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- W4300372883 abstract "Approximate message passing (AMP) emerges as an effective iterative paradigm for solving high-dimensional statistical problems. However, prior AMP theory -- which focused mostly on high-dimensional asymptotics -- fell short of predicting the AMP dynamics when the number of iterations surpasses $obig(frac{log n}{loglog n}big)$ (with $n$ the problem dimension). To address this inadequacy, this paper develops a non-asymptotic framework for understanding AMP in spiked matrix estimation. Built upon new decomposition of AMP updates and controllable residual terms, we lay out an analysis recipe to characterize the finite-sample behavior of AMP in the presence of an independent initialization, which is further generalized to allow for spectral initialization. As two concrete consequences of the proposed analysis recipe: (i) when solving $mathbb{Z}_2$ synchronization, we predict the behavior of spectrally initialized AMP for up to $Obig(frac{n}{mathrm{poly}log n}big)$ iterations, showing that the algorithm succeeds without the need of a subsequent refinement stage (as conjectured recently by citet{celentano2021local}); (ii) we characterize the non-asymptotic behavior of AMP in sparse PCA (in the spiked Wigner model) for a broad range of signal-to-noise ratio." @default.
- W4300372883 created "2022-10-03" @default.
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- W4300372883 date "2022-08-05" @default.
- W4300372883 modified "2023-09-30" @default.
- W4300372883 title "A Non-Asymptotic Framework for Approximate Message Passing in Spiked Models" @default.
- W4300372883 doi "https://doi.org/10.48550/arxiv.2208.03313" @default.
- W4300372883 hasPublicationYear "2022" @default.
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