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.

Cite

Text

Rhodes et al. "Telescoping Density-Ratio Estimation." Neural Information Processing Systems, 2020.

Markdown

[Rhodes et al. "Telescoping Density-Ratio Estimation." Neural Information Processing Systems, 2020.](https://mlanthology.org/neurips/2020/rhodes2020neurips-telescoping/)

BibTeX

@inproceedings{rhodes2020neurips-telescoping,
  title     = {{Telescoping Density-Ratio Estimation}},
  author    = {Rhodes, Benjamin and Xu, Kai and Gutmann, Michael U.},
  booktitle = {Neural Information Processing Systems},
  year      = {2020},
  url       = {https://mlanthology.org/neurips/2020/rhodes2020neurips-telescoping/}
}