Hierarchical recognition of sparse patterns in large-scale simultaneous inference

Wenguang Sun and Zhi Wei

Biometrika, 2015, vol. 102, issue 2, 267-280

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 large-scale 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.

Date: 2015
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