Hierarchical recognition of sparse patterns in large-scale simultaneous inference

Wenguang Sun, Zhi Wei

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We study how to separate signals from noisy data accurately and determine the patterns of the selected signals. Controlling the inflation of false positive errors is important in largescale simultaneous inference but has not been addressed in the pattern recognition literature. We develop a decision-theoretic framework and formulate the sparse pattern recognition problem as a simultaneous inference problem with multiple decision trees. Oracle and adaptive classifiers are proposed for maximizing the expected number of true positives subject to a constraint on the overall false positive rate. Existing results on multiple testing are extended by allowing more than two states of nature, hierarchical decision-making and new error rate concepts.

Original languageEnglish (US)
Pages (from-to)267-280
Number of pages14
JournalBiometrika
Volume102
Issue number2
DOIs
StatePublished - Jun 2015

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Keywords

  • Classification with reject option
  • Compound decision theory
  • False discovery rate
  • Hierarchical multiple testing
  • Multi-stage analysis

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