Mismatched Binary Hypothesis Testing: Error Exponent Sensitivity

TL;DR

This paper investigates how mismatched assumptions about data distributions affect error exponents in binary hypothesis testing, revealing greater sensitivity to distribution mismatch than to adversarial tampering.

Contribution

It provides a detailed analysis of error exponent deviations under distribution mismatch and adversarial tampering in binary hypothesis testing.

Findings

Error exponents are more sensitive to distribution mismatch than to tampering.

Quantifies the deviation of error exponents within divergence balls.

Analyzes multiple testing methods including likelihood ratio and Hoeffding's test.

Abstract

We study the problem of mismatched binary hypothesis testing between i.i.d. distributions. We analyze the tradeoff between the pairwise error probability exponents when the actual distributions generating the observation are different from the distributions used in the likelihood ratio test, sequential probability ratio test, and Hoeffding's generalized likelihood ratio test in the composite setting. When the real distributions are within a small divergence ball of the test distributions, we find the deviation of the worst-case error exponent of each test with respect to the matched error exponent. In addition, we consider the case where an adversary tampers with the observation, again within a divergence ball of the observation type. We show that the tests are more sensitive to distribution mismatch than to adversarial observation tampering.