Telescoping Density-Ratio Estimation
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.
Keywords
Cite
@article{arxiv.2006.12204,
title = {Telescoping Density-Ratio Estimation},
author = {Benjamin Rhodes and Kai Xu and Michael U. Gutmann},
journal= {arXiv preprint arXiv:2006.12204},
year = {2020}
}