%, 2%, and 5%.
  3. To mitigate the strong imbalances in the training data sets, we apply three different upsampling techniques:
    • naive oversampling (red box in fig. 1) duplicating existing examples of the minority classes (scikit-learn, RandomOverSampler)
    • SMOTE-NC (blue box in fig. 1): applying the SMOTE-NC upsampling technique (scikit-learn, SMOTENC)
    • Hybrid (green box in fig. 1): The hybrid data set represents the concept of enriching unbalanced training data with AI-generated synthetic data. It is composed of the training data (including majority samples and a limited number of minority samples) along with additional synthetic minority samples that are created using an AI-based synthetic data generator. This generator is trained on the highly unbalanced training data set. In this study, we use the MOSTLY AI synthetic data platform. It is freely accessible for generating highly realistic AI-based synthetic data.

      In all cases, we upsample the minority class to achieve a 50:50 balance between the majority and minority classes, resulting in the naively balanced, the SMOTE-NC balanced, and the balanced hybrid data set.
  4. We assess the benefits of the different upsampling techniques by training three popular classifiers: RandomForest, XGB, and LightGBM, on the balanced data sets. Additionally, we train the classifiers on the heavily unbalanced training data sets as a baseline in the evaluation of the predictive model performance.
  5. The classifiers are scored on the holdout set, and we calculate the AUC-ROC score and AUC-PR score across all upsampling techniques and initial imbalance ratios for all 5 folds. We report the average scores over five different samplings and model predictions. We opt for AUC metrics to eliminate dependencies on thresholds, as seen in, e.g., F1 scores.

The results of upsampling

We run four publicly available data sets (Figure 1) of varying sizes through steps 1–5: Adult Credit Card, Insurance, and Census (Kohavi and Becker). All data sets tested are of mixed type (categorical and numerical features) with a binary, that is, a categorical target column.

In step 2 (Fig. 1), we downsample minority classes to induce strong imbalances. For the smaller data sets with ~30k records, downsampling to minority-class fractions of 0.1% results in extremely low numbers of minority records.

The downsampled Adult and Credit Card unbalanced training data sets contain as little as 19 and 18 minority records, respectively. This scenario mimics situations where data is limited and extreme cases occur rarely. Such setups create significant challenges for predictive models, as they may encounter difficulty making accurate predictions and generalizing well on unseen data.

Please note that the holdout sets on which the trained predictive models are scored are not subject to extreme imbalances as they are sampled from the original data before downsampling is applied. The imbalance ratios of the holdout set are moderate and vary from 6 to 24%.

In the evaluation, we report both the AUC-ROC and the AUC-PR due to the moderate but inhomogeneous distribution of minority fractions in the holdout set. The AUC-ROC is a very popular and expressive metric, but it is known to be overly optimistic on unbalanced optimization problems. While the AUC-ROC considers both classes, making it susceptible to neglecting the minority class, the AUC-PR focuses on the minority class as it is built up by precision and recall.

Upsampling the Adult income dataset

The largest differences between upsampling techniques are observed in the AUC-ROC when balancing training sets with a substantial class imbalance of 0.05% to 0.5%. This scenario involves a very limited number of minority samples, down to 19 for the Adult unbalanced training data set.

For the RF and the LGBM classifiers trained on the balanced hybrid data set, the AUC-ROC is larger than the ones obtained with other upsampling techniques. Differences can go up to 0.2 (RF classifier, minority fraction of 0.05%) between the AI-based synthetic upsampling and the second-best method.

The AUC-PR shows similar yet less pronounced differences. LGBM and XGB classifiers trained on the balanced hybrid data set perform best throughout almost all minority fractions. Interestingly, results for the RF classifier are mixed. Upsampling with synthetic data does not always lead to better performance, but it is always among the best-performing methods.

While synthetic data upsampling improves results through most of the minority fractions for the XGB classifier, too, the differences in performance are less pronounced. Especially the XGB classifier trained on the highly unbalanced training data performs surprisingly well. This suggests that the XGB classifier is better suited for handling unbalanced data.

The reason for the performance differences in the AUC-ROC and AUC-PR is due to the low diversity and, consequently, overfitting when using naive or SMOTE-NC upsampling. These effects are visible in, e.g., the ROC and PR curves of the LGBM classifier for a minority fraction of 0.1% (fig. 3).

Every point on these curves corresponds to a specific prediction threshold for the classifier. The set of threshold values is defined by the variance of probabilities predicted by the models when scored on the holdout set. For both the highly unbalanced training data and the naively upsampled one, we observe very low diversity, with more than 80% of the holdout samples predicted to have an identical, very low probability of belonging to the minority class.

In the plot of the PR curve, this leads to an accumulation of points in the area with high precision and low recall, which means that the model is very conservative in making positive predictions and only makes a positive prediction when it is very confident that the data point belongs to the positive, that is, the minority class. This demonstrates the effect of overfitting on a few samples in the minority group.

SMOTE-NC has a much higher but still limited diversity, resulting in a smoother PR curve which, however, still contains discontinuities and has a large segment where precision and recall change rapidly with small changes in the prediction threshold.

The hybrid data set offers high diversity during model training, resulting in almost every holdout sample being assigned a unique probability of belonging to the minority class. Both ROC and PR curves are smooth and have a threshold of ~0.5 at the center, the point that is closest to the perfect classifier.

The limited power in creating diverse samples in situations where the minority class is severely underrepresented stems from naive upsampling and SMOTE-NC being limited to duplicating and interpolating between existing minority samples. Both methods are bound to a limited region in feature space.

Upsampling with AI-based synthetic minority samples, on the other hand, can, in principle, populate any region in feature space and can leverage and learn from properties of the majority samples which are transferable to minority examples, resulting in more diverse and realistic synthetic minority samples.

We analyze the difference in diversity by further “drilling down” the minority class (feature “income” equals “high”) and comparing the distribution of the feature “education” for the female subgroup (feature “sex” equals “female”) in the upsampled data sets (fig. 4).

For a minority fraction of 0.1%, this results in only three female minority records. Naive upsampling and SMOTE-NC have a very hard time generating diversity in such settings. Both just duplicate the existing categories “Bachelors”, “HS-grade”, and "Assoc-acdm,” resulting in a strong distortion of the distribution of the “education” feature as compared to the distribution in the holdout data set.

The distribution of the hybrid data has some imperfections, too, but it recovers the holdout distribution to a much better degree. Many more “education” categories are populated, and, with a few exceptions, the frequencies of the holdout data set are recovered to a satisfactory level. This ultimately leads to a larger diversity in the hybrid data set than in the naively balanced or SMOTE-NC balanced one.

Diversity assessment with the Shannon entropy

We quantitatively assess diversity with the Shannon entropy, which measures the variability within a data set particularly for categorical data. It provides a measure of how uniformly the different categories of a specific feature are distributed within the data set.

The Shannon Entropy (SE) of a specific feature is defined as

Shannon entropy for diversity assessment

where p(i) represents the probability of occurrence, i.e. the relative frequency of category i. SE ranges from 0 to log2(N), where N is the total number of categories. A value of 0 indicates maximum certainty with only one category, while higher entropy implies greater diversity and uncertainty, indicating comparable probabilities p(i) across categories.

In Figure 5, we report the Shannon entropy for different features and subgroups of the high-income population. In all cases, data diversity is the largest for the holdout data set. The downsampled training data set (unbalanced) has a strongly reduced SE, especially when focusing on the small group of high-income women. Naive and SMOTE-NC upsampling cannot recover any of the diversity in the holdout as both are limited to the categories present in the minority class. In line with the results presented in the paragraph above, synthetic data recovers the SE, i.e., the diversity of the holdout data set, to a large degree.

Upsampling the Credit Card data set

The Credit Card data set has similar properties as the Adult data set. The number of records, features, and the original, moderate imbalance are comparable. This again results in a very small number of minority records (18) after downsampling to a 0.1% minority fraction.

The main difference between them is the fact that Credit Card consists of more numeric features. The performance of different upsampling techniques on the unbalanced Credit Card training data set shows similar results to the Adult Data set, too. AUC-ROC and AUC-PR for both LGBM and RF classifiers improve over naive upsampling and SMOTE-NC when using the hybrid data set.

Again, the performance of the XGB model is more comparable between the different balanced data sets and we find very good performance for the highly-unbalanced training data set. Here, too, the hybrid data set is always among the best-performing upsampling techniques.

Interestingly, SMOTE-NC performs worst almost throughout all the metrics. This is surprising because we expect this data set, consisting mainly of numerical features, to be favorable for the SMOTE-NC upsampling technique.

Upsampling the Insurance data set

The Insurance data set is larger than Adult and Census resulting in a larger number of minority records (268) when downsampling to the 0.1% minority fraction. This leads to a much more balanced performance between different upsampling techniques.

A notable difference in performance only appears for very small minority fractions. For minority fractions below 0.5%, both the AUC-ROC and AUC-PR of LGBM and XGB classifiers trained on the hybrid data set are consistently larger than for classifiers trained on other balanced data sets. The maximum performance gains, however, are smaller than those observed for “Adult” and “Credit Card”.

Upsampling the Census data set

The Census data set has the largest number of features of all the data sets tested in this study. Especially, the 28 categorical features pose a challenge for SMOTE-NC, leading to poor performance in terms of AUC-PR.

Comparably to the Insurance data set, the performance of the LGBM classifier severely deteriorates when trained on highly unbalanced data sets. On the other hand, the XGB model excels and performs very well even on unbalanced training sets.

The Census data set highlights the importance of carefully selecting the appropriate model and upsampling technique when working with data sets that have high dimensionality and unbalanced class distributions, as performances can vary a lot.

Upsampling with synthetic data mitigates this variance, as all models trained on the hybrid data set are among the best performers across all classifiers and ranges of minority fractions.

Synthetic data for upsampling

AI-based synthetic data generation can provide an effective solution to the problem of highly unbalanced data sets in machine learning. By creating diverse and realistic samples, upsampling with synthetic data generation can improve the performance of predictive models. This is especially true for cases where not only the minority fraction is low but also the absolute number of minority records is at a bare minimum. In such extreme settings, training on data upsampled with AI-generated synthetic records leads to better performance of prediction models than upsampling with SMOTE-NC or naive upsampling. Across all parameter settings explored in this study, synthetic upsampling resulted in predictive models which rank among the top-performing ones.

In this tutorial, you will learn how to use synthetic rebalancing to improve the performance of machine-learning (ML) models on imbalanced classification problems. Rebalancing can be useful when you want to learn more of an otherwise small or underrepresented population segment by generating more examples of it. Specifically, we will look at classification ML applications in which the minority class accounts for less than 0.1% of the data. 

We will start with a heavily imbalanced dataset. We will use synthetic rebalancing to create more high-quality, statistically representative instances of the minority class. We will compare this method against 2 other types of rebalancing to explore their advantages and pitfalls. We will then train a downstream machine learning model on each of the rebalanced datasets and evaluate their relative predictive performance. The Python code for this tutorial is publicly available and runnable in this Google Colab notebook.

