On fenchel mini-max learning

Chenyang Tao, Liqun Chen, Shuyang Dai, Junya Chen, Ke Bai, Dong Wang, Jianfeng Feng, Wenlian Lu, Georgiy Bobashev, Lawrence Carin

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

2 Scopus citations

Abstract

Inference, estimation, sampling and likelihood evaluation are four primary goals of probabilistic modeling. Practical considerations often force modeling approaches to make compromises between these objectives. We present a novel probabilistic learning framework, called Fenchel Mini-Max Learning (FML), that accommodates all four desiderata in a flexible and scalable manner. Our derivation is rooted in classical maximum likelihood estimation, and it overcomes a longstanding challenge that prevents unbiased estimation of unnormalized statistical models. By reformulating MLE as a mini-max game, FML enjoys an unbiased training objective that (i) does not explicitly involve the intractable normalizing constant and (ii) is directly amendable to stochastic gradient descent optimization. To demonstrate the utility of the proposed approach, we consider learning unnormalized statistical models, nonparametric density estimation and training generative models, with encouraging empirical results presented.
Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems
PublisherNeural information processing systems foundation
StatePublished - Jan 1 2019
Externally publishedYes

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