Title

Asymptotically optimal approximation of multidimensional pdf's by lower dimensional pdf's

Document Type

Article

Date of Original Version

2-1-2007

Abstract

Probability density functions (pdf's) of high dimensionality are impractical to estimate from real data. For accurate estimation, the dimensionality of the pdf can be at most 5-10. In order to reduce the dimensionality a sufficient statistic is usually employed. When none is available, there is no universal agreement on how to proceed. We show how to construct a high-dimension pdf based on the pdf of a low-dimensional statistic that is closest to the true one in the sense of divergence. The latter criterion asymptotically minimizes the probability of error in a decision rule. An application to feature selection for classification is described. © 2006 IEEE.

Publication Title

IEEE Transactions on Signal Processing

Volume

55

Issue

2

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