Synthetic rebalancing

Fig 1 - Synthetic rebalancing creates more statistically representative instances of the minority class

Why should I rebalance my dataset?

In heavily imbalanced classification projects, a machine learning model has very little data to effectively learn patterns about the minority class. This will affect its ability to correctly class instances of this minority class in the real (non-training) data when the model is put into production. A common real-world example is credit card fraud detection: the overwhelming majority of credit card transactions are perfectly legitimate, but it is precisely the rare occurrences of illegitimate use that we would be interested in capturing. 

Let’s say we have a training dataset with 100,000 credit card transactions which contains 999,900 legitimate transactions and 100 fraudulent ones. A machine-learning model trained on this dataset would have ample opportunity to learn about all the different kinds of legitimate transactions, but only a small sample of 100 records in which to learn everything it can about fraudulent behavior. Once this model is put into production, the probability is high that fraudulent transactions will occur that do not follow any of the patterns seen in the small training sample of 100 fraudulent records. The machine learning model is unlikely to classify these fraudulent transactions.

So how can we address this problem? We need to give our machine learning model more examples of fraudulent transactions in order to ensure optimal predictive performance in production. This can be achieved through rebalancing.

Rebalancing Methods 

We will explore three types of rebalancing:

  1. Random (or “naive”) oversampling
  2. SMOTE upsampling
  3. Synthetic rebalancing

The tutorial will give you hands-on experience with each type of rebalancing and provide you with in-depth understanding of the differences between them so you can choose the right method for your use case. We’ll start by generating an imbalanced dataset and showing you how to perform synthetic rebalancing using MOSTLY AI's synthetic data generator. We will then compare performance metrics of each rebalancing method on a downstream ML task.

But first things first: we need some data.

Generate an Imbalanced Dataset

For this tutorial, we will be using the UCI Adult Income dataset, as well as the same training and validation split, that was used in the Train-Synthetic-Test-Real tutorial. However, for this tutorial we will work with an artificially imbalanced version of the dataset containing only 0.1% of high-income (>50K) records in the training data, by downsampling the minority class. The downsampling has already been done for you, but if you want to reproduce it yourself you can use the code block below:

def create_imbalance(df, target, ratio):
    val_min, val_maj = df[target].value_counts().sort_values().index
    df_maj = df.loc[df[target]==val_maj]
    n_min = int(df_maj.shape[0]/(1-ratio)*ratio)
    df_min = df.loc[df[target]==val_min].sample(n=n_min, random_state=1)
    df_maj = df.loc[df[target]==val_maj]
    df_imb = pd.concat([df_min, df_maj]).sample(frac=1, random_state=1)
    return df_imb

df_trn = pd.read_csv(f'{repo}/census-training.csv')
df_trn_imb = create_imbalance(df_trn, 'income', 1/1000)
df_trn_imb.to_csv('census-training-imbalanced.csv', index=False)

Let’s take a quick look at this imbalanced dataset by randomly sampling 10 rows. For legibility let’s select only a few columns, including the income column as our imbalanced feature of interest:

trn = pd.read_csv(f'{repo}/census-training-imbalanced.csv')

You can try executing the line above multiple times to see different samples. Still, due to the strong class imbalance, the chance of finding a record with high income in a random sample of 10 is minimal. This would be problematic if you were interested in creating a machine learning model that could accurately classify high-income records (which is precisely what we’ll be doing in just a few minutes).

The problem becomes even more clear when we try to sample a specific sub-group in the population. Let’s sample all the female doctorates with a high income in the dataset. Remember, the dataset contains almost 30 thousand records.

    & (trn.sex=='Female') 
    & (trn.education=='Doctorate')

It turns out there are actually no records of this type in the training data. Of course, we know that these kinds of individuals exist in the real world and so our machine learning model is likely to encounter them when put in production. But having had no instances of this record type in the training data, it is likely that the ML model will fail to classify this kind of record correctly. We need to provide the ML model with a higher quantity and more varied range of training samples of the minority class to remedy this problem.

Synthetic rebalancing with MOSTLY AI

MOSTLY AI offers a synthetic rebalancing feature that can be used with any categorical column. Let’s walk through how this works:

  1. Download the imbalanced dataset here if you haven’t generated it yourself already. Use Ctrl+S or Cmd+S to save the file locally. 
  1. Go to your MOSTLY AI account and navigate to “Synthetic Datasets”. Upload census-training-imbalanced.csv and click “Proceed”.
data upload for synthetic data generation

Fig 2 - Upload the original dataset to MOSTLY AI’s synthetic data generator.

  1. On the next page, click “Data Settings” and then click on the “Income” column
Data settings for synthetic data generation

Fig 3 - Navigate to the Data Settings of the Income column.

  1. Set the Encoding Type to “Categorical” and select the option to “Use this column to rebalance the table”. Then add a new row and rebalance the “>50K” column to be “50%” of the dataset. This will synthetically upsample the minority class to create an even split between high-income and low-income records. 
Rebalancing using a synthetic data generator

Fig 4 - Set the relevant settings to rebalance the income column.

  1. Click “Save” and on the next page click “Create a synthetic dataset” to launch the job.
Start synthetic data generation

Fig 5 - Launch the synthetic data generation

Once the synthesization is complete, you can download the synthetic dataset to disk. Then return to wherever you are running your code and use the following code block to create a DataFrame containing the synthetic data.

# upload synthetic dataset
import pandas as pd

    # check whether we are in Google colab
    from google.colab import files
    print("running in COLAB mode")
    repo = 'https://github.com/mostly-ai/mostly-tutorials/raw/dev/rebalancing'
    import io
    uploaded = files.upload()
    syn = pd.read_csv(io.BytesIO(list(uploaded.values())[0]))
    print(f"uploaded synthetic data with {syn.shape[0]:,} records and {syn.shape[1]:,} attributes")
    print("running in LOCAL mode")
    repo = '.'
    print("adapt `syn_file_path` to point to your generated synthetic data file")
    syn_file_path = './census-synthetic-balanced.csv'
    syn = pd.read_csv(syn_file_path)
    print(f"read synthetic data with {syn.shape[0]:,} records and {syn.shape[1]:,} attributes")

Let's now repeat the data exploration steps we performed above with the original, imbalanced dataset. First, let’s display 10 randomly sampled synthetic records. We'll subset again for legibility. You can run this line multiple times to get different samples. 

# sample 10 random records
syn_sub = syn[['age','education','marital_status','sex','income']]

This time, you should see that the records are evenly distributed across the two income classes.

Let's now investigate all female doctorates with a high income in the synthetic, rebalanced dataset:  

    & (syn_sub.sex=='Female') 
    & (syn_sub.education=='Doctorate')

The synthetic data contains a list of realistic, statistically sound female doctorates with a high income. This is great news for our machine learning use case because it means that our ML model will have plenty of data to learn about this particular important subsegment.

Evaluate ML performance using TSTR

Let’s now compare the quality of different rebalancing methods by training a machine learning model on the rebalanced data and evaluating the predictive performance of the resulting models. 

We will investigate and compare 3 types of rebalancing:

  1. Random (or “naive”) oversampling
  2. SMOTE upsampling
  3. Synthetic rebalancing

The code block below defines the functions that will preprocess your data, train a LightGBM model and evaluate its performance using a holdout dataset. For more detailed descriptions of this code, take a look at the Train-Synthetic-Test-Real tutorial.

# import necessary libraries
import lightgbm as lgb
from lightgbm import early_stopping
from sklearn.model_selection import train_test_split
from sklearn.metrics import roc_auc_score, f1_score
import seaborn as sns
import matplotlib.pyplot as plt

# define target column and value
target_col = 'income'
target_val = '>50K'

# define preprocessing function
def prepare_xy(df: pd.DataFrame):
    y = (df[target_col]==target_val).astype(int)
    str_cols = [
        col for col in df.select_dtypes(['object', 'string']).columns if col != target_col
    for col in str_cols:
        df[col] = pd.Categorical(df[col])
    cat_cols = [
        col for col in df.select_dtypes('category').columns if col != target_col
    num_cols = [
        col for col in df.select_dtypes('number').columns if col != target_col
    for col in num_cols:
        df[col] = df[col].astype('float')
    X = df[cat_cols + num_cols]
    return X, y

# define training function
def train_model(X, y):
    cat_cols = list(X.select_dtypes('category').columns)
    X_trn, X_val, y_trn, y_val = train_test_split(X, y, test_size=0.2, random_state=1)
    ds_trn = lgb.Dataset(
    ds_val = lgb.Dataset(
    model = lgb.train(
            'verbose': -1,
            'metric': 'auc',
            'objective': 'binary'
    return model

# define evaluation function
def evaluate_model(model, hol):
    X_hol, y_hol = prepare_xy(hol)
    probs = model.predict(X_hol)
    preds = (probs >= 0.5).astype(int)
    auc = roc_auc_score(y_hol, probs)
    f1 = f1_score(y_hol, probs>0.5, average='macro')
    probs_df = pd.concat([
        pd.Series(probs, name='probability').reset_index(drop=True),
        pd.Series(y_hol, name=target_col).reset_index(drop=True)
    ], axis=1)
    plt.title(f"AUC: {auc:.1%}, F1 Score: {f1:.2f}", fontsize = 20)
    return auc

# create holdout dataset
df_hol = pd.read_csv(f'{repo}/census-holdout.csv')
df_hol_min = df_hol.loc[df_hol['income']=='>50K']
print(f"Holdout data consists of {df_hol.shape[0]:,} records",
f"with {df_hol_min.shape[0]:,} samples from the minority class")

ML performance of imbalanced dataset 

Let’s now train a LightGBM model on the original, heavily imbalanced dataset and evaluate its predictive performance. This will give us a baseline against which we can compare the performance of the different rebalanced datasets.

X_trn, y_trn = prepare_xy(trn)
model_trn = train_model(X_trn, y_trn)
auc_trn = evaluate_model(model_trn, df_hol)
AUC and F1 score of imbalanced data

With an AUC of about 50%, the model trained on the imbalanced dataset is just as good as a flip of a coin, or, in other words, not worth very much at all. The downstream LightGBM model is not able to learn any signal due to the low number of minority-class samples.

Let’s see if we can improve this using rebalancing.

Naive rebalancing

First, let’s rebalance the dataset using the random oversampling method, also known as “naive rebalancing”. This method simply takes the minority class records and copies them to increase their quantity. This increases the number of records of the minority class but does not increase the statistical diversity. We will use the imblearn library to perform this step, feel free to check out their documentation for more context.

The code block performs the naive rebalancing, trains a LightGBM model using the rebalanced dataset and evaluates its predictive performance:

from imblearn.over_sampling import RandomOverSampler

X_trn, y_trn = prepare_xy(trn)
sm = RandomOverSampler(random_state=1)
X_trn_up, y_trn_up = sm.fit_resample(X_trn, y_trn)
model_trn_up = train_model(X_trn_up, y_trn_up)
auc_trn_up = evaluate_model(model_trn_up, df_hol)
AUC and F1 score with naive rebalancing

We see a clear improvement in predictive performance, with an AUC score of around 70%. This is better than the baseline model trained on the imbalanced dataset, but still not great. We see that a significant portion of the “0” class (low-income) is being incorrectly classified as “1” (high-income).

