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Unformatted text preview: 2013 page 440 (of 239) HMMs HMMs as GMs Other HMM queries What HMMs can do MPE Summ HMMs and message passing/LBP LBP messages on an HMM are straightforward, and again since an
HMM is a tree, we can use any message order that obeys the
messagepassing protocol. q1 q3 q4 q5 x1 Prof. Jeﬀ Bilmes q2 x2 x3 x4 x5 EE596A/Winter 2013/DGMs – Lecture 4  Jan 23rd, 2013 page 441 (of 239) HMMs HMMs as GMs Other HMM queries What HMMs can do MPE Summ HMM, and junction tree  rightstate 3clique
Can view as junction tree with cliques/separators. One solution:
node a separator, & a 3clique for a state & observation variable at
time t, & another state to the right (& a ﬁnal 2clique 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 4  Jan 23rd, 2013 Q TXT QT XT
page 442 (of 239) HMMs HMMs as GMs Other HMM queries What HMMs can do MPE Summ HMM, and junction tree  leftstate 3clique
Another solution has each node a separator, and a 3clique for a
state and observation variable at time t, and another state to the
left (and an initial 2clique 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 T1 ... X5 EE596A/Winter 2013/DGMs – Lecture 4  Jan 23rd, 2013 Q T1XTQ T QT XT
page 443 (of 239) HMMs HMMs as GMs Other HMM queries What HMMs can do MPE Summ HMM, and junction tree  two 2cliques
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 1Q 2 Q2 Q2 Q 1Q 2 Q2 Q 1Q 2 Q2 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 T1Q T Q TXT ... EE596A/Winter 2013/DGMs – Lecture 4  Jan 23rd, 2013 QT XT
page 444 (of 239) HMMs HMMs as GMs Other HMM queries What HMMs can do MPE Summ Discussion of the above three What are the advantages/disadvantages of the above (if any)? Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 4  Jan 23rd, 2013 page 445 (of 239) HMMs HMMs as GMs Other HMM queries What HMMs can do MPE Summ 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 4  Jan 23rd, 2013 page 445 (of 239) HMMs HMMs as GMs Other HMM queries What HMMs can do MPE Summ 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(xq ) with x
highdimensional realvalued Gaussian mixture). Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 4  Jan 23rd, 2013 page 445 (of 239) HMMs HMMs as GMs Other HMM queries What HMMs can do MPE Summ HMM, and junction tree Using either of these junction trees, we can deﬁne a forward and/or
backwards recursion, and we’ll again, in some cases, either recover
exactly the α, β recursions, or computations that are quite similar.
For example, Hugin message passing computes the backward
messages based on the forward (if we go right and then left), or
computes the forward messages based on the backwards (if we go
left and then right). Prof. Jeﬀ Bilmes EE596A/Winter 2013/DGMs – Lecture 4  Jan 23r...
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