# Not all Jensen-Shannon Divergence Estimators are Equal

arXiv: https://arxiv.org/abs/2606.16411 · HTML: https://mlsanity.com/paper/2606.16411/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 49 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Builds on (most cited first, 21 of 21)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second](https://mlsanity.com/paper/2207.01848/) (2022)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [Adversarial Feature Learning](https://mlsanity.com/paper/1605.09782/) (2016)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [A note on the evaluation of generative models](https://mlsanity.com/paper/1511.01844/) (2015)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [When Do Neural Nets Outperform Boosted Trees on Tabular Data?](https://mlsanity.com/paper/2305.02997/) (2023)
- [DP-MERF: Differentially Private Mean Embeddings with Random Features for Practical Privacy-Preserving Data Generation](https://mlsanity.com/paper/2002.11603/) (2020)
- [On a generalization of the Jensen-Shannon divergence and the JS-symmetrization of distances relying on abstract means](https://mlsanity.com/paper/1904.04017/) (2019)
- [Jensen-Shannon Information Based Characterization of the Generalization Error of Learning Algorithms](https://mlsanity.com/paper/2010.12664/) (2020)
- [Scaling While Privacy Preserving: A Comprehensive Synthetic Tabular Data Generation and Evaluation in Learning Analytics](https://mlsanity.com/paper/2401.06883/) (2024)
- [Assessing the ability of generative adversarial networks to learn canonical medical image statistics](https://mlsanity.com/paper/2204.12007/) (2022)
- [A Consensus Privacy Metrics Framework for Synthetic Data](https://mlsanity.com/paper/2503.04980/) (2025)
- [Synthetic Tabular Data Validation: A Divergence-Based Approach](https://mlsanity.com/paper/2405.07822/) (2024)
- [Connecting Jensen-Shannon and Kullback-Leibler Divergences: A New Bound for Representation Learning](https://mlsanity.com/paper/2510.20644/) (2025)
- [Artificial Inductive Bias for Synthetic Tabular Data Generation in Data-Scarce Scenarios](https://mlsanity.com/paper/2407.03080/) (2024)

## Abstract (arXiv)

The Jensen-Shannon divergence is widely reported as a scalar measure of fidelity for synthetic tabular data. Yet, in practice, it is estimated from finite samples using protocols that are often underspecified. This creates a measurement problem. Although the population divergence is well defined, the empirical value depends on the estimator family, sampling protocol, calibration, dimensionality, and class balance. We show that different protocols can yield non-comparable values: marginal-based estimators ignore dependencies in the joint distribution and can severely underestimate divergence, while classifier-based estimators capture joint structure but exhibit strong estimator dependence. We systematically study this behavior across controlled settings with reference divergences and real-world synthetic tabular benchmarks. Our analysis reveals dependence blindness in marginal estimators, prior-shift bias under class imbalance, and estimator sensitivity in high dimensions. To address prior shift, we derive a closed-form posterior correction for classifier-based Jensen-Shannon estimation. Our results show that empirical Jensen-Shannon divergence values are inherently protocol-dependent, making explicit specification of the estimation procedure necessary for meaningful comparison. We provide practical guidelines and an open-source tool for estimator-aware Jensen-Shannon evaluation.