This is not surprising because, as stated above, this rebalancing method just copies the existing  minority class records. This increases their quantity but does not add any new statistical information into the model and therefore does not offer the model much data that it can use to learn about minority-class instances that are not present in the training data.

Let’s see if we can improve on this using another rebalancing method.

SMOTE rebalancing

SMOTE upsampling is a state-of-the art upsampling method which, unlike the random oversampling seen above, does create novel, statistically representative samples. It does so by interpolating between neighboring samples. It’s important to note, however, that SMOTE upsampling is non-privacy-preserving.

The following code block performs the rebalancing using SMOTE upsampling, trains a LightGBM model on the rebalanced dataset, and evaluates its performance:

from imblearn.over_sampling import SMOTENC

X_trn, y_trn = prepare_xy(trn)
X_trn_smote, y_trn_smote = sm.fit_resample(X_trn, y_trn)
model_trn_smote = train_model(X_trn_smote, y_trn_smote)
auc_trn_smote = evaluate_model(model_trn_smote, df_hol)
AUC and F1 score with SMOTE rebalancing

We see another clear jump in performance: the SMOTE upsampling boosts the performance of the downstream model to close to 80%. This is clearly an improvement from the random oversampling we saw above, and for this reason, SMOTE is quite commonly used. 

Let’s see if we can do even better.

Synthetic rebalancing with MOSTLY AI

In this final step, let’s take the synthetically rebalanced dataset that we generated earlier using MOSTLY AI to train a LightGBM model. We’ll then evaluate the performance of this downstream ML model and compare it against those we saw above.

The code block below prepares the synthetically rebalanced data, trains the LightGBM model, and evaluates it:

X_syn, y_syn = prepare_xy(syn)
model_syn = train_model(X_syn, y_syn)
auc_syn = evaluate_model(model_syn, df_hol)
AUC and F1 score with synthetic rebalancing

Both performance measures, the AUC as well as the macro-averaged F1 score, are significantly better for the model that was trained on synthetic data than if it were trained on any of the other methods. We can also see that the portion of “0”s incorrectly classified as “1”s has dropped significantly. 

The synthetically rebalanced dataset has enabled the model to make fine-grained distinctions between the high-income and low-income records. This is strong proof of the value of synthetic rebalancing for learning more about a small sub-group within the population.

The value of synthetic rebalancing

In this tutorial, you have seen firsthand the value of synthetic rebalancing for downstream ML classification problems. You have gained an understanding of the necessity of rebalancing when working with imbalanced datasets in order to provide the machine learning model with more samples of the minority class. You have learned how to perform synthetic rebalancing with MOSTLY AI and observed the superior performance of this rebalancing method when compared against other methods on the same dataset. Of course, the actual lift in performance may vary depending on the dataset, the predictive task, and the chosen ML model.

What’s next?

In addition to walking through the above instructions, we suggest experimenting with the following in order to get an even better grasp of synthetic rebalancing:

In this tutorial, you will explore the relationship between the size of your training sample and synthetic data accuracy. This is an important concept to master because it can help you significantly reduce the runtime and computational cost of your training runs while maintaining the optimal accuracy you require.

We will start with a single real dataset, which we will use to create 5 different synthetic datasets, each with a different training sample size. We will then evaluate the accuracy of the 5 resulting synthetic datasets by looking at individual variable distributions, by verifying rule-adherence and by evaluating their performance on a downstream machine-learning (ML) task. The Python code for this tutorial is runnable and publicly available in this Google Colab notebook.

Size vs synthetic data accuracy tradeoff

Our working hypothesis is that synthetic data accuracy will increase as the number of training samples increases: the more data the generative AI model has to learn from, the better it will perform. 

Synthetic data accuracy vs training sample size

Fig 1 - The Size vs Accuracy Tradeoff

But more training samples also means more data to crunch; i.e. more computational cost and a longer runtime. Our goal, then, will be to find the sweet spot at which we achieve optimal accuracy with the lowest number of training samples possible. 

Note that we do not expect synthetic data to ever perfectly match the original data. This would only be satisfied by a copy of the data, which obviously would neither satisfy any privacy requirements nor would provide any novel samples. That being said, we shall expect that due to sampling variance the synthetic data can deviate. Ideally this deviation will be just as much, and not more, than the deviation that we would observe by analyzing an actual holdout dataset.

Synthesize your data

For this tutorial, we will be using the same UCI Adult Income dataset, as well as the same training and validation split, that was used in the Train-Synthetic-Test-Real tutorial. This means we have a total of 48,842 records across 15 attributes, and will be using up to 39,074 (=80%) of those records for the synthesis.

  1. Download the training data census-training.csv by clicking here and pressing Ctrl+S or Cmd+S to save the file locally. This is an 80% sample of the full dataset. The remaining 20% sample (which we’ll use for evaluation later) can be fetched from here.
Download original data

Fig 2 - Download the original training data and save it to disk.

  1. Synthesize census-training.csv via MOSTLY AI's synthetic data generator multiple times, each time with a different number of maximum training samples. We will use the following training sample sizes in this tutorial: 100, 400, 1600, 6400, 25600. Always generate a consistent number of subjects, e.g. 10,000. You can leave all other settings at their default.
  2. Download the generated datasets from MOSTLY AI as CSV files, and rename each CSV file with an appropriate name (eg. syn_00100.csv, syn_00400.csv, etc.)
  1. Now ensure you can access the synthetic datasets from wherever you are running the code for this tutorial. If you are working from the Colab notebook, you can upload the synthetic datasets by executing the code block below:
# upload synthetic dataset
import pandas as pd
    # check whether we are in Google colab
    from google.colab import files
    print("running in COLAB mode")
    repo = 'https://github.com/mostly-ai/mostly-tutorials/raw/dev/size-vs-accuracy'
    import io
    uploaded = files.upload()
    synthetic_datasets = {
        file_name: pd.read_csv(io.BytesIO(uploaded[file_name]), skipinitialspace=True)
        for file_name in uploaded
    print("running in LOCAL mode")
    repo = '.'
    print("upload your synthetic data files to this directory via Jupyter")
    from pathlib import Path
    syn_files = sorted(list(Path('.').glob('syn*csv')))
    synthetic_datasets = {
        file_name.name: pd.read_csv(file_name)
        for file_name in syn_files

for k, df in synthetic_datasets.items():
    print(f"Loaded Dataset `{k}` with {df.shape[0]:,} records and {df.shape[1]:,} attributes")

Evaluate synthetic data accuracy

Now that you have your 5 synthetic datasets (each trained on a different training sample size) let’s take a look at the high-level accuracy scores of these synthetic datasets.

  1. Navigate to your MOSTLY AI account and note the reported overall synthetic data accuracy as well as the runtime of each job:
Synthetic data accuracy in MOSTLY AI's QA report

Fig 3 - Note the accuracy score in the QA Report tab of your completed synthetic dataset job.

Training time in synthetic data generation

Fig 4 - Note the training time from the Logs tab.

  1. Update the following DataFrame accordingly:
results = pd.DataFrame([
{'file': 'syn_00100.csv', 'samples': 100, 'accuracy': 0.830, 'runtime': 37},
{'file': 'syn_00400.csv', 'samples': 400, 'accuracy': 0.914, 'runtime': 45},
{'file': 'syn_01600.csv', 'samples': 1600, 'accuracy': 0.956, 'runtime': 48},
{'file': 'syn_06400.csv', 'samples': 6400, 'accuracy': 0.972, 'runtime': 54},
{'file': 'syn_25600.csv', 'samples': 25600, 'accuracy': 0.980, 'runtime': 75},
  1. Visualize the results using the code block below:
import seaborn as sns
import matplotlib.pyplot as plt

sns.catplot(data=results, y='accuracy', x='file', kind='point', color='black')
plt.title('QA Report - Overall Accuracy')
Synthetic data accuracy results

From both the table and the plot we can see that, as expected, the overall accuracy of the synthetic data improves as we increase the number of training samples. But notice that the increase is not strictly linear: while we see big jumps in accuracy performance between the first three datasets (100, 400 and 1600 samples, respectively), the jumps get smaller as the training samples increase in size. Between the last two datasets (trained on 6,400 and 25,600 samples, respectively) the increase in accuracy is less than 0.1%, while the runtime increases by more than 35%.

Synthetic data quality deep-dive

The overall accuracy score is a great place to start when assessing the quality of your synthetic data, but let’s now dig a little deeper to see how the synthetic dataset compares to the original data from a few different angles. We’ll take a look at:

Before you jump into the next sections, run the code block below to concatenate all the 5 synthetic datasets together in order to facilitate comparison:

# combine synthetics
df = pd.concat([d.assign(split=k) for k, d in synthetic_datasets.items()], axis=0)
df['split'] = pd.Categorical(df['split'], categories=df["split"].unique())
df.insert(0, 'split', df.pop('split'))

# combine synthetics and original
df_trn = pd.read_csv(f'{repo}/census-training.csv')
df_hol = pd.read_csv(f'{repo}/census-holdout.csv')
dataset = synthetic_datasets | {'training': df_trn, 'holdout': df_hol}
df_all = pd.concat([d.assign(split=k) for k, d in dataset.items()], axis=0)
df_all['split'] = pd.Categorical(df_all['split'], categories=df_all["split"].unique())
df_all.insert(0, 'split', df_all.pop('split'))

Single variable distributions

Let’s explore the distributions of some individual variables.

The more training samples have been used for the synthesis, the closer the synthetic distributions are expected to be to the original ones. Note that we can also see deviations within statistics between the target and the holdout data. This is expected due to the sampling variance. The smaller the dataset, the larger the sampling variance will be. The ideal synthetic dataset would deviate from the original dataset just as much as the holdout set does.

Start by taking a look at the average age, split by marital status:

stats = (
    df_all.groupby(['split', 'marital_status'])['age']
stats = (
    .isin(['_RARE_', 'Married-AF-spouse', 'Married-spouse-absent', 'Separated'])]
stats = (
    stats.pivot_table(index='split', columns=['marital_status'])
Synthetic data sample

Then explore the age distribution, split by income:

plt.legend(loc='upper right', title='', prop={'size': 8})
Synthetic data visualization

In both of these cases we see, again, that the synthetic datasets trained on more training samples resemble the original dataset more closely. We also see that the difference between the dataset trained on 6,400 samples and that trained on 25,600 seems to be minimal. This means that if the accuracy of these specific individual variable distributions is most important to you, you could confidently train your synthetic data generation model using just 6,400 samples (rather than the full 39,074 records). This will save you significantly in computational costs and runtime.

Rule Adherence

The original data has a 1:1 relationship between the education and education_num columns: each textual education level in the education column has a corresponding numerical value in the education_num column.

