Asymptotically Optimal Approximation of Multidimensional pdf's by Lower Dimensional pdf's

  • Authors:
  • Steven Kay

  • Affiliations:
  • Dept. of Electr. & Comput. Eng., Rhode Island Univ., Kingston, RI

  • Venue:
  • IEEE Transactions on Signal Processing
  • Year:
  • 2007

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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