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Unformatted text preview: 2013/DGMs – Lecture 5  Jan 25th, 2013 page 546 (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 547 (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 548 (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 548 (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 548 (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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 Winter '14

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