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CATEGORIES:Data Science and Computational Statistics Seminar
SUMMARY:Replica Analysis of the Linear Model with Markov o
r Hidden Markov Signal Priors - Lan Truong (Univer
sity of Cambridge)
DTSTART:20220208T130000Z
DTEND:20220208T140000Z
UID:TALK4769AT
URL:/talk/index/4769
DESCRIPTION:In this talk\, we discuss the estimation of free e
nergy\, average mutual information\, and minimum m
ean square error (MMSE) of a linear model under tw
o assumptions: (1) the source is generated by a Ma
rkov chain\, (2) the source is generated via a hid
den Markov model. Our estimates are based on the r
eplica method in statistical physics. We show that
under the posterior mean estimator\, the linear m
odel with Markov sources or hidden Markov sources
is decoupled into single-input AWGN channels with
state information available at both encoder and de
coder where the state distribution follows the lef
t Perron-Frobenius eigenvector with unit Manhattan
norm of the stochastic matrix of Markov chains. N
umerical results show that the free energies and M
SEs obtained via the replica method are closely ap
proximate to their counterparts achieved by the Me
tropolis-Hastings algorithm or some well-known app
roximate message passing algorithms in the researc
h literature.
LOCATION:https://bham-ac-uk.zoom.us/j/95645638485?pwd=eDh3d
lR3QjRlVWRHdExvaDBWdEo4UT09
CONTACT:Hong Duong
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