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• W4386747131 abstract "Approximate Message Passing (AMP) is a class of iterative algorithms that have found applications in many problems in high-dimensional statistics and machine learning. In its general form, AMP can be formulated as an iterative procedure driven by a matrix M. Theoretical analyses of AMP typically assume strong distributional properties on M, such as M has i.i.d. sub-Gaussian entries or is drawn from a rotational invariant ensemble. However, numerical experiments suggest that the behavior of AMP is universal as long as the eigenvectors of M are generic. In this paper we take the first step in rigorously understanding this universality phenomenon. In particular, we investigate a class of memory-free AMP algorithms (proposed by Çakmak and Opper for mean-field Ising spin glasses) and show that their asymptotic dynamics is universal on a broad class of semirandom matrices. In addition to having the standard rotational invariant ensemble as a special case, the class of semirandom matrices that we define in this work also includes matrices constructed with very limited randomness. One such example is a randomly signed version of the sine model, introduced by Marinari, Parisi, Potters, and Ritort for spin glasses with fully deterministic couplings." @default.
• W4386747131 created "2023-09-15" @default.
• W4386747131 creator A5028478821 @default.
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• W4386747131 date "2023-09-01" @default.
• W4386747131 modified "2023-09-26" @default.
• W4386747131 title "Universality of approximate message passing with semirandom matrices" @default.
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• W4386747131 doi "https://doi.org/10.1214/23-aop1628" @default.
• W4386747131 hasPublicationYear "2023" @default.
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