Telescoping Density-Ratio Estimation

• URL: http://arxiv.org/abs/2006.12204v2
• Date: Tue, 24 Nov 2020 13:13:20 GMT
• Title: Telescoping Density-Ratio Estimation
• Authors: Benjamin Rhodes, Kai Xu and Michael U. Gutmann
• Abstract summary: We introduce a new framework, telescoping density-ratio estimation (TRE) TRE 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.
• Score: 21.514983459970903
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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