  The ever-increasing use of generative models in various fields where tabular
data is used highlights the need for robust and standardized validation metrics
to assess the similarity between real and synthetic data. Current methods lack
a unified framework and rely on diverse and often inconclusive statistical
measures. Divergences, which quantify discrepancies between data distributions,
offer a promising avenue for validation. However, traditional approaches
calculate divergences independently for each feature due to the complexity of
joint distribution modeling. This paper addresses this challenge by proposing a
novel approach that uses divergence estimation to overcome the limitations of
marginal comparisons. Our core contribution lies in applying a divergence
estimator to build a validation metric considering the joint distribution of
real and synthetic data. We leverage a probabilistic classifier to approximate
the density ratio between datasets, allowing the capture of complex
relationships. We specifically calculate two divergences: the well-known
Kullback-Leibler (KL) divergence and the Jensen-Shannon (JS) divergence. KL
divergence offers an established use in the field, while JS divergence is
symmetric and bounded, providing a reliable metric. The efficacy of this
approach is demonstrated through a series of experiments with varying
distribution complexities. The initial phase involves comparing estimated
divergences with analytical solutions for simple distributions, setting a
benchmark for accuracy. Finally, we validate our method on a real-world dataset
and its corresponding synthetic counterpart, showcasing its effectiveness in
practical applications. This research offers a significant contribution with
applicability beyond tabular data and the potential to improve synthetic data
validation in various fields.
