Telescoping Density-Ratio Estimation

TL;DR

This paper introduces telescoping density-ratio estimation (TRE), a novel framework that accurately estimates ratios between highly dissimilar densities, overcoming limitations of existing methods especially when densities differ significantly.

Contribution

The paper presents TRE, a new approach for density-ratio estimation that works effectively with highly dissimilar densities in high-dimensional spaces, improving over existing methods.

Findings

TRE outperforms existing methods in mutual information estimation

TRE improves representation learning tasks

TRE enhances energy-based modelling accuracy

Abstract

Density-ratio estimation via classification is a cornerstone of unsupervised learning. It has provided the foundation for state-of-the-art methods in representation learning and generative modelling, with the number of use-cases continuing to proliferate. However, it suffers from a critical limitation: it fails to accurately estimate ratios p/q for which the two densities differ significantly. Empirically, we find this occurs whenever the KL divergence between p and q exceeds tens of nats. To resolve this limitation, we introduce a new framework, telescoping density-ratio estimation (TRE), that enables the estimation of ratios between highly dissimilar densities in high-dimensional spaces. Our experiments demonstrate that TRE can yield substantial improvements over existing single-ratio methods for mutual information estimation, representation learning and energy-based modelling.