Maximally Informative Statistics

Details Maximally Informative Statistics Maximally Informative Statistics

2000-10-15

arxiv.org/abs/physics/0010039v1

Monograph on Bayesian Methods in the Sciences, Rev. R. Acad. Sci. Exacta. Fisica. Nat. Vol. 93, No. 3, pp. 381--386, 1999

Physics

Data Analysis, Statistics and Probability

13 pages. Presented Bayesian Statistics 6, Valencia, 1998. Arxiv version asserts bold vectors dropped in print

Scientific paper

In this paper we propose a Bayesian, information theoretic approach to dimensionality reduction. The approach is formulated as a variational principle on mutual information, and seamlessly addresses the notions of sufficiency, relevance, and representation. Maximally informative statistics are shown to minimize a Kullback-Leibler distance between posterior distributions. Illustrating the approach, we derive the maximally informative one dimensional statistic for a random sample from the Cauchy distribution.

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