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An Estimate of Mutual Information that Permits Closed-Form Optimisation

Raymond Liu, Duncan Gillies

Journal Article
Entropy
Volume 15
Issue 5
pp.1690–1704
May, 2013
ISSN 1099-4300
DOI 10.3390/e15051690
Abstract

We introduce a new estimate of mutual information between a dataset and a target variable that can be maximised analytically and has broad applicability in the field of machine learning and statistical pattern recognition. This estimate has previously been employed implicitly as an approximation to quadratic mutual information. In this paper we will study the properties of these estimates of mutual information in more detail, and provide a derivation from a perspective of pairwise interactions. From this perspective, we will show a connection between our proposed estimate and Laplacian eigenmaps, which so far has not been shown to be related to mutual information. Compared with other popular measures of mutual information, which can only be maximised through an iterative process, ours can be maximised much more efficiently and reliably via closed-form eigendecomposition.

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