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

David R. Wolf and Edward I. George
 
 

Abstract:

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. (Also presented Bayesian Statistics 6, Valencia, 1998)
 
 

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