Zepeng Zhang, Songtao Lu, et al.
IEEE JSTSP
Agnostic matrix phase retrieval (AMPR) is a general low-rank matrix recovery problem given a set of noisy high-dimensional data samples. To be specific, AMPR is targeting at recovering an r-rank matrix Min Rd1×d2 as the parametric component from n instantiations/samples of a semi-parametric model y=f(langle M, Xrangle, epsilon), where the predictor matrix is denoted as Xin Rd1×d2, link function f(cdot, epsilon) is agnostic under some mild distribution assumptions on X, and epsilon represents the noise. In this paper, we formulate AMPR as a rank-restricted largest eigenvalue problem by applying the second-order Stein's identity and propose a new spectrum truncation power iteration (STPower) method to obtain the desired matrix efficiently. Also, we show a favorable rank recovery result by adopting the STPower method, i.e., a near-optimal statistical convergence rate under some relatively general model assumption from a wide range of applications. Extensive simulations verify our theoretical analysis and showcase the strength of STPower compared with the other existing counterparts.
Zepeng Zhang, Songtao Lu, et al.
IEEE JSTSP
Yujia Wang, Shiqiang Wang, et al.
ICML 2024
Songtao Lu, Siliang Zeng, et al.
NeurIPS 2022
Pu Zhao, Parikshit Ram, et al.
IJCAI 2022