Let's check in how many cases the generated synthetic data has correctly retained that specific rule between these two columns.

First, display the matching columns in the original training data:

# display unique combinations of `education` and `education_num`
(df_trn[['education', 'education_num']]
Data sample

Now, convert the education column to Categorical dtype, sort and calculate the ratio of correct matches:

# convert `education` to Categorical with proper sort order
df['education'] = pd.Categorical(

# calculate correct match
stats = (
    .apply(lambda x: (x['education'].cat.codes+1 == x['education_num']).mean())
stats = stats.to_frame('matches').reset_index()

Visualize the results:

plt.title('Share of Matches')
Share of matches in synthetic data

We can see from both the table and the plot that the dataset trained on just 100 samples severely underperforms, matching the right values in the columns only half of the time. While performance improves as the training samples increase, only the synthetic dataset generated using 25,600 samples is able to reproduce this rule adherence 100%. This means that if rule adherence for these columns is crucial to the quality of your synthetic data, you should probably opt for a training size of 25,600.

Downstream ML task

Finally, let’s evaluate the 5 synthetic datasets by evaluating their performance on a downstream machine learning task. This is also referred to as the Train-Synthetic-Test-Real evaluation methodology. You will train a ML model on each of the 5 synthetic datasets and then evaluate them on their performance against an actual holdout dataset containing real data which the ML model has never seen before (the remaining 20% of the dataset, which can be downloaded here).

The code block below defines the functions that will preprocess your data, train a LightGBM model and evaluate its performance. For more detailed descriptions of this code, take a look at the Train-Synthetic-Test-Real tutorial.

# import necessary libraries
import lightgbm as lgb
from lightgbm import early_stopping
from sklearn.model_selection import train_test_split
from sklearn.metrics import roc_auc_score

# define target column and value
target_col = 'income'
target_val = '>50K'

# prepare data, and split into features `X` and target `y`
def prepare_xy(df: pd.DataFrame):
    y = (df[target_col]==target_val).astype(int)
    str_cols = [
        col for col in df.select_dtypes(['object', 'string']).columns if col != target_col
    for col in str_cols:
        df[col] = pd.Categorical(df[col])
    cat_cols = [
        col for col in df.select_dtypes('category').columns if col != target_col
    num_cols = [
        col for col in df.select_dtypes('number').columns if col != target_col
    for col in num_cols:
        df[col] = df[col].astype('float')
    X = df[cat_cols + num_cols]
    return X, y

# train ML model with early stopping
def train_model(X, y):
    cat_cols = list(X.select_dtypes('category').columns)
    X_trn, X_val, y_trn, y_val = train_test_split(X, y, test_size=0.2, random_state=1)
    ds_trn = lgb.Dataset(
    ds_val = lgb.Dataset(
    model = lgb.train(
            'verbose': -1,
            'metric': 'auc',
            'objective': 'binary'
    return model

# apply ML Model to some holdout data, report key metrics, and visualize scores
def evaluate_model(model, hol):
    X_hol, y_hol = prepare_xy(hol)
    probs = model.predict(X_hol)
    preds = (probs >= 0.5).astype(int)
    auc = roc_auc_score(y_hol, probs)
    return auc

def train_and_evaluate(df):
    X, y = prepare_xy(df)
    model = train_model(X, y)
    auc = evaluate_model(model, df_hol)
    return auc

Now calculate the performance metric for each of the 5 ML models:

aucs = {k: train_and_evaluate(df) for k, df in synthetic_datasets.items()}
aucs = pd.Series(aucs).round(3).to_frame('auc').reset_index()

And visualize the results:

plt.title('Predictive Performance (AUC) on Holdout')
AUC curve on holdout data

We see, again, that optimal performance is achieved with the largest training sample size. Interestingly, the difference in performance between the dataset trained on 1,600 samples and the one trained on 6,400 samples is minimal in this case. This means that if your use case allows you to sacrifice a fraction of ML performance, you could train your synthetic data generator on just 1,600 samples and still get pretty great results.

In most cases, however, a 1% difference in ML accuracy is crucial to preserve and so most likely you would end up training on 25,600 samples. A worthwhile exercise here would be to train a synthetic generator using the full 39,074 training samples to see whether that performs even better.

Optimize your training sample size for synthetic data accuracy

In this tutorial you have seen first-hand the relationship between the size of your training samples and the resulting synthetic data quality. You have quantified and evaluated this relationship from multiple angles and with various use cases in mind, including looking at single variable distributions, rule adherence and ML utility. For the given dataset and the given synthesizer we can clearly observe an increase in synthetic data quality with a growing number of training samples across the board.  

We have also observed that a holdout dataset will exhibit deviations from the training data due to sampling variance. With the holdout data being actual data that hasn't been seen before, it serves as a north star in terms of maximum achievable synthetic data accuracy. Read our paper on benchmarking synthetic data generators for more on this topic.

What’s next?

In addition to walking through the above instructions, we suggest experimenting with the following in order to get an even better grasp of the relationship between training sample size and synthetic data accuracy:


Generating synthetic data from original data

Understanding Model Collapse

Mitigating Model Collapse

Balance between privacy, generalization and accuracy

Synthetic data generation & validation on original data

Up-to-date original data for reliable synthetic data generators

Validation using a holdout data set

Data augmentation



The phrase synthetic data generation has gained a lot of traction in the world of data. At its core, synthetic data refers to artificially generated data that mimics the statistical properties and patterns of real-world data. This approach has shown to be an effective tool in a variety of domains, including machine learning and data analysis, as well as privacy protection and risk assessment.

The increased demand for high-quality data to train and test models and rising concerns about data privacy and security have highlighted the importance of synthetic data generation. This strategy handles data shortage while protecting sensitive information and private knowledge. What happens, though, when the synthetic data is created directly from the original data at a specific point?

Generating synthetic data from original data

Consider the following scenario: an organization has a valuable dataset collecting consumer behaviors, market trends, or medical diagnoses at a certain point in time. This dataset has enormous potential for research and model development, but sharing it risks disclosing sensitive information or violating privacy restrictions.

This is where the concept of generating synthetic data from the original dataset comes into play. Instead of releasing the real data, which may raise privacy issues, companies and researchers can employ advanced techniques to produce synthetic data that closely resembles the statistical properties of the original dataset. The created data serves as a snapshot of the original at that point in time, keeping its essence while disclosing no individual-level information.

The primary advantage is the ability to exploit the insights contained within the original data while adhering to privacy standards and reducing security threats. This strategy encourages innovation, creativity, and collaboration by allowing data professionals and researchers to experiment, construct models, and conduct analysis without jeopardizing data integrity or infringing on privacy rights. Furthermore, by producing synthetic data from the original dataset, organizations may overcome data shortage challenges. When obtaining more data is difficult or expensive, synthetic data can efficiently magnify the given dataset, improving model training and validation.

Understanding model collapse

In machine learning, "model collapse" often refers to a situation in which the model fails to provide varied or relevant outputs and instead produces a narrow collection of repeated or low-quality outputs. This can happen for a variety of reasons and in a variety of models, but it most commonly happens while training generative adversarial networks (GANs) or other complicated models. 

Recent advances in generative AI, notably for images and text, have piqued the attention of researchers interested in using synthetic data to train new models. There is, however, a concept known as 'Model Autophagy Disorder' (MAD), which compares the process of employing synthetic data in a self-consuming loop. This indicates that unless there is enough injection of new real-world data at each generation, the quality and variety of subsequent generative models would ultimately deteriorate.

Model collapse

The MAD notion emphasizes the vital necessity for a careful mix of synthetic and real data to prevent model quality and variety from deteriorating during subsequent training sessions. Understanding the complexities of how to use synthetic data successfully while preventing model collapse is a continuous endeavor in the evolution of generative AI and synthetic data consumption. In this blog, we present some of our suggestions on how to mitigate model collapse in the context of tabular synthetic data and hence deflating the MAD concept.

Jumping specifically into tabular synthetic data, model collapse can also be a concern. Tabular synthetic data generation involves creating new data samples that resemble the original dataset in terms of its structure, statistical properties, and relationships between variables. In this context, model collapse refers to the situation where the generative model produces synthetic data that lacks diversity and fails to capture the complexity of the original data. As a result, new models become excessively reliant on patterns present in the generated data, leading to a degradation in the model's capacity to produce novel and meaningful results.

Therefore, data professionals and researchers need to be very careful and aware of the situation where any new models become too dependent on patterns in the synthetically generated data, leading to their inability to adapt to unseen scenarios effectively. The root of the problem is frequently the complex relationship between data distribution and model learning dynamics. It's imperative to recognize that model collapse often emerges due to a combination of factors, primarily stemming from the quality of synthetic data and how it's employed. While synthetic data generation can be a powerful ally, its misuse or generation of low-quality data can indeed trigger the collapse phenomenon.

Low-quality synthetic data significantly contributes to model collapse. Models trained on such data are sure to overfit on limited patterns if the generated data lacks diversity, and accuracy, or fails to accurately represent the underlying distributions. This limits their ability to adjust to unknown conditions and compromises their overall effectiveness.

Similarly, the misuse of synthetic data increases the likelihood of model collapse. Models might accidentally depend on erroneous patterns if synthetic data is utilised arbitrarily, without sufficient validation or consideration of its alignment with the original data distribution.

Mitigating Model Collapse

Balance between privacy, generalization and accuracy

In data science, there is a balance between protecting privacy, achieving robust generalization, and reaching high accuracy. This balance is frequently difficult to achieve, but it is critical to the success of data-driven models. Let's explore how synthetic data generation with MOSTLY AI emerges as a potential solution.

Many models try for extreme accuracy by methodically collecting small details in the data. However, this effort frequently comes at the expense of privacy. To safeguard individual privacy, traditional methods include introducing excessive noise or changing data distribution. Differential privacy, for example, adds noise to data to avoid reidentification. However, this might reduce the model's accuracy and generalization capacities.

Models that prioritize privacy, on the other hand, may face a trade-off. While they take great care to protect individual information, they may oversample majority classes or compromise their ability to model outliers and unusual events. As a result, the model's ability for rigorous generalization and complete comprehension is hampered.

This is where MOSTLY AI’s synthetic data generator comes in as a solution for navigating the complex combination of accuracy, privacy protection, and generalization. MOSTLY AI’s synthetic data avoids the need for excessive noise or alteration of data by creating data points that perfectly mimic the statistical features of the original data. It protects privacy while maintaining data integrity.

Furthermore, it is adaptable enough to overcome the constraints of previous methodologies. Models trained on well-crafted synthetic data generated by MOSTLY AI are well-positioned to recognize both majority trends and outlier occurrences. This equilibrium promotes the model's capacity to generalize well, even in new territory, without sacrificing privacy or accuracy.

Utilizing synthetic data, though, might introduce the notion of model collapse in models built for a downstream task. The complex patterns within synthetic data require careful handling to maintain equilibrium. As we are discussing in the next sections, through a combination of validation against actual data and a thorough understanding of data distributions, we could strengthen the models against collapse while upholding their ability to grasp the statistical properties and characteristics of the original data.

