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- W4387385590 abstract "We study estimation in the linear model y = Aβ*+ϵ, in a Bayesian setting where β* has an entrywise i.i.d. prior and the design A is rotationally-invariant in law. In the large system limit as dimension and sample size increase proportionally, a set of related conjectures have been postulated for the asymptotic mutual information, Bayes-optimal mean squared error, and TAP mean-field equations that characterize the Bayes posterior mean of β*. In this work, we prove these conjectures for a general class of signal priors and for arbitrary rotationally-invariant designs A, under a “high-temperature” condition that restricts the range of eigenvalues of A <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>⊤</sup> A and encompasses regimes of sufficiently low signal-to-noise ratio. Our proof uses a conditional secondmoment method argument, where we condition on the iterates of a version of the Vector AMP algorithm for solving the TAP mean-field equations." @default.
- W4387385590 created "2023-10-06" @default.
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- W4387385590 date "2023-01-01" @default.
- W4387385590 modified "2023-10-16" @default.
- W4387385590 title "Random Linear Estimation with Rotationally-Invariant Designs: Asymptotics at High Temperature" @default.
- W4387385590 doi "https://doi.org/10.1109/tit.2023.3321575" @default.
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