Telescoping Density-Ratio Estimation
This addresses a critical limitation in unsupervised learning for researchers and practitioners, though it appears incremental as it builds on existing density-ratio estimation methods.
The paper tackles the problem of density-ratio estimation failing for highly dissimilar densities, introducing telescoping density-ratio estimation (TRE) to enable accurate estimation in such cases, with experiments showing substantial improvements in mutual information estimation, representation learning, and energy-based modelling.
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.