Synthetic data generation & validation on original data

It is crucial to understand that training your model on original data provided by users can indeed help mitigate the risk of synthetic data poisoning the downstream machine learning models. However, ensuring the safety and reliability of the generated data is a multi-faceted process that involves more than just using original data. Let's dive deeper into two critical aspects: the importance of using up-to-date original data for generating synthetic data and the significance of validating your models using a holdout set.

Up-to-date original data for reliable synthetic data generators

To build reliable and effective synthetic data generators, the original data used for generating synthetic samples should ideally be up to date. The underlying patterns and distributions within your dataset may change over time due to evolving user behaviors, market dynamics, or other factors. If your generators are based on outdated data, they might fail to capture these changes accurately, leading to discrepancies between the synthetic and real data distributions. This, in turn, could negatively impact downstream tasks where the synthetic data is used.

By continuously updating your generators with fresh, current original data, you enhance their ability to create ML models that faithfully represent the most recent data patterns. This ensures that any model development based on the SD remains relevant and applicable to the context in which it will be used.

Validation using a holdout data set

In the context of model validation, the concept of a "holdout set" plays a crucial role in assessing the performance and reliability of your models, including those that utilize synthetic data. A holdout set is a portion of your original data that is set aside during the training process and not used for model training. Instead, it serves as an independent dataset for evaluating the model's performance.

An important point here is that the holdout set should not be used to create the generator as well. It should be a portion of the dataset that will only be used to validate a downstream task's outcome. Incorporating a holdout set into your validation process adds a layer of assurance that the models trained using synthetic data are reliable, effective, and aligned with the behavior of real-world data.

When working with synthetic data, the utilization of a holdout set takes on heightened significance due to several compelling reasons.

Upsampling training data with MOSTLY AI's synthetic data generator

Data augmentation

If the primary purpose is to augment the original dataset, you may use a variety of data augmentation techniques to generate variants of the existing data points. This can assist in increasing the dataset's variety and boost model generalization, mitigating the risk of model collapse.

MOSTLY AI's AI-powered data augmentation capabilities may assist you in transforming the data you already have into high-quality data that represents your real-world customers and the settings in which they operate. Features like Smart Imputation and Rebalancing could assist you in achieving your goal of generating different versions of your original data points.


We've explored strategies such as training a synthetic data generator on up-to-date real data and using the data augmentation feature, all of which contribute to the generation of reliable and adaptable synthetic data. We've strengthened the trustworthiness of the synthetic data that fuels our models by combining up-to-date real data with rigorous validation.

When utilized properly, synthetic data generation can act as a solution to protect machine learning growth against model collapse, reducing the danger of models becoming excessively reliant on specific patterns.

AI-generated data synthesis is on the rise and the number of software solutions available on the market is growing. Users of synthetic data have to make important decisions about which solution to use. But evaluating the quality of AI-generated synthetic datasets is challenging. How should you go about comparing different solutions?

MOSTLY AI co-developed a research-based empirical framework for evaluating the quality of mixed-type tabular synthetic data. This framework provides empirical methods to quantify both the accuracy (utility) and privacy of a synthetic dataset. This article explains how the methodology works and presents the benchmarking results of 8 synthetic data generators on 4 different datasets. 

The evaluation framework allows you to confidently make the switch to generative AI synthetic data by comparing the performance of different solutions so that you can choose the best platform for your use case. You can reproduce the results or compare other solutions for yourself using the code in the public Github repository.

Performance comparison of data synthesis techniques
Performance of various data synthesis techniques on one of the four datasets. 
The black dot in the top-right corner is the ‘North Star’ of maximum privacy and utility preservation. 

Privacy vs. Utility

Traditional data anonymization techniques struggle with the privacy-utility tradeoff for today’s datasets, which consist of more than just a handful of attributes per individual. Let’s illustrate this fundamental tradeoff with an example: you could easily add enough noise to a dataset to guarantee its privacy. However, except for the most trivial cases, the resulting data will then no longer be realistic nor representative of the original dataset. An analysis performed or a model trained on this kind of perturbed data will yield totally inaccurate results. You’ve lost your data utility.

On the other hand, you could decide to only add a marginal amount of noise. This would preserve the data utility, but would not protect against even the most basic forms of re-identification attacks. Thus, while you maintain utility, you offer no meaningful privacy protection.

Privacy utility trade-off for classic synthetic data techniques
Traditional synthetic data techniques struggle with compromises due to the classic privacy-utility tradeoff.

AI-generated synthetic data promises to be better than these conventional data anonymization techniques. But how can you quantify their ability to deliver on this promise?

How to benchmark synthetic data generators

Building a robust evaluation methodology for synthetic data generators is no easy task. This technical section will walk you through a specific evaluation framework, co-developed by MOSTLY AI. This section guides you step by step so that you gain an understanding of how the framework is built and can confidently use it to evaluate different synthetic data solutions for yourself. If you are not interested in the technical details, you can skip straight to the results.

A perfect data synthesizer should be capable of generating data samples that closely resemble actual data points that the model has never seen before. The synthetic dataset should have the same statistical characteristics as the original dataset; without revealing any private information. To assess this property, we therefore split the original data into a training and a holdout set. The generated synthetic data samples should then be just as close to the training dataset as the points in the holdout set, which are real data records that the model has never seen before.

So how does it work? 

The first step is taking the original dataset and splitting it in half to yield the training and the holdout datasets. The synthesizer is only trained on the training samples (50% of the original dataset) and is then used to generate synthetic data samples. The holdout samples are never exposed to the synthesis process but kept aside for the evaluation.

Synthetic data evaluation - first step - splitting
The first step in evaluating synthetic data generators is splitting the dataset into a training and holdout set. The generators are trained on the training set and evaluated on the holdout set.

We can then evaluate the quality of this generated synthetic data by evaluating whether the synthetic samples created by the trained generator are any “closer” to the training data than the holdout data. 

If the synthetic data is significantly closer to the training data than to the holdout, the generative model has likely been overfitted. This would indicate that the synthetic data potentially contains information that is specific to the individuals of the training data and that does not generalize beyond those individuals. On the other hand, if the synthetic data is significantly farther away from the training data than the holdout set, we are apparently not representative of the actual data. In that scenario, we would be compromising the fidelity of the data, which negatively impacts the utility of our downstream models trained on this data.

So how do we quantify this fidelity “closeness”?

Remember that the benchmark model starts out by randomly splitting the original dataset into 2 equal halves: a training set and a holdout set. Since these are all samples from the same dataset, these two sets will exhibit the same statistics and the same distributions. Naturally, however, there will be some difference between the training and holdout sets, simply because they consist of different samples. This difference in statistics is thus due to the so-called sampling variance.

After training our synthetic data generator on the training dataset, we will then use it to generate some new, synthetic data samples. Ideally, these synthetic data should be just as far from the training data as the holdout data in terms of accuracy. In other words, there should be just as much difference between the statistics of the synthetic samples and the statistics of the training samples as between the corresponding statistics of the training samples and the statistics of the holdout samples (the difference being the magnitude of the sampling variance).

If the synthetic data is significantly closer to the training data than the holdout data, this means that some information specific to the training data has leaked into the synthetic dataset. If the synthetic data is significantly farther from the training data than the holdout data, this means that we have lost information in terms of accuracy or fidelity.

synthetic data generation methods
A perfect synthetic data generator creates data samples that are just as different from the training data as the holdout data. If this is not the case, we are compromising on either privacy or utility.

The specific distance metric used to evaluate the fidelity of the synthetic dataset is the Total Variational Distance (TVD) between the empirical marginal distributions. It is calculated by treating all the variables in the dataset as categoricals (and thus binning any numerical features) and then measuring the sum of all deviations between the empirical marginal distributions.

This can be done for univariate, bivariate, and to some extent, also for all higher-dimensional marginal distributions. For more details on the exact implementation, read the original paper published in Frontiers in Big Data or take a look at the reproducible code in the dedicated Github repository. An Accuracy metric can then be easily defined as 1 - TVD to yield a percentage value: a synthetic dataset with a TVD of 0.05 from the holdout dataset thus translates to an accuracy of 95%, which is also reported as part of MOSTLY AI’s Quality Assurance report.

Synthetic data should match the original real-world datasets as closely as possible. This is true not only for the distribution of individual attributes or features but also for their multivariate combinations and the relationships among the set of attributes. This becomes complex very fast due to the curse of dimensionality: a dataset of 50 attributes (or columns in a traditional tabular dataset) will have 1,225 bivariate interactions and 19,600 three-way interactions (!) How do we quantify the closeness of the synthetic dataset across so many dimensions?

The solution proposed in the framework co-developed by MOSTLY AI is a non-parametric, model- and assumption-free approach to empirically measure the fidelity as the Total Variational Distance of the empirical marginal distributions.

This may sound complex but becomes intuitive when translated into a visualization such as the one below. It’s relatively easy to identify which distributions resemble that of the HOLDOUT set and which don’t. The copulagan distribution for age by “widowed”, for example, is clearly deviating significantly from the distribution in the HOLDOUT set.

For each multivariate combination, the framework evaluates  the similarity between the distributions as the Total Variational Distance and measures an average of all these similarities to report a single summary metric.

Distributions of synthetic data


Just as for accuracy, we start by splitting the dataset into equal training and holdout sets, train the generator on the training set and then use the generator to create a synthetic dataset.

For each individual in the synthetic dataset, we then find its nearest neighbor in the training dataset. The nearest neighbor is the individual in the training set which most closely resembles it. We measure the distance between these two neighbors using the Distance to Closest Record method and compare the distance to its nearest neighbor in the holdout dataset. We repeat this for every synthetic sample to calculate the share of records that are closer to a training than to a holdout record. 

A resulting share of 50% would mean that the synthetic dataset is just as different from the original training data as from the holdout set. This would give a strong signal that no private information from the training dataset has made it into the synthetic dataset.

synthetic data generation method
A perfect synthetic data generator creates synthetic records that are just as different from the training data as from the holdout data.

Benchmark results

To see the benchmarking framework in action, we used it to evaluate 8 publicly accessible synthetic data generators on 4 unique datasets. 

The following generators are included in the benchmark:

Both Gretel and MOSTLY AI were accessed through their web-based browser applications. The other generators were accessed using their respective Python and R APIs. All generators were used with their default settings, so no parameter-tuning was performed. The code to reproduce the benchmarks is available on Github.

The datasets included in the benchmarks are:

Fidelity performance on a single dataset

The plot below shows the Total Variational Distance of each synthetic dataset trained on the adult dataset, measured once for all univariate distributions, once for all bivariate distributions, and once for all 3-way interactions. The higher the TVD value, the further away the synthetic data points are from the training data, indicating a loss in terms of accuracy.

Only MOSTLY AI and synthpop achieve proximity to the original data, measured as their distance from the holdout dataset. All other synthesizers seem significantly less performant in terms of accuracy, resulting in insights or ML models that are not necessarily representative of the real world. If one looks close, then one can see that synthpop actually seems to do its job too well – its synthetic samples are closer to the training data than the holdout which may be a sign of an overfitted model. 

