{"ID":2826246,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.19334","arxiv_id":"2512.19334","title":"Orthogonal Approximate Message Passing with Optimal Spectral Initializations for Rectangular Spiked Matrix Models","abstract":"We propose an orthogonal approximate message passing (OAMP) algorithm for signal estimation in the rectangular spiked matrix model with general rotationally invariant (RI) noise. We establish a rigorous state evolution that precisely characterizes the algorithm's high-dimensional dynamics and enables the construction of iteration-wise optimal denoisers. Within this framework, we accommodate spectral initializations under minimal assumptions on the empirical noise spectrum. In the rectangular setting, where a single rank-one component typically generates multiple informative outliers, we further propose a procedure for combining these outliers under mild non-Gaussian signal assumptions. For general RI noise models, the predicted performance of the proposed optimal OAMP algorithm agrees with replica-symmetric predictions for the associated Bayes-optimal estimator, and we conjecture that it is statistically optimal within a broad class of iterative estimation methods.","short_abstract":"We propose an orthogonal approximate message passing (OAMP) algorithm for signal estimation in the rectangular spiked matrix model with general rotationally invariant (RI) noise. We establish a rigorous state evolution that precisely characterizes the algorithm's high-dimensional dynamics and enables the construction o...","url_abs":"https://arxiv.org/abs/2512.19334","url_pdf":"https://arxiv.org/pdf/2512.19334v1","authors":"[\"Haohua Chen\",\"Songbin Liu\",\"Junjie Ma\"]","published":"2025-12-22T12:28:53Z","proceeding":"cs.IT","tasks":"[\"cs.IT\",\"cs.LG\",\"math.ST\"]","methods":"[]","has_code":false}