21 m rr t 1 522 and the forward equation for storing

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Unformatted text preview: 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-46 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch MPE on the HMM Trellis The trellis is also useful to view MPE/Viterbi, and is the reason it is sometimes called “Viterbi path.” p(q2 |q2 ) bq1 (x1 ) q1 p(q q 1) 2| bq1 (x2 ) q4 p( q 1) 2| p(q 1) q 2) 3| bq2 (x4 ) |q p(q p(q2 |q2 ) bq1 (x3 ) p(q1 |q1 ) 2 bq3 (x4 ) p(q bq2 (x3 ) |q 1) 4 |q 1) p(q q 2) 3| p(q p(q2 |q2 ) p(q1 |q1 ) 1 q 3) 4| |q 2) q4 p( |q 1) p(q bq2 (x2 ) q3 q2 q 2) 3| p(q p(q3 |q3 ) p( p( p(q q3 bq2 (x1 ) bq3 (x3 ) 2) q 3) 4| p(q p(q3 |q3 ) 4 |q 1) p(q3 |q3 ) p(q4 |q4 ) |q 2) bq3 (x2 ) bq4 (x4 ) 4 |q 1) q 3) 4| q4 q3 Prof. Jeff Bilmes p(q p(q4 |q4 ) |q bq3 (x1 ) bq4 (x3 ) q3 p(q4 |q4 ) p( q4 bq4 (x2 ) p( bq4 (x1 ) q 1) 2| p(q bq1 (x4 ) p(q1 |q1 ) 3 EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 4 page 5-47 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Atypical explanations E.g., the 1st best might not be a good reflection of the typical states that explain the observation. Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-48 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Atypical explanations E.g., the 1st best might not be a good reflection of the typical states that explain the observation. Simple example of “typicality”, flip a P (H ) = 0.9 = 1 − P (T ) biased coin 100 times. Most probable sequence is 100 heads. A typical sequence will be one that has about 90 heads and 10 tails. Much more likely we’ll get one of the 90,10 sequences than the all heads sequence. Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-48 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Atypical explanations E.g., the 1st best might not be a good reflection of the typical states that explain the observation. Simple example of “typicality”, flip a P (H ) = 0.9 = 1 − P (T ) biased coin 100 times. Most probable sequence is 100 heads. A typical sequence will be one that has about 90 heads and 10 tails. Much more likely we’ll get one of the 90,10 sequences than the all heads sequence. Viterbi path is potentially giving us an atypical sequence. Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-48 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Atypical explanations E.g., the 1st best might not be a good reflection of the typical states that explain the observation. Simple example of “typicality”, flip a P (H ) = 0.9 = 1 − P (T ) biased coin 100 times. Most probable sequence is 100 heads. A typical sequence will be one that has about 90 heads and 10 tails. Much more likely we’ll get one of the 90,10 sequences than the all heads sequence. Viterbi path is potentially giving us an atypical sequence. Two solutions: sample from the posterior distribution p(q1:T |x1:T ),...
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