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DESCRIPTION:Song Mei\, UC Berkeley\n\nWe study mean-field variational Bayes
ian inference using the TAP approach\, for Z2-synchronization as a prototyp
ical example of a high-dimensional Bayesian model. We show that for any sig
nal strength lambda > 1 (the weak-recovery threshold)\, there exists a uniq
ue local minimizer of the TAP free energy functional near the mean of the B
ayes posterior law. Furthermore\, the TAP free energy in a local neighborho
od of this minimizer is strongly convex. Consequently\, a natural-gradient/
mirror-descent algorithm achieves linear convergence to this minimizer from
a local initialization\, which may be obtained by a finite number of itera
tes of Approximate Message Passing (AMP). This provides a rigorous foundati
on for variational inference in high dimensions via minimization of the TAP
free energy. We also analyze the finite-sample convergence of AMP\, showin
g that AMP is asymptotically stable at the TAP minimizer for any lambda > 1
\, and is linearly convergent to this minimizer from a spectral initializat
ion for sufficiently large lambda. Such a guarantee is stronger than result
s obtainable by state evolution analyses\, which only describe a fixed numb
er of AMP iterations in the infinite-sample limit.
DTEND:20211022T233000Z
DTSTAMP:20230202T122208Z
DTSTART:20211022T223000Z
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SEQUENCE:0
SUMMARY:Probability and Statistics Seminar: Local convexity of the TAP free
energy and AMP convergence for Z2-synchronization
UID:tag:localist.com\,2008:EventInstance_38058450932595
URL:https://calendar.usc.edu/event/probability_and_statistics_seminar_local
_convexity_of_the_tap_free_energy_and_amp_convergence_for_z2-synchronizatio
n
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