Replica Analysis of the Linear Model with Markov or Hidden Markov Signal Priors

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• Lan Truong (University of Cambridge)
• Tuesday 08 February 2022, 13:00-14:00
• https://bham-ac-uk.zoom.us/j/95645638485?pwd=eDh3dlR3QjRlVWRHdExvaDBWdEo4UT09.

If you have a question about this talk, please contact Hong Duong.

In this talk, we discuss the estimation of free energy, average mutual information, and minimum mean square error (MMSE) of a linear model under two assumptions: (1) the source is generated by a Markov chain, (2) the source is generated via a hidden Markov model. Our estimates are based on the replica method in statistical physics. We show that under the posterior mean estimator, the linear model with Markov sources or hidden Markov sources is decoupled into single-input AWGN channels with state information available at both encoder and decoder where the state distribution follows the left Perron-Frobenius eigenvector with unit Manhattan norm of the stochastic matrix of Markov chains. Numerical results show that the free energies and MSEs obtained via the replica method are closely approximate to their counterparts achieved by the Metropolis-Hastings algorithm or some well-known approximate message passing algorithms in the research literature.

This talk is part of the Data Science and Computational Statistics Seminar series.

This talk is included in these lists:

• Analysis Seminar
• Data Science and Computational Statistics Seminar
• School of Mathematics Events
• https://bham-ac-uk.zoom.us/j/95645638485?pwd=eDh3dlR3QjRlVWRHdExvaDBWdEo4UT09

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