Robust Binary Hypothesis Testing Under Contaminated Likelihoods

TL;DR

This paper introduces a robust hypothesis testing method that optimizes decision rules under contaminated likelihoods with unknown contamination parameters, using a minimax approach and linear programming, motivated by workforce analytics applications.

Contribution

It develops a novel minimax framework for binary hypothesis testing under label noise without requiring knowledge of true likelihoods or contamination rates.

Findings

Provides a linear programming-based solution for robust decision rules.

Demonstrates effectiveness in scenarios with unknown contamination.

Addresses label noise issues in workforce analytics.

Abstract

In hypothesis testing, the phenomenon of label noise, in which hypothesis labels are switched at random, contaminates the likelihood functions. In this paper, we develop a new method to determine the decision rule when we do not have knowledge of the uncontaminated likelihoods and contamination probabilities, but only have knowledge of the contaminated likelihoods. In particular we pose a minimax optimization problem that finds a decision rule robust against this lack of knowledge. The method simplifies by application of linear programming theory. Motivation for this investigation is provided by problems encountered in workforce analytics.