Back to Search
Start Over
Spectrum Truncation Power Iteration for Agnostic Matrix Phase Retrieval.
- Source :
-
IEEE Transactions on Signal Processing . 11/1/2021, p3991-4006. 16p. - Publication Year :
- 2021
-
Abstract
- 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 $\mathbf {M}^*\in \mathbb {R}^{d_1\times d_2}$ as the parametric component from $n$ instantiations/samples of a semi-parametric model $y=f(\langle \mathbf {M}^*, \mathbf {X}\rangle, \epsilon)$ , where the predictor matrix is denoted as $\mathbf {X}\in \mathbb {R}^{d_1\times d_2}$ , link function $f(\cdot, \epsilon)$ is agnostic under some mild distribution assumptions on $\mathbf {X}$ , 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 1053587X
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Signal Processing
- Publication Type :
- Academic Journal
- Accession number :
- 153880508
- Full Text :
- https://doi.org/10.1109/TSP.2021.3090335