Orthogonal Approximate Message Passing Algorithms for Rectangular Spiked Matrix Models with Rotationally Invariant Noise

• URL: http://arxiv.org/abs/2602.03283v1
• Date: Tue, 03 Feb 2026 09:06:20 GMT
• Title: Orthogonal Approximate Message Passing Algorithms for Rectangular Spiked Matrix Models with Rotationally Invariant Noise
• Authors: Haohua Chen, Songbin Liu, Junjie Ma,
• Abstract summary: We propose an approximate message passing (OAMP) algorithm for signal estimation in the rectangular spiked matrix model.<n>We establish a rigorous state evolution that exactly characterizes the high-dimensional dynamics of the algorithm.<n>Building on this framework, we derive an optimal variant of OAMP that minimizes the predicted mean-squared error at each iteration.
• Score: 4.705915211123485
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 exactly characterizes the high-dimensional dynamics of the algorithm. Building on this framework, we derive an optimal variant of OAMP that minimizes the predicted mean-squared error at each iteration. For the special case of i.i.d. Gaussian noise, the fixed point of the proposed OAMP algorithm coincides with that of the standard AMP algorithm. For general RI noise models, we conjecture that the optimal OAMP algorithm is statistically optimal within a broad class of iterative methods, and achieves Bayes-optimal performance in certain regimes.

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