Practical and Consistent Estimation of f-Divergences

TL;DR

This paper introduces a practical, high-dimensional estimator for f-divergences that leverages structural assumptions common in modern machine learning, demonstrating improved convergence and empirical performance.

Contribution

It proposes a new estimator for f-divergences under realistic structural assumptions, with better convergence rates and ease of implementation in high-dimensional settings.

Findings

Performs well in high dimensions

Faster convergence rates compared to traditional methods

Validated on synthetic and real datasets

Abstract

The estimation of an f-divergence between two probability distributions based on samples is a fundamental problem in statistics and machine learning. Most works study this problem under very weak assumptions, in which case it is provably hard. We consider the case of stronger structural assumptions that are commonly satisfied in modern machine learning, including representation learning and generative modelling with autoencoder architectures. Under these assumptions we propose and study an estimator that can be easily implemented, works well in high dimensions, and enjoys faster rates of convergence. We verify the behavior of our estimator empirically in both synthetic and real-data experiments, and discuss its direct implications for total correlation, entropy, and mutual information estimation.