University of Birmingham > Talks@bham > Data Science and Computational Statistics Seminar > Replica Analysis of the Linear Model with Markov or Hidden Markov Signal Priors

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

Add to your list(s) Download to your calendar using vCal

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.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

Talks@bham, University of Birmingham. Contact Us | Help and Documentation | Privacy and Publicity.
talks@bham is based on talks.cam from the University of Cambridge.