Je bilmes ee596awinter 2013dgms lecture 5 jan 25th

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

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 5-60 (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 5-60 (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 5-60 (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 5-60 (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 5-60 (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). 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 currentl...
View Full Document

This document was uploaded on 04/05/2014.

Ask a homework question - tutors are online