Many of the synthetic data generators create data that is significantly different from the holdout adult dataset, indicating a loss of data utility. Only MOSTLY AI and synthpop closely resemble the holdout dataset.

Fidelity Performance on all Four Datasets

The table below shows the performance of the 8 data synthesizers on all 4 benchmarked datasets, measured as the TVD. The HOLDOUT row shows the deviation measured for the holdout dataset, and serves us a reference to quantify deviations expected due to the sampling variance. The synthetic datasets should match the Holdout fidelity score as closely as possible.

Many of the synthetic data generators create data that is significantly different from the holdout data, indicating a loss of data utility. The copulagan synthesizer failed to complete the online-shoppers benchmark. Only MOSTLY AI and synthpop closely resemble the holdout dataset. 

The patterns seen on the adult dataset above are consistent across synthesizers and datasets. The Synthetic Data Vault and Synthcity generators compromise significantly on accuracy. The Gretel synthesizer does better but is still quite far (different) from the holdout set, especially for the bivariate and three-way interactions. Only MOSTLY AI and synthpop closely resemble the distribution of the holdout dataset, with synthpop consistently being closer to the training dataset than the holdout (i.e. potentially overfitting the training data).

Privacy Performance on a Single Dataset

The plot below shows the privacy evaluation of the 8 benchmarked synthetic data generators, as well as for a varying degree of classic perturbation techniques, on the adult dataset. On the one hand, we report the ratio of the distance to the closest record (DCR) with respect to the training samples vs. with respect to the holdout samples. Here, a ratio of 1 would indicate that the synthetic samples are not any closer to the training samples than to the holdout samples. On the other hand, we also report the share of samples that is closer to a training sample than to a holdout sample. A share of 50% would indicate that the synthetic samples are just as likely to be closer to training than to a holdout record. 

Almost all of the synthetic data generators are able to achieve a Privacy Share close to 50% (respectively a DCR Ratio close to 1) indicating that they are doing a good job of preserving the privacy of the records in the training dataset. Only synthpop seems to be slightly overfitting on the training data, confirming the previously reported results. All of the synthesizers seem fair to excellent when compared to the classic perturbation techniques that simply try to protect data by randomly substituting values. 

AI-driven synthesizers outperform classic perturbation techniques in terms of privacy measures.

Privacy Performance on all Four Datasets

The patterns seen on the adult dataset above are again consistent across synthesizers and datasets, with some greater variability on the credit-default and online-shoppers datasets. See below for full details. However, as argued before, privacy is only half the picture, and cannot be looked at in isolation. For that reason, it’s crucial to evaluate privacy and fidelity together, as shown in this final section.

MOSTLY AI consistently ranks among the best synthesizers in terms of privacy measures.

The Full Picture

AI-driven synthetic data generators promise to deliver synthetic data that overcomes the classic privacy-utility tradeoff: preserving maximum data utility without compromising on the privacy of the training data. The visualizations below show to what extent the benchmarked synthetic data generators deliver on this promise.

MOSTLY AI consistently ranks at the top of the benchmarked synthetic data generators in terms of both accuracy and privacy.

The black dot in the top right corner is the North Star of maximum utility and privacy preservation. The orange dots represented traditional anonymization techniques using various degrees of data perturbation. The turqoise dot is MOSTLY AI which consistently ranks at the top of the benchmark results, both in terms of accuracy and privacy.

If you’re looking for a synthetic data generator that is able to consistently deliver optimal privacy and utility performance, give MOSTLY AI a try today and let us know what you think – the first 100K rows of synthetic data are on us!

You are expected to build kick-ass models with shitty data. We get it. We've been there before, trying to explain why garbage in is garbage out and no amount of fancy tech can change that. Spending hours, days even weeks trying to manually fix data issues is the collective nightmare of data scientists. You are expected to AI-powered data augmentation is here to help with your gap-filled, bias-ridden and limited data that eventually lead to incorrect or even unfair business decisions.

MOSTLY AI’s AI-powered data augmentation capabilities can help you turn the data that you have on hand right now into high-quality data that reflects your real-world customers and the scenarios they operate in. And this is just the cherry on the cake, because synthetic data also provides you automated data privacy on the tap. If you use synthetic data, you'll never have to worry about exposing customer data again.

Who should use data augmentation and why?

If you’re a test engineer, this can help you with creating sufficient test data for your next product release. Business Analysts can use AI-powered data augmentation to complete common gaps in their customer surveys, such as missing income details as customers are often reluctant to report them. And ML/AI engineers can use it to unbias and rebalance their training data, so that your models have a stronger capacity to generalize, adjust to unfamiliar situations, and generate more precise and meaningful insights. 

Keep reading to find out how you can use the MOSTLY AI synthetic data generator to supercharge your data assets and make confident, spot-on decisions for your business.

What is AI-powered data augmentation?

Data augmentation is the go-to solution for data scientists when there's not enough data or they need to spice up the diversity and quality of their dataset. It’s a process that generates additional data points to the existing ones in your dataset and is traditionally done using random over and undersampling techniques.

MOSTLY AI's synthetic data generator provides a simpler, smarter, and far more reliable way to achieve high quality results, than traditional data augmentation techniques. It uses machine learning models to learn the underlying patterns and correlations in the data. Once the generator has learned these patterns, it can use them to generate new data points that are statistically similar to the original data.

Smart imputation - no more missing or random data

Smart imputation learns the data’s underlying patterns and correlations and then generates new data points. This AI-powered data imputation allows the MOSTLY AI synthetic data generator to perform some nifty tricks, such as imputing the missing values in your data source. The smart imputation method produces more reliable and realistic results compared to commonly used techniques, such as mean/median imputation and frequent category imputation. Filling in the missing values with meaningful synthetic data points is especially important for creating human-readable datasets in downstream analytics tasks.

Rebalancing - no more imbalanced datasets

One of the main advantages of using AI-powered synthetic data for data augmentation is that it can create data points that are more diverse and representative of the underlying population than traditional augmentation techniques. You can use the MOSTLY AI synthetic data generator’s “Rebalance categories” feature to create additional data points for underrepresented business cases in your data. This can rebalance or improve the diversity of the data, leading to better accuracy and robustness of machine learning models, especially when working with small or biased datasets.

The rebalancing feature in MOSTLY AI's synthetic data generator
Rebalancing in MOSTLY AI's synthetic data generator

Data anonymization automated for privacy

Another benefit of using synthetic data is that it can help preserve the privacy and confidentiality of sensitive data by generating synthetic data that is not directly linked to individual users or customers. This can be particularly important in industries such as insurance, finance or healthcare, where data privacy is a top concern.

Overall, data augmentation using AI-powered synthetic data is a powerful technique that can help improve the quality and diversity of your dataset and, depending on the setup, boost the performance of your machine learning models.

Try data augmentation now

MOSTLY AI's synthetic data platform is free to use for synthesizing up to 100K rows of data daily. Register an account and experiment with rebalancing, smart imputation and experience the easiest and safest tool for synthetic data generation first hand!

Why is data augmentation important?

Data augmentation is essential because it helps overcome the limitations of real-world data. Real-world data can be limited in quantity, quality, and diversity, which can impact the accuracy of models and predictions.

Additionally, when dealing with missing or incomplete data, imputation techniques can be used to fill in the gaps and allow for a more complete analysis. This is especially important in industries like finance, where missing data on customers can hinder accurate risk assessments and financial forecasting.

Synthetic data augmentation can easily solve classification problems–if there are more instances of one class than another, the model may be biased towards the overrepresented class. Using MOSTLY AI’s synthetic data generator, you can help solve this problem by generating new data points for the underrepresented class.

Moreover, data augmentation can improve the robustness of your AI/ML models. It allows models to be trained on a larger, more diverse dataset, which helps them learn to generalize better to new, unseen data points. This results in more accurate predictions.

Data augmentation can also prevent overfitting in machine learning models. Overfitting occurs when the model is too complex and starts learning the noise in the data rather than the underlying patterns. By introducing variability in the data, data augmentation can help models learn to distinguish between relevant and irrelevant information. For instance, if a model is trained on a dataset with only one class label, it may not generalize to new data points with different class labels. However, by introducing synthetic data points with different class labels, the model can learn to identify the underlying patterns in the data, rather than just memorizing the existing data points.

Overall, data augmentation is a powerful tool that can improve the accuracy, robustness, and generalization of AI/ML models.

Benefits of using synthetic data generators for data augmentation

Reduced cost of model development

Generating synthetic data can be a cost-effective alternative to collecting new data, which can be time-consuming and expensive, especially if the data needs to be collected from multiple sources. By generating synthetic data, you can save time and resources, opening up opportunities to focus on data analysis and model development. MOSTLY AI's synthetic data generator can also help to reduce the cost and time required for data collection and preparation, in turn accelerating your research and development projects.

Last but not least, MOSTLY AI's synthetic data generator is free to use, so it doesn’t break the bank either.

Faster time to market

Using synthetic data can reduce the time it takes to train and test models. By augmenting the existing data with synthetic data, you can create a more robust dataset and train the model faster, allowing them to bring products or services to market faster.

More data for training machine learning models

An imbalanced dataset poses a challenge for predictive modelling as most of the machine learning algorithms used for classification were designed around the assumption of an equal number of examples for each class. Using rebalancing as a data augmentation technique, a dataset could be constructed in such a way as to have the same number or a close number of observations of the same class. Depending on the use case, this can be beneficial because it will give the opportunity for a machine learning model to learn from more data.

Let's say you're building a machine learning model to detect credit card fraud. You have a dataset of credit card transactions with labels indicating whether each transaction is fraudulent or not. However, your dataset has a class imbalance, with only a small percentage of transactions being fraudulent.

To address this data imbalance, you could use traditional data augmentation techniques like oversampling or undersampling. However, this may not be enough to create a diverse and representative dataset, especially if the original data is biased or incomplete.

Instead, you could use MOSTLY AI's synthetic data generator to create new synthetic fraudulent transactions. This synthetic data can then be combined with the original dataset to create a larger and more balanced dataset for training your machine learning model. With a more diverse and representative dataset, your machine learning model is more likely to generalize well to new, unseen data, leading to improved accuracy in detecting credit card fraud.

Reduced bias

Data bias can occur when the data used to train the model is not representative of the real-world scenarios. By generating synthetic data that reflects the real-world scenarios, bias can be reduced, and the model can make more accurate predictions.

Suppose you are tasked with building a machine learning model to predict loan defaults using historical loan data. However, you suspect that your dataset may be biased due to its limited geographic region and demographic representation.

To address this issue, you could use traditional data augmentation techniques like oversampling or undersampling to try to balance the dataset. However, this may not be enough to remove the underlying bias in the data.

Instead, you could leverage MOSTLY AI's synthetic data generator to create new synthetic loan data that is representative of a more diverse population. By rebalancing your data based on underrepresented different geographic and demographic characteristics, you can create a more diverse and representative dataset.

