This preview shows page 1. Sign up to view the full content.
Unformatted text preview: y stationary, with
stationary distribution π . Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 5  Jan 25th, 2013 page 561 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Correlation over time of simple HMM
Consider singlecomponent 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 561 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Correlation over time of simple HMM
Consider singlecomponent 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 561 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Correlation over time of simple HMM
Consider singlecomponent 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 561 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Correlation over time of simple HMM
Consider singlecomponent 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 = xQt = i)πi dx (5.44) EE596A/Winter 2013/DGMs – Lecture 5  Jan 25th, 2013 page 561 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Correlation over time of simple HMM
Consider singlecomponent 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 = xQt = i)πi dx (5.44)
(5.45) µi π i
i EE596A/Winter 2013/DGMs – Lecture 5  Jan 25th, 2013 page 561 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Correlation over time of simple HMM
Consider singlecomponent 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.
 Winter '14

Click to edit the document details