# E for each state the observation distribution is a

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: y stationary, with stationary distribution π . Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-61 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Correlation over time of simple HMM Consider single-component Gaussian HMM (i.e., for each state, the observation distribution is a single multivariate Gaussian). Assume that the Markov chain is currently stationary, with stationary distribution π . What about cov(Xt , Xt+h )? Is it zero? How does it decay? Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-61 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Correlation over time of simple HMM Consider single-component Gaussian HMM (i.e., for each state, the observation distribution is a single multivariate Gaussian). Assume that the Markov chain is currently stationary, with stationary distribution π . What about cov(Xt , Xt+h )? Is it zero? How does it decay? Computing E [Xt ] EXt Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-61 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Correlation over time of simple HMM Consider single-component Gaussian HMM (i.e., for each state, the observation distribution is a single multivariate Gaussian). Assume that the Markov chain is currently stationary, with stationary distribution π . What about cov(Xt , Xt+h )? Is it zero? How does it decay? Computing E [Xt ] EXt = Prof. Jeﬀ Bilmes xp(Xt = x)dx EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-61 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Correlation over time of simple HMM Consider single-component Gaussian HMM (i.e., for each state, the observation distribution is a single multivariate Gaussian). Assume that the Markov chain is currently stationary, with stationary distribution π . What about cov(Xt , Xt+h )? Is it zero? How does it decay? Computing E [Xt ] EXt = xp(Xt = x)dx = x i Prof. Jeﬀ Bilmes p(Xt = x|Qt = i)πi dx (5.44) EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-61 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Correlation over time of simple HMM Consider single-component Gaussian HMM (i.e., for each state, the observation distribution is a single multivariate Gaussian). Assume that the Markov chain is currently stationary, with stationary distribution π . What about cov(Xt , Xt+h )? Is it zero? How does it decay? Computing E [Xt ] EXt = xp(Xt = x)dx = x i = i Prof. Jeﬀ Bilmes E [Xt |Qt = i]πi = p(Xt = x|Qt = i)πi dx (5.44) (5.45) µi π i i EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-61 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Correlation over time of simple HMM Consider single-component Gaussian HMM (i.e., for each state, the observation distribution is a single multivariate Gaussian). Assume that the Markov chain is currently stationary, with stationary...
View Full Document

## This document was uploaded on 04/05/2014.

Ask a homework question - tutors are online