Je bilmes ee596awinter 2013dgms lecture 5 jan 25th

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Unformatted text preview: MPE Sampling What HMMs can do Summary Scratch HMMs and stationarity (cont.) . . . continuing = q1 p(Qt1 +h = q1 )p(Xt1 +h = x1 |Qt1 +h = q1 ) (5.36) n q2:T i=2 = q1 p(Xti +h = xi |Qti +h = qi )p(Qti +h = qi |Qti−1 +h = qi−1 ) p(Qt1 +h = q1 )p(Xt1 +h = x1 |Qt1 +h = q1 ) (5.37) n q2:T i=2 = q1 Prof. Jeff Bilmes p(Xti = xi |Qti = qi )p(Qti = qi |Qti−1 = qi−1 ) p(Qt1 +h = q1 )p(Xt1 = x1 |Qt1 = q1 )f (x2:n , q1 ) EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 (5.38) page 5-57 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch HMMs and stationarity (cont.) . . . continuing = q1 p(Qt1 +h = q1 )p(Xt1 +h = x1 |Qt1 +h = q1 ) (5.36) n q2:T i=2 = q1 p(Xti +h = xi |Qti +h = qi )p(Qti +h = qi |Qti−1 +h = qi−1 ) p(Qt1 +h = q1 )p(Xt1 +h = x1 |Qt1 +h = q1 ) (5.37) n q2:T i=2 = q1 p(Xti = xi |Qti = qi )p(Qti = qi |Qti−1 = qi−1 ) p(Qt1 +h = q1 )p(Xt1 = x1 |Qt1 = q1 )f (x2:n , q1 ) (5.38) where f (x2:n , q1 ) is a function that is independent of the variable h. Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-57 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch HMMs and stationarity (cont.) . . . continuing = q1 p(Qt1 +h = q1 )p(Xt1 +h = x1 |Qt1 +h = q1 ) (5.36) n q2:T i=2 = q1 p(Xti +h = xi |Qti +h = qi )p(Qti +h = qi |Qti−1 +h = qi−1 ) p(Qt1 +h = q1 )p(Xt1 +h = x1 |Qt1 +h = q1 ) (5.37) n q2:T i=2 = q1 p(Xti = xi |Qti = qi )p(Qti = qi |Qti−1 = qi−1 ) p(Qt1 +h = q1 )p(Xt1 = x1 |Qt1 = q1 )f (x2:n , q1 ) (5.38) where f (x2:n , q1 ) is a function that is independent of the variable h. For HMM stationarity to hold, it is required that p(Qt1 +h = q1 ) = p(Qt1 = q1 ) for all h. Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-57 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch HMMs stationarity depends on MC Therefore, the HMM’s stationarity condition is entirely determined by the stationarity condition of the underlying hidden Markov chain. Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-58 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch HMMs stationarity depends on MC Therefore, the HMM’s stationarity condition is entirely determined by the stationarity condition of the underlying hidden Markov chain. Consider the way in which HMMs are often used: Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-58 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch HMMs stationarity depends on MC Therefore, the HMM’s stationarity condition is entirely determined by the stationarity condition of the underlying hidden Markov chain. Consider the way in which HMMs are often used: Long chains Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-58 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch HMMs stationarity depends on MC Therefore, the HMM’s stationarity condition is entirely determined by the stationarity condition of the underlying hidden Markov chain. Consider the way in which HMMs are often used: Long chains Chains with cycle transition matrices Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 -...
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