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Paper · 2006.12204 · 2020

Telescoping Density-Ratio Estimation

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 3 functions out of this paper's own repositories and ran 1 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
benrhodes26/tre_code canonical 1 of 3
FunctionStatusWhere it lives
get_dimwise_mixing_ordering_event_shape Ran benrhodes26/tre_code/build_bridges.py
code served (permissive licence) · get_code("59aa3084ed774116")
build_placeholders Not yet run benrhodes26/tre_code/representation_learning_evaluation.py
code served (permissive licence) · get_code("a64420d5d222f119")
nll_loss Not yet run benrhodes26/tre_code/representation_learning_evaluation.py
code served (permissive licence) · get_code("bc6b7cfb69c9976e")

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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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