With the resulting dataset, your machine learning model is less likely to be biased towards any particular group or region, leading to more fair and equitable predictions of loan defaults.

Use cases for AI-powered data augmentation

Whether you’re in finance, insurance, or software development, AI-powered data augmentation is a suitable technique to build better models. Read on to learn how rebalancing can help you have AI models with stronger capacity to generalize, adjust to unfamiliar situations, generate more precise and meaningful insights and have data sources without missing values for exploratory data analysis.

Data augmentation in the wild - how to rebalance for credit scoring

A great example of how rebalancing can be used in everyday machine learning tasks is in the financial industry, particularly in credit scoring and risk categorization processes. These processes rely heavily on data, but often face imbalanced datasets due to a lack of data points for defaulted customers. By using appropriate rebalancing techniques, financial institutions can improve the accuracy of their machine learning models and correctly classify customers into the right risk category, helping to mitigate financial risks and improve overall performance.

Synthetic data augmentation outperforms the original data

In our analysis of credit score datasets, we compared four different versions to determine the impact of rebalancing:

The impact of AI-powered rebalancing

The dataset that augmented the original data with a synthetic version of the minority class outperformed the original data’s accuracy by approximately 4%. In real-world scenarios, this can be beneficial as the resulting model may have an important impact on ROI as well as cost savings.

Synthetic data generated with normal synthetization and those with the rebalancing feature enabled have not increased the accuracy of the model. However, MOSTLY AI’s synthetic data generator manages to come really close to the original data’s accuracy which indicates that the platform can perceive the trends and the predictive power that the original dataset holds.

Using synthetic data augmentation as a simulation tool

Unfortunately, most real-world datasets do not represent real-world situations 100%. Many organizations, especially financial institutions, struggle since the data gathered throughout the years are highly skewed and show bias towards a specific behavior. Many examples of datasets are skewed/biased when exploring gender, age, ethnicity, or even occupation. Therefore, decision-makers find it hard or downright impossible to make the correct decision that helps their organization to grow.

This is where MOSTLY AI's rebalancing feature comes in handy. When it comes to the topic of an imbalanced dataset, the first thing that ML practitioners and Data Scientists are thinking about is how to make a dataset to be equally distributed across the majority vs. the minority class. However, one can use MOSTLY AI's rebalancing feature as a simulation tool. The aim is to provide decision-makers with an effective tool to understand better and exploit new information that might affect their dichotomous decision. Rebalancing can be a critical and effective tool to test numerous hypotheses and 'what-if' scenarios that may affect the whole organization's shift in its strategy.

A rebalancing case study from the insurance industry

Let's take as an example the insurance industry. Two of the main KPIs all insurers around the world have are the total annual premiums and the total claims amount.

Using rebalancing as a simulation tool, one could aim to answer questions such as:

We have shifted the insurer customer mix distribution toward younger audiences using MOSTLY AI's Rebalancing capability. The remainder of the dataset's features were then generated based on the new information by MOSTLY AI's synthetic data generator. The two aforementioned KPIs have now been recalculated, and a decision-maker may see that revenue has risen and costs have decreased.

Rebalancing data for simulations

Now that they have a thorough study, stakeholders can use it to inform their decisions and possibly change their organizational strategy.

Improve data consistency with smart imputation

Finance is a prime example of an industry that is faced with the challenge of maintaining consistent customer records, often resulting in incomplete datasets. The lack of data and missing values can lead to bias and produce unreliable results for data analysts and data scientists. A common missing value in the finance industry is customer income, which is often self-declared and not updated or never obtained from the customer at all. However, this example is not limited to finance, as many industries are also faced with similar challenges of incomplete and inconsistent datasets, and can benefit from utilizing advanced data imputation techniques to improve the quality and reliability of their data.

Data augmentation empowers data scientists to overcome real-world limitations

MOSTLY AI’s data augmentation capabilities provide you an effective way to overcome the limitations of real-world data. By generating synthetic data that reflects the real-world scenarios, you can improve the accuracy of your AI models, reduce bias, save costs, and bring products or services to market faster. Data augmentation can also be used to make your exploratory data analyses more accurate and reflective of real-world scenarios and to generate test data for software product changes and new features. As data scientists continue to rely on data to gain insights and drive decision-making, AI-powered data augmentation becomes an essential tool to enhance the quality of your analyses and stay ahead of the competition.

TL;DR We present a reproducible case study on synthesizing large-scale population data to gain granular-level insights without compromising on privacy. Accordingly, MOSTLY AI’s unparalleled accuracy combined with its ease-of-use allows any organization to generate highly realistic synthetic replicas of their own customer base. These allow the privacy-safe utilization of data assets - across teams, across borders, across corporate boundaries. See also here for a slideset version of this blog post.


The UCI Adult dataset is a widely used resource for machine learning and data analysis. It contains detailed information on over 48,000 individuals, including their age, education, income, and other demographic characteristics. The dataset is often used to test and develop algorithms for predicting income levels based on these various factors. Over the past years it has also become the go-to standard to test-drive, showcase and benchmark synthetic data solutions. And any new user of our highly popular free version is guided through the synthetization of that very same dataset as part of their onboarding tutorial. With just a few clicks, and within less than a minute, a highly realistic, statistically representative, and yet truly novel synthetic replica is being generated [Make sure to give it a try!].

But just as AI advances, we also need to advance the datasets it’s being tested on. For years MNIST, a collection of hand-written digits, served as the go-to dataset to test-drive image recognition algorithms, but by now has become “too easy” of a task. Accordingly, it’s also high time to level up the game for structured data synthesis, and publicly showcase its capabilities on bigger, wider and more complex datasets. This shall allow for a more realistic demonstration of capabilities, as any of the real-word datasets of our customers, is orders of magnitudes richer than the commonly demo-ed “toy datasets”. Thus, let’s use the handy Python package folktables to extract a significantly larger and also more recent version of the UCI Adult dataset directly from the US Census Bureau. For this blog post we pulled records from the 2018 American community survey (ACS) on 1,476,217 working individuals of age 17 or older, together with 4 numerical and 28 categorical attributes.

Synthesize data 

No matter whether your dataset is small or large in size, using MOSTLY AI to synthesize it, is always the same easy 3-step process. You first upload or connect to your dataset, you then configure and launch the synthetization, and once the job is completed, you then access and freely use your generated synthetic data. Yes, it's that easy!

Fig 1. AI-generated synthetic data with MOSTLY AI

Using our free version, the complete end-to-end process of our introduced dataset takes less than 12 minutes. This includes the fully automated steps of data analysis, data encoding, model training, synthetic data generation as well as the creation of the quality assurance report. The resulting 1,476,217 synthetic records are shown to be statistically representative, highly realistic, truly anonymous, and yet at granular level. These records therefore serve as a safe drop-in alternative to the original data, and allow for any type of data exploration, analysis as well as machine learning task. All without compromising the privacy of any individual.

Explore data

Let’s start out by analyzing MOSTLY AI’s generated synthetic data with Tableau, a popular data visualization platform. Note, that deriving statistical insights should not be understood as an exercise in reporting metrics with excess precision. Deriving statistical insights is much rather the art and science of exploring and spotting relationships and trends within the data, that were previously unknown. And this ability, to explore data in any way needed, is the major benefit of synthetic data when compared to any other privacy-enhancing technology. As a data consumer one is NOT restricted to pre-selected subsets of data attributes, to pre-defined numeric buckets, or to pre-calculated data aggregates, that all severely limit the scope of an analysis. As a data consumer one can freely combine, transform and tabulate any dimension and any measure.

Fig 2. Cross-tabulated synthetic population dataset in Tableau

One of the 32 captured attributes within the dataset is information about the surveyed state, representing geographical information, that can be nicely visualized on a map. Figure 3 shows the share of respondents, with an annual income of $50,000 or more, displayed as a choropleth map. The darker the color, the higher the share of high income earners. And one can immediately see, side-by-side, that the very same patterns emerge. States on the west, respectively on the north east coast exhibit significantly higher incomes than other states.

Fig 3. High income earners by US State, visualized in Tableau

Figure 4 exhibits the share of high income earners across education level and age group, and displays similarly strong, yet consistent patterns. The higher the educational level, the higher the likelihood to earn more than $50k per year. And in addition, there is a significant difference between people below 25 years, people between 26 and 35 years, as well as people of 36 years of age and older.

Fig 4. High income earners by Education and Age, visualized in Tableau

Let’s next explore income across genders, and across occupation, which is an attribute consisting of over 500 (!) distinct values. Most other synthesization solutions struggle with capturing the signals for high cardinality features like these. Figure 5 shows side-by-side the large income gap across occupation, discriminating between high income jobs like physicians and software developers on the one end of the spectrum, and cashiers and fast food workers on the other end. Plus, it also shows a consistent gender pay gap across all occupation. Thus, the analysis shows that men are consistently more likely to earn a high income than women, even when controlling for the type of occupation. Synthetic data can play a pivotal role in uncovering such types of systematic injustices, that are currently locked up due to the private nature of the underlying datasets.

Fig 5. Top earning occupations by Gender, visualized in Tableau

The complete analytical workbook, and each of the presented interactive visualizations, can be accessed through this link hosted on Tableau Public.

Build models

Visual analytics, as shown in the previous section, is an excellent and essential mean to quickly gain a deeper understanding of a dataset and its inherent patterns. However, at the same time it also requires some level of caution, in order to avoid misinterpreting spurious relations by overlooking confounding factors. Machine learning models, that are trained to predict a specific target attribute of interest based on a wide range of other variables, help to mitigate this problem. These models can account for the combined effect of attributes, and with that can report the net impact of individual attributes.

Let’s therefore train a state-of-the-art ML model on top of the synthetic data 1) to benchmark its overall predictive performance with respect to real data, and 2) to identify the key drivers, and their net effect on the attribute of interest, in our case the likelihood of a respondent earning a high income salary. The model of our choice is LightGBM, a gradient boosting machine learning algorithm, that is fast to train and evaluate, even for larger datasets. In our case, training the model on over 1 million records for 31 attributes to predict high income takes less than 1 minute on a commodity laptop.

In order to assess the model’s predictive accuracy on a true holdout dataset, we need to split the original dataset into a training and a holdout set. We randomly assign 80% of the original records to the former, and the remaining 20% to the latter. The synthetic dataset is generated based on the 80% training set. The LightGBM model is then trained on the synthetic data, and finally evaluated on the 20% holdout data, that wasn’t being accessed before. Similarly, the same model is being trained on the original training data, and evaluated on the same holdout as well. This serves us as a very strong benchmark for the ML performance of synthetic data. See figure 6 for a schematic representation of the setup. The holdout, the training as well as a synthetic dataset can be accessed via our Github repository for popular public datasets. There you will also find a corresponding Jupyter notebook that, in combination with our free version, allows anyone to easily reproduce all results from this blog post.

