Je bilmes q2 x2 x3 x1 x2 x3 x4 x5 ee596awinter

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Unformatted text preview: 2 x3 x4 q1 q2 q3 q1 q2 q3 q4 q5 x1 x2 x3 x1 x2 x3 x4 x5 Involves re-sending messages (red). Each step requires O(T ) additional messages, in total O(T 2 ) computation. Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-36 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Edge Marginals Need p(qt , qt+1 |x1:T ) for learning tasks Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-37 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Edge Marginals Need p(qt , qt+1 |x1:T ) for learning tasks Easy to obtain with both the α and β quantities, since: p(qt−1 , qt |x1:T ) = Prof. Jeff Bilmes p(qt−1 , qt , x1:T ) p(x1:T ) EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 (5.5) page 5-37 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Edge Marginals Need p(qt , qt+1 |x1:T ) for learning tasks Easy to obtain with both the α and β quantities, since: p(qt−1 , qt |x1:T ) = p(qt−1 , qt , x1:T ) p(x1:T ) (5.5) and (5.6) p(qt−1 , qt , x1:T ) Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-37 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Edge Marginals Need p(qt , qt+1 |x1:T ) for learning tasks Easy to obtain with both the α and β quantities, since: p(qt−1 , qt |x1:T ) = p(qt−1 , qt , x1:T ) p(x1:T ) (5.5) and (5.6) p(qt−1 , qt , x1:T ) = p(xt |qt )p(qt−1 , qt , x1:t−1 , xt+1:T ) Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 (5.7) page 5-37 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Edge Marginals Need p(qt , qt+1 |x1:T ) for learning tasks Easy to obtain with both the α and β quantities, since: p(qt−1 , qt |x1:T ) = p(qt−1 , qt , x1:T ) p(x1:T ) (5.5) and (5.6) p(qt−1 , qt , x1:T ) = p(xt |qt )p(qt−1 , qt , x1:t−1 , xt+1:T ) (5.7) = p(xt |qt )p(xt+1:T |qt )p(qt , qt−1 , x1:t−1 ) Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 (5.8) page 5-37 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Edge Marginals Need p(qt , qt+1 |x1:T ) for learning tasks Easy to obtain with both the α and β quantities, since: p(qt−1 , qt |x1:T ) = p(qt−1 , qt , x1:T ) p(x1:T ) (5.5) and (5.6) p(qt−1 , qt , x1:T ) = p(xt |qt )p(qt−1 , qt , x1:t−1 , xt+1:T ) (5.7) = p(xt |qt )βt (qt )p(qt |qt−1 , x1:t−1 )p(qt−1 , x1:t−1 ) (5.9) = p(xt |qt )p(xt+1:T |qt )p(qt , qt−1 , x1:t−1 ) Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 (5.8) page 5-37 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Edge Marginals Need p(qt , qt+1 |x1:T ) for learning tasks Easy to obtain with both the α and β quantities, since: p(qt−1 , qt |x1:T ) = p(qt−1 , qt , x1:T ) p(x1:T ) (5.5) and (5.6) p(qt−1 , qt , x1:T ) = p(xt |qt )p(qt−1 , qt , x1:t−1 , xt+1:T...
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This document was uploaded on 04/05/2014.

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