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.
Original language | English (US) |
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Journal | ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings |
DOIs | |
State | Published - 2023 |
Event | 48th IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2023 - Rhodes Island, Greece Duration: Jun 4 2023 → Jun 10 2023 |
Keywords
- Bayesian setting
- Moment robust test
- converge
- exponentially consistent
- tractable approximation
ASJC Scopus subject areas
- Software
- Signal Processing
- Electrical and Electronic Engineering