Q1 prof je bilmes q2 q3 ee596awinter 2013dgms lecture

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Unformatted text preview: ransition Matrix Consider the following four-state state-transition diagram for a 1st order Markov chain. q1 Prof. Jeff Bilmes q2 q3 EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 q4 page 5-25 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch HMM Markov Transition Matrix Consider the following four-state state-transition diagram for a 1st order Markov chain. q1 q2 q3 q4 when seen as an HMM, this shows only the Markov chain but not the observation distributions. Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-25 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch HMM Markov Transition Matrix Consider the following four-state state-transition diagram for a 1st order Markov chain. q1 q2 q3 q4 when seen as an HMM, this shows only the Markov chain but not the observation distributions. Also, this doesn’t show the “data flow” of the computation of the α-recursion. Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-25 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch HMM Markov Transition Matrix Consider the following four-state state-transition diagram for a 1st order Markov chain. q1 q2 q3 q4 when seen as an HMM, this shows only the Markov chain but not the observation distributions. Also, this doesn’t show the “data flow” of the computation of the α-recursion. It is possible to use yet another graph (a trellis graph) that can show this. Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-25 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch HMM Trellis/Lattice/Grid q4 ... q3 q2 q1 q2 q3 q4 q 1 1 2 3 4 T On the left we have the trellis (4 states and T time frames). Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-26 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch HMM Trellis/Lattice/Grid q4 ... q3 q2 q1 q2 q3 q4 q 1 1 2 3 4 T On the left we have the trellis (4 states and T time frames). on the right we see the state transition diagrams. Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-26 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch HMM Trellis/Lattice/Grid q4 ... q3 q2 q1 q2 q3 q4 q 1 1 2 3 4 T On the left we have the trellis (4 states and T time frames). on the right we see the state transition diagrams. Both are graphs (but display very different information), the left graph shows the allowable state transitions at each t ∈ {1, 2, . . . , T }. Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-26 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch HMM Trellis/Lattice/Grid q4 ... q3 q2 q1 q2 q3 q4 q 1 1 2 3 4 T On the left we have the trellis (4 states and T time frames). on the right we see the st...
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