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CATEGORIES:Lecture / Talk / Workshop
DESCRIPTION:NOTE: There will be a projector screen in KAP 414 for those who
would like to gather and watch the talk. Note the speaker will not be pres
ent in KAP 414.\n\nSong Mei\, UC Berkeley\n\nAbstract: We study mean-field
variational Bayesian inference using the TAP approach\, for Z2-synchronizat
ion as a prototypical example of a high-dimensional Bayesian model. We show
that for any signal strength lambda > 1 (the weak-recovery threshold)\, th
ere exists a unique local minimizer of the TAP free energy functional near
the mean of the Bayes posterior law. Furthermore\, the TAP free energy in a
local neighborhood of this minimizer is strongly convex. Consequently\, a
natural-gradient/mirror-descent algorithm achieves linear convergence to th
is minimizer from a local initialization\, which may be obtained by a finit
e number of iterates of Approximate Message Passing (AMP). This provides a
rigorous foundation for variational inference in high dimensions via minimi
zation of the TAP free energy. We also analyze the finite-sample convergenc
e of AMP\, showing that AMP is asymptotically stable at the TAP minimizer f
or any lambda > 1\, and is linearly convergent to this minimizer from a spe
ctral initialization for sufficiently large lambda. Such a guarantee is str
onger than results obtainable by state evolution analyses\, which only desc
ribe a fixed number of AMP iterations in the infinite-sample limit.
DTEND:20211022T233000Z
DTSTAMP:20230327T075600Z
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_38058511955060
URL:https://calendar.usc.edu/event/probability_and_statistics_seminar_local
_convexity_of_the_tap_free_energy_and_amp_convergence_for_z2-synchronizatio
n_4527
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