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Unformatted text preview: HMMs can do Summary Scratch Correlated & Covariance
Correlation between two real random vectors X and Y
cor(X, Y ) = E [XY ] (5.42) Covariance between two real random vectors X and Y
cov(X, Y ) = E [(X − EX ) (Y − EY ) ] = E [XY ] − E [X ]E [Y ]
(5.43) Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 5  Jan 25th, 2013 page 560 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Correlated & Covariance
Correlation between two real random vectors X and Y
cor(X, Y ) = E [XY ] (5.42) Covariance between two real random vectors X and Y
cov(X, Y ) = E [(X − EX ) (Y − EY ) ] = E [XY ] − E [X ]E [Y ]
(5.43)
X and Y are uncorrelated if cov(X, Y ) = 0. Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 5  Jan 25th, 2013 page 560 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Correlated & Covariance
Correlation between two real random vectors X and Y
cor(X, Y ) = E [XY ] (5.42) Covariance between two real random vectors X and Y
cov(X, Y ) = E [(X − EX ) (Y − EY ) ] = E [XY ] − E [X ]E [Y ]
(5.43)
X and Y are uncorrelated if cov(X, Y ) = 0.
cov(X, Y ) = cor(X, Y ) if either the means are zero. Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 5  Jan 25th, 2013 page 560 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Correlated & Covariance
Correlation between two real random vectors X and Y
cor(X, Y ) = E [XY ] (5.42) Covariance between two real random vectors X and Y
cov(X, Y ) = E [(X − EX ) (Y − EY ) ] = E [XY ] − E [X ]E [Y ]
(5.43)
X and Y are uncorrelated if cov(X, Y ) = 0.
cov(X, Y ) = cor(X, Y ) if either the means are zero.
If X ⊥ Y then cov(X, Y ) = 0 but vice verse only if X, Y are jointly
⊥
Gaussian. Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 5  Jan 25th, 2013 page 560 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Correlated & Covariance
Correlation between two real random vectors X and Y
cor(X, Y ) = E [XY ] (5.42) Covariance between two real random vectors X and Y
cov(X, Y ) = E [(X − EX ) (Y − EY ) ] = E [XY ] − E [X ]E [Y ]
(5.43)
X and Y are uncorrelated if cov(X, Y ) = 0.
cov(X, Y ) = cor(X, Y ) if either the means are zero.
If X ⊥ Y then cov(X, Y ) = 0 but vice verse only if X, Y are jointly
⊥
Gaussian.
cov(X, Y ) = 0 is indication of lack of linear dependence, and hint
there might not be strong dependence at all.
Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 5  Jan 25th, 2013 page 560 (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). 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 currentl...
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This document was uploaded on 04/05/2014.
 Winter '14

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