Eewashington edubilmesclassesee512afall2011 see

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Unformatted text preview: = ψU U ide ψU U \S alize margin φ∗∗ S φ∗ S φS =1 ∗∗ φS = ∗ ψW ∗∗ ψW W\ S margin alize ly multip py co multip multiply ∗ ψW ∗ ψW = φ∗ S ψW φS multiply divid e S ψW W For more details, see 2011 lectures http://j.ee.washington. edu/~bilmes/classes/ee512a_fall_2011/ (see lectures 14 and 15, in lecture 14 the section header entitled “Inference on JTs) and also see doc.pdf (described from pages 180—184) Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-14 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch HMM, and junction tree - right-state 3-clique Can view as junction tree with cliques/separators. One solution: node a separator, & a 3-clique for a state & observation variable at time t, & another state to the right (& a final 2-clique at the end). Q1 Q2 Q3 Q4 X1 X2 X3 X4 X5 Q 1X1Q 2 Q2 Q 2X2Q 3 Q2 Q3 Q4 Q5 X1 X2 X3 X4 QT XT ... Q3 Q1 Prof. Jeff Bilmes ... Q5 QT ... X5 EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 Q TXT QT XT page 5-15 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch HMM, and junction tree - left-state 3-clique Another solution has each node a separator, and a 3-clique for a state and observation variable at time t, and another state to the left (and an initial 2-clique at the beginning). Q1 Q2 Q3 Q4 X1 X2 X3 X4 X5 Q 1X1 Q 1X2Q 2 Q1 Q 2X3Q 3 Q2 Q1 Q2 Q3 Q4 Q5 X1 Prof. Jeff Bilmes ... Q5 X2 X3 X4 QT XT ... Q T-1 ... X5 EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 Q T-1XTQ T QT XT page 5-16 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch HMM, and junction tree - two 2-cliques Yet another solution has cliques for successive states and for state/observation pair at each t. Q1 Q2 Q3 Q4 Q5 X1 X2 X3 X4 X5 Q 1Q 2 Q 2Q 3 Q2 Q3 Q 3Q 4 Q4 Q 4Q 5 Q5 Q 1X1 Q 3X3 Q 4X4 Q2 Q3 Q4 Q5 X1 X2 X3 X4 ... Q 5X5 Q1 Prof. Jeff Bilmes Q 2X2 ... X5 QT XT Q T-1Q T Q TXT ... EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 QT XT page 5-17 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Discussion of the above three What are the advantages/disadvantages of the above (if any)? Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-18 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Discussion of the above three What are the advantages/disadvantages of the above (if any)? State space is the same. Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-18 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Discussion of the above three What are the advantages/disadvantages of the above (if any)? State space is the same. What are implications of summing over states observations if observation distribution is complex (e.g., if p(x|q ) with x high-dimensional real-valued Gaussian mixture). Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-18 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch HMM, and junction tree Using either of these junction trees, we can define a forward and/or backwards re...
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