# Empirically Estimable Classification Bounds Based on a New Divergence Measure

arXiv: https://arxiv.org/abs/1412.6534 · HTML: https://mlsanity.com/paper/1412.6534/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2014.

## Built on by (most cited first, 12 of 12)

- [Is the Performance of My Deep Network Too Good to Be True? A Direct Approach to Estimating the Bayes Error in Binary Classification](https://mlsanity.com/paper/2202.00395/) (2022)
- [Evaluating State-of-the-Art Classification Models Against Bayes Optimality](https://mlsanity.com/paper/2106.03357/) (2021)
- [Evaluating Bayes Error Estimators on Real-World Datasets with FeeBee](https://mlsanity.com/paper/2108.13034/) (2021)
- [Certified Robust Accuracy of Neural Networks Are Bounded due to Bayes Errors](https://mlsanity.com/paper/2405.11547/) (2024)
- [How Does Bayes Error Limit Probabilistic Robust Accuracy](https://mlsanity.com/paper/2405.14923/) (2024)
- [Bayes Error Rate Estimation in Difficult Situations](https://mlsanity.com/paper/2506.03159/) (2025)
- [Optimal Transport-based Adaptation in Dysarthric Speech Tasks](https://mlsanity.com/paper/2104.02535/) (2021)
- [Bounding Neyman-Pearson Region with f-Divergences](https://mlsanity.com/paper/2505.08899/) (2025)
- [Towards Provably Unlearnable Examples via Bayes Error Optimisation](https://mlsanity.com/paper/2511.08191/) (2025)
- [Deep Learning-Driven Friendly Jamming for Secure Multicarrier ISAC Under Channel Uncertainty](https://mlsanity.com/paper/2603.05062/) (2026)
- [The Calibration Channel Determines the Bayes-Error Proxy: An Exact Law for Temperature-Induced Distortion](https://mlsanity.com/paper/2607.18162/) (2026)
- [ProbabilityBench: Model Evaluation and Calibration with Exact Ground-Truth Uncertainty](https://mlsanity.com/paper/2610.17016/) (2026)

## Abstract (arXiv)

Information divergence functions play a critical role in statistics and information theory. In this paper we show that a non-parametric f-divergence measure can be used to provide improved bounds on the minimum binary classification probability of error for the case when the training and test data are drawn from the same distribution and for the case where there exists some mismatch between training and test distributions. We confirm the theoretical results by designing feature selection algorithms using the criteria from these bounds and by evaluating the algorithms on a series of pathological speech classification tasks.