Universal Outlying Sequence Detection for Continuous Observations

Shaofeng Zou1, Venugopal Veeravalli2, Yingbin Liang1, Yuheng Bu3

  • 1Syracuse University
  • 2University Of Illinois-Urbana Champagne
  • 3University Of Illinois - Urbana Champaign

Details

13:30 - 15:30 | Tue 22 Mar | Poster Area F | SPTM-P1.4

Session: Detection

Abstract

The following detection problem is studied, in which there are M sequences of samples out of which one outlier sequence needs to be detected. Each typical sequence contains n independent and identically distributed (i.i.d.) continuous observations from a known distribution π, and the outlier sequence contains n i.i.d. observations from an outlier distribution μ, which is distinct from π, but otherwise unknown. A universal test based on Kullback-Leibler (KL) divergence is built to approximate the maximum likelihood test, with known π and unknown μ. A KL divergence estimator based on data-dependent partitions is employed, and is shown to converge to its true value exponentially fast when the density ratio satisfies 0