E for each state the observation distribution is a

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

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