Rate analysis for detection of sparse mixtures

Jonathan G. Ligo, George V. Moustakides, Venugopal V. Veeravalli

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we study the rate of decay of the probability of error for distinguishing between a sparse signal with noise, modeled as a sparse mixture, from pure noise. This problem has many applications in signal processing, evolutionary biology, bioinformatics, astrophysics and feature selection for machine learning. We let the mixture probability tend to zero as the number of observations tends to infinity and derive oracle rates at which the error probability can be driven to zero for a general class of signal and noise distributions. In contrast to the problem of detection of non-sparse signals, we see the log-probability of error decays sublinearly rather than linearly and is characterized through the x2-divergence rather than the Kullback-Leibler divergence. This work provides the first characterization of the rate of decay of the error probability for this problem.

Original languageEnglish (US)
Title of host publication2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4244-4248
Number of pages5
ISBN (Electronic)9781479999880
DOIs
StatePublished - May 18 2016
Event41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Shanghai, China
Duration: Mar 20 2016Mar 25 2016

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2016-May
ISSN (Print)1520-6149

Other

Other41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016
CountryChina
CityShanghai
Period3/20/163/25/16

Keywords

  • Detection theory
  • error exponents
  • large deviations
  • likelihood ratio test
  • sparse detection

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Electrical and Electronic Engineering

Fingerprint Dive into the research topics of 'Rate analysis for detection of sparse mixtures'. Together they form a unique fingerprint.

Cite this