Kernel exponential family estimation via doubly dual embedding

Bo Dai, Hanjun Dai, Arthur Gretton, Le Song, Dale Schuurmans, Niao He

Research output: Contribution to conferencePaperpeer-review

Abstract

We investigate penalized maximum log-likelihood estimation for exponential family distributions whose natural parameter resides in a reproducing kernel Hilbert space. Key to our approach is a novel technique, doubly dual embedding, that avoids computation of the partition function. This technique also allows the development of a flexible sampling strategy that amortizes the cost of Monte-Carlo sampling in the inference stage. The resulting estimator can be easily generalized to kernel conditional exponential families. We establish a connection between kernel exponential family estimation and MMD-GANs, revealing a new perspective for understanding GANs. Compared to the score matching based estimators, the proposed method improves both memory and time efficiency while enjoying stronger statistical properties, such as fully capturing smoothness in its statistical convergence rate while the score matching estimator appears to saturate. Finally, we show that the proposed estimator empirically outperforms state-of-the-art methods in both kernel exponential family estimation and its conditional extension.

Original languageEnglish (US)
StatePublished - 2020
Externally publishedYes
Event22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019 - Naha, Japan
Duration: Apr 16 2019Apr 18 2019

Conference

Conference22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019
Country/TerritoryJapan
CityNaha
Period4/16/194/18/19

ASJC Scopus subject areas

  • Artificial Intelligence
  • Statistics and Probability

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