Unformatted text preview: e., for each state, the
observation distribution is a single multivariate Gaussian). Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 4  Jan 23rd, 2013 page 465 (of 239) HMMs HMMs as GMs Other HMM queries What HMMs can do MPE Summ 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 . Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 4  Jan 23rd, 2013 page 465 (of 239) HMMs HMMs as GMs Other HMM queries What HMMs can do MPE Summ 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 4  Jan 23rd, 2013 page 465 (of 239) HMMs HMMs as GMs Other HMM queries What HMMs can do MPE Summ 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 4  Jan 23rd, 2013 page 465 (of 239) HMMs HMMs as GMs Other HMM queries What HMMs can do MPE Summ 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 4  Jan 23rd, 2013 page 465 (of 239) HMMs HMMs as GMs Other HMM queries What HMMs can do MPE Summ 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 p(Xt = xQt = i)πi dx (4.60)
i Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 4  Jan 23rd, 2013 page 465 (of 239) HMMs HMMs as GMs Other HMM queries What HMMs can do MPE Summ 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 ]
xp(Xt = x)dx = EXt = x p(Xt = xQt = i)πi dx (4.60)
i E [Xt Qt = i]πi...
View
Full
Document
 Winter '14

Click to edit the document details