Approximating Mutual Information by Maximum Likelihood Density Ratio Estimation

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Taiji Suzuki, Masashi Sugiyama, Jun Sese, Takafumi Kanamori ;
Proceedings of the Workshop on New Challenges for Feature Selection in Data Mining and Knowledge Discovery at ECML/PKDD 2008, PMLR 4:5-20, 2008.

Abstract

Mutual information is useful in various data processing tasks such as feature selection or independent component analysis. In this paper, we propose a new method of approximating mutual information based on maximum likelihood estimation of a density ratio function. Our method, called Maximum Likelihood Mutual Information (MLMI), has several attractive properties, e.g., density estimation is not involved, it is a single-shot procedure, the global optimal solution can be efficiently computed, and cross-validation is available for model selection. Numerical experiments show that MLMI compares favorably with existing methods.

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