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Estimating Mutual Information for Discrete-Continuous Mixtures
Weihao Gao · Sreeram Kannan · Sewoong Oh · Pramod Viswanath

Tue Dec 05 03:45 PM -- 03:50 PM (PST) @ Hall C

Estimation of mutual information from observed samples is a basic primitive in machine learning, useful in several learning tasks including correlation mining, information bottleneck, Chow-Liu tree, and conditional independence testing in (causal) graphical models. While mutual information is a quantity well-defined for general probability spaces, estimators have been developed only in the special case of discrete or continuous pairs of random variables. Most of these estimators operate using the 3H -principle, i.e., by calculating the three (differential) entropies of X, Y and the pair (X,Y). However, in general mixture spaces, such individual entropies are not well defined, even though mutual information is. In this paper, we develop a novel estimator for estimating mutual information in discrete-continuous mixtures. We prove the consistency of this estimator theoretically as well as demonstrate its excellent empirical performance. This problem is relevant in a wide-array of applications, where some variables are discrete, some continuous, and others are a mixture between continuous and discrete components.

Author Information

Weihao Gao (UIUC)
Sreeram Kannan (University of Washington)
Sewoong Oh (UIUC)
Pramod Viswanath (UIUC)

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