Mismatched Binary Hypothesis Testing: Error Exponent Sensitivity

• Published in: IEEE transactions on information theory Vol. 68; no. 10; pp. 6738 - 6761
• Main Authors: Boroumand, Parham, Guillen i Fabregas, Albert
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Bayes methods; Error analysis; Error probability; generalized likelihood ratio test; Hypotheses; Hypothesis testing; Likelihood ratio; likelihood ratio test; mismatch; Pairwise error probability; Probability distribution; sequenstial probability ratio test; Signal processing algorithms; Testing; Training data
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2022.3171438

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.