Fig 6. Train-Real-Test-Real (TRTR) vs. Train-Synthetic-Test-Real (TSTR)

Figure 7 visualizes the distribution of the predicted scores for each of the models, split by income group. We can see that the model can discriminate well between these two groups, and assigns higher probabilities to high income earners, and vice versa. This can be also quantified via the ROC Area-Under-Curve measure, which reflects the probability of the model to correctly recognize the high income earner among a pair of two subjects. We can see that training a state-of-the-art ML model on synthetic data yields identical results, both in terms of scores as well as accuracy. The model trained on synthetic data, with an AUC of 0.881, is on-par with the model trained on real data (AUC: 0.885). This is a particularly strong and robust result, considering that we’ve used nearly 300,000 holdout records for the evaluation.

Fig 7. Identical model scores and model performance for synthetic data

In order to explore the trained models further, we turn towards SHAP, a highly popular framework to explain ML models. Below we show the SHAP summary plot side-by-side, which already reveals the key attributes for predicting income. As one can see, occupation, age, and education are the top 3 drivers that allow to determine whether a person earns a high income or not. After that it is the information on insurance, gender, state and marital status. Further features contribute less to the model predictions. And note again, that these findings are identical for real and for synthetic data, with the key advantage that none of the private information is getting exposed while using the latter.

Fig 8. Identical findings for SHAP summary analysis

Aside from the overall impact of an attribute with respect to the predicted target, it is of great interest to study the value-dependent net effect of each of those attributes in details. These can be visualized via SHAP dependency plots, and show for each attribute the shift in predictions given their attribute value. Figure 9 displays the corresponding plots for age, state as well as gender. The x-axes show attribute values, and the y-axes the shift in predicted score. Thus, it is for example very unlikely for a young person below 25 years to be in the high income class, no matter what occupation, education or other features that person has. But once a person has reached 40 years, any further age increase does not change his or her likelihood to earn more. On the other hand, we can also see that, all other things being equal, male respondents are significantly more likely to earn a high income than their female counterparts. I.e., even for the same job, the same location, the same age, the same education, etc., women systematically earn less than men.

Fig 9. Identical findings for SHAP dependency analysis

The power (and beauty) of synthetic data is the ability to drill down to granular level at any time. So, even though the generated subjects do not exist in real life, but “merely” are statistically representative, they do allow to reason about machine learning models by studying their impact on individual samples. This is a key enabler for involving a broader community of stakeholders (within and across organizations) in a much needed debate on machine learning models. Everyone - engineers, designers, lawyers, managers, customers all alike - is capable to argue a case based on representative samples. Yet, without access to samples, any discussion remains abstract. Figure 10 shows the SHAP values for our predictive income model, that has been trained on synthetic data, then evaluated and explained on synthetic, yet realistic samples. The randomly sampled case is for a 50-year old married woman from New Hampshire, who has a Master’s Degree and works in Education. The model assesses her to have an annual income of more than $50k with 85% likelihood, with her combination of education, occupation and age contribute the most for this assessment. The same type of analysis can be easily done not just for one sample, but for any of the millions of generated synthetic samples, and thus allows to test in detail the behavior as well as the robustness of the developed model, without exposing the privacy of any individuals.

Fig 10. Individual-level analysis of ML model behavior


It’s the dawn of a new era. Generative AI is being recognized for its immense power to inform us all, humans and algorithms alike. And high-quality structured synthetic data, as delivered by MOSTLY AI, is key to overcome the privacy hurdles of data access. It’s key to help us see and understand the world as it is, as well as it could be.

In this blog post we’ve provided a new, publicly reproducible benchmark for state-of-the-art structured synthetic data at scale. We’ve shown how MOSTLY AI allows to easily synthesize large-scale population data, and how the generated data reliably yields identical statistical insights without compromising on privacy. It’s this level of accuracy, its reliability, and last but not least its ease of use, that makes MOSTLY AI stand out on the market. But don’t take our word for it. Go ahead, and start generating synthetic data today!

Here at MOSTLY AI, we are big fans of open-source software. We are leveraging more than 90 open-source software packages for our synthetic data generator. It is safe to say that without open-source software libraries, it would have been impossible to get where we are today so quickly. We sometimes get asked by prospects why they should choose MOSTLY AI’s Synthetic Data Platform over freely available open-source solutions, like MIT’s Synthetic Data Vault, to synthesize data. This blog post provides an answer.

Update: SDV changed their license model in 2023, and is NOT open-source anymore.

SDV vs MOSTLY AI: Synthetic data quality

The answer is multifaceted, but the main point is the quality of the synthetic data you can generate. We pride ourselves on delivering synthetic data that is so close to the real data that it can be used as a drop-in replacement without sacrificing any meaningful quality. And, of course, all while guaranteeing full privacy.

Already two years ago, we looked at the quality of synthetic data generated with two popular open-source models: CTGAN and TVAE. Back then, we showed how MOSTLY AI’s synthetic data had higher accuracy on multiple dimensions. This time we look more broadly at the open-source software library developed by MIT,  the Synthetic Data Vault (SDV). It was initially released in 2018 based on research work led by Kalyan Veeramachaneni. SDV is a Python library that supports three types of data: single table data, relational data, and time series data. In addition, SDV provides an evaluation and benchmarking framework, SDGym, and comes with 100+ datasets that can be used to explore the functionality.

For this benchmarking exercise, we picked five of the 19 provided single table datasets to get a good variety of data in terms of size and structure:

SDV Synthetic data benchmarking

Currently, SDV offers five different models for synthesizing single table data: Tabular Preset (FAST_ML), GaussianCopula, CTGAN, CopulaGAN, and TVAE. To get a proper overview of the state of the art of open-source data synthesis, we spun up some virtual machines and synthesized all five datasets with all available models. And of course, we used the latest release of the MOSTLY AI Synthetic Data Platform to synthesize these datasets to compare. For the record – we used the standard configurations of all models and of our platform. We did not specifically try to tune any dataset. In total, we created more than 5 million rows of synthetic data or 300 million synthetic data points.

The big picture of quality includes the functionality of the synthetic data

Since we wanted to check out SDV more broadly, we also had a look at the functionality to evaluate the quality of generated synthetic data. SDV’s Evaluation Framework takes a real and a synthetic dataset as input and then calculates up to 29 different metrics comparing these two. It returns the average of the scores of the individual metrics, which results in an overall score from 0 to 1, with 0 being the worst and 1 being the best (= the synthetic data is really close to the real data).

For our benchmark, we picked three metrics that worked without any further configuration (LogisticDetection, CSTest, and KSTest) and had SDV report the aggregate score. CSTest (Chi-Squared test) and KSTest (two-sample Kolmogorov–Smirnov test) are statistical metrics that compare the tables by running different statistical tests. LogisticDetection is part of the detection metrics, which evaluate how hard it is to distinguish the synthetic data from the real data by using an ML model (in this case a LogisticRegression classifier).

The results are summarized in the chart below:

Comparison of synthetic data generators

* Please note that no synthetic data for covtype could be created with CopulaGAN due to time-out issues, even on a VM with 224 vCPUs

In short: MOSTLY AI beat every single open-source model for every single dataset. Unsurprisingly the less compute intense FAST_ML, and GaussianCopula models cannot create highly realistic synthetic data with average scores of 0.68 and 0.63, respectively. From the more sophisticated models, TVAE performs best with an average score of 0.82, followed by CopulaGAN (0.78) and CTGAN (0.74). MOSTLY AI’s average score is 0.97.

SDV vs MOSTLY AI: Beyond the hard metrics & further evaluations on synthetic data generation

In practice, you will want to evaluate synthetic data on more dimensions than statistical and detection metrics. High-level metrics give you a first assessment of the quality of the created synthetic data, but the real deal is when synthetic data is actually evaluated by performing the exact same downstream tasks you would have performed using the real data.

Again and again, these analyses confirm what we already know: MOSTLY AI’s Synthetic Data Platform delivers the most accurate synthetic data consistently. But don’t take my word for it: you can find all the created synthetic datasets as a download here to perform whatever kind of analysis you wish.

The heart of our synthetic data platform is where we do not rely on open source but instead have developed our own proprietary IP. The approach and the deep learning architecture used to train a generative model. We have done so because this is what really matters when it comes to achievable synthetic data quality.

There are other reasons to consider when choosing a synthetic data generator. In addition to unmatched synthetic data quality, some of the reasons for choosing MOSTLY AI’s Synthetic Data Platform include:

SDV vs MOSTLY AI: In conclusion

In conclusion, at MOSTLY AI, we are enthusiastic supporters of open-source software and recognize its significant contribution to our synthetic data generator. Our rapid progress and success can be attributed to leveraging over 90 open-source software packages. However, when prospects inquire about why they should choose our Synthetic Data Platform over freely available open-source solutions like Synthetic Data Vault (SDV), we have compelling reasons to offer.

The key factor that sets us apart is the exceptional quality of the synthetic data we generate. We take great pride in delivering synthetic data that closely resembles real data, allowing for seamless integration without compromising privacy or sacrificing quality. In a previous analysis, we compared the accuracy of synthetic data generated using two popular open-source models, CTGAN and TVAE, and demonstrated that MOSTLY AI's synthetic data exhibited superior accuracy across multiple dimensions. This time, we conducted a broader evaluation by examining SDV, an open-source software library developed by MIT.

To assess the quality of the generated synthetic data, we utilized SDV's evaluation framework, which employs various metrics to compare real and synthetic datasets. The results were consistently in our favor, highlighting the superiority of MOSTLY AI's Synthetic Data Platform.

Beyond statistical and detection metrics, we firmly believe in evaluating synthetic data through practical applications. Repeated analyses have validated that our platform consistently delivers the most accurate synthetic data. However, we don't expect you to take our word for it. We invite you to explore and analyze the synthetic datasets we have created, which are available for download.

While open-source software plays a crucial role in our work, we have developed our proprietary intellectual property to ensure the highest possible synthetic data quality. The heart of our Synthetic Data Platform lies in our unique approach and deep learning architecture for training generative models.

In addition to exceptional data quality, there are other reasons to consider our Synthetic Data Platform. We prioritize user experience, offering a straightforward and code-free platform that eliminates the need for choosing generative models or fine-tuning hyperparameters. Moreover, our platform ensures speed and efficiency, leading to significant cost savings compared to training sophisticated generative models using open-source solutions. We also provide flexible data ingestion capabilities, enabling direct connections to various data sources, saving time and effort on pre- and post-processing steps.

Privacy is of utmost importance, and our synthetic data generator automatically handles outliers and extreme values, ensuring privacy. Lastly, we offer dedicated support, leveraging our extensive experience in the synthetic data domain to provide assistance to our enterprise clients with guaranteed service level agreements (SLAs).

If you would like to experience the power of the MOSTLY AI Synthetic Data Platform, we encourage you to sign up and generate synthetic data for free. We are confident that our platform's capabilities and the quality of synthetic data it produces will exceed your expectations.

Experience the power of the MOSTLY AI Synthetic Data Platform for yourself and sign up to generate synthetic data for free.