Tight Mutual Information Estimation With Contrastive Fenchel-Legendre Optimization

Qing Guo, Junya Chen, Dong Wang, Yuewei Wang, Xinwei Deng, Lawrence Carin, Fan Li, Jing Huang, Chenyang Tao

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

Successful applications of InfoNCE (Information Noise-Contrastive Estimation) and its variants have popularized the use of contrastive variational mutual information (MI) estimators in machine learning. While featuring superior stability, these estimators crucially depend on costly large-batch training, and they sacrifice bound tightness for variance reduction. To overcome these limitations, we revisit the mathematics of popular variational MI bounds from the lens of unnormalized statistical modeling and convex optimization. Our investigation yields a new unified theoretical framework encompassing popular variational MI bounds, and leads to a new simple and powerful contrastive MI estimator we name FLO. Theoretically, we show that the FLO estimator is tight, and it converges under stochastic gradient descent. Empirically, the FLO estimator overcomes the limitations of its predecessors and learns more efficiently. The utility of FLO is verified using extensive benchmarks, and we further inspire the community with novel applications in meta-learning. Our presentation underscores the foundational importance of variational MI estimation in data-efficient learning.
Original languageEnglish (US)
Title of host publication36th Conference on Neural Information Processing Systems, NeurIPS 2022
PublisherNeural information processing systems foundation
ISBN (Print)9781713871088
StatePublished - Jan 1 2022

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