# Consider the way in which hmms are often used long

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Unformatted text preview: re 4 - Jan 23rd, 2013 page 4-62 (of 239) HMMs HMMs as GMs Other HMM queries What HMMs can do MPE Summ 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 4 - Jan 23rd, 2013 page 4-62 (of 239) HMMs HMMs as GMs Other HMM queries What HMMs can do MPE Summ 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 4 - Jan 23rd, 2013 page 4-62 (of 239) HMMs HMMs as GMs Other HMM queries What HMMs can do MPE Summ 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 Chains with upper-triangular matrices Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 4 - Jan 23rd, 2013 page 4-62 (of 239) HMMs HMMs as GMs Other HMM queries What HMMs can do MPE Summ 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 Chains with upper-triangular matrices Chains with strictly left-to-right transitions. Ex: speech recognition Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 4 - Jan 23rd, 2013 page 4-62 (of 239) HMMs HMMs as GMs Other HMM queries What HMMs can do MPE Summ 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 Chains with upper-triangular matrices Chains with strictly left-to-right transitions. Ex: speech recognition Hence, in only rare cases, when HMMs are used, are they stationary stochastic processes. Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 4 - Jan 23rd, 2013 page 4-62 (of 239) HMMs HMMs as GMs Other HMM queries What HMMs can do MPE Summ Gaussian Mixture HMM One of the most widely used HMMs in practice is one where the observation distributions are Gaussian mixtures, where p(x|q ) = p(x|q, c)p(c|q ) (4.55) N (x|µqm , Σqm ) cmq (4.56) c = m and where N (x|µ, Σ) = Prof. Jeﬀ Bilmes 1 1 exp − (x − µ) Σ−1 (x − µ) d/2 2 |2π Σ| EE596A/Winter 2013/DGMs – Lecture 4 - Jan 23rd, 2013 (4.57) page 4-63 (of 239) HMMs HMMs as GMs Other HMM queries What HMMs can do MPE Summ Gaussian Mixture HMM One of the most widely used HMMs in practice is one where the observation distributions are Gaussian mixtures, where p(x|q ) = p(x|q, c)p(c|q ) (4.55) N (x|µqm , Σqm ) cmq (4.56) c = m and where 1 1 exp...
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## This document was uploaded on 04/05/2014.

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