Robust Hypothesis Testing With Moment Constrained Uncertainty Sets
Akshayaa Magesh, Zhongchang Sun, Venugopal V. Veeravalli, Shaofeng Zou
Abstract
The problem of robust binary hypothesis testing is studied. Under both hypotheses, the data-generating distributions are assumed to belong to uncertainty sets constructed through moments; in particular, the sets contain distributions whose moments are centered around the empirical moments obtained from training observations. The goal is to design a test that performs well under all distributions in the uncertainty sets, i.e., minimize the worst-case error probability over the uncertainty sets. In the finite-alphabet case, the optimal test is obtained. In the infinite-alphabet case, a tractable approximation to the worst-case error is derived that converges to the optimal value A test is further constructed to generalize to the entire alphabet. An exponentially consistent test for testing batch samples is also proposed. Numerical results are provided to demonstrate the performance of the proposed robust tests.
BibTeX
@inproceedings{icassp2023_robusthypothesis,
title = {Robust Hypothesis Testing With Moment Constrained Uncertainty Sets},
author = {Akshayaa Magesh and Zhongchang Sun and Venugopal V. Veeravalli and Shaofeng Zou},
booktitle = {ICASSP 2023},
year = {2023}
}