TY - CONF
AB - We study the performance of a Bayesian statistician who estimates a rank-one signal corrupted by non-symmetric rotationally invariant noise with a generic distribution of singular values. As the signal-to-noise ratio and the noise structure are unknown, a Gaussian setup is incorrectly assumed. We derive the exact analytic expression for the error of the mismatched Bayes estimator and also provide the analysis of an approximate message passing (AMP) algorithm. The first result exploits the asymptotic behavior of spherical integrals for rectangular matrices and of low-rank matrix perturbations; the second one relies on the design and analysis of an auxiliary AMP. The numerical experiments show that there is a performance gap between the AMP and Bayes estimators, which is due to the incorrect estimation of the signal norm.
AU - Fu, Teng
AU - Liu, YuHao
AU - Barbier, Jean
AU - Mondelli, Marco
AU - Liang, ShanSuo
AU - Hou, TianQi
ID - 14923
SN - 9781665475549
T2 - Proceedings of 2023 IEEE International Symposium on Information Theory
TI - Mismatched estimation of non-symmetric rank-one matrices corrupted by structured noise
ER -