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Unformatted text preview: “(” “)” EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-83 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Mealy vs. Moore HMMs Two ways to show the pronunciation model for the word “and” ε æ ε ε ε n ε ε d ε n:ε ε q0 æ:ε :ε q1 ε n:ε q2 d:ε q4 page 5-84 (of 232) n:ε :ε Left: Moore machine, Right: Mealy machine. Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Mealy vs. Moore HMMs Two ways to show the pronunciation model for the word “and” ε æ ε ε ε n ε ε d ε n:ε ε q0 æ:ε :ε q1 ε n:ε q2 d:ε q4 n:ε :ε Left: Moore machine, Right: Mealy machine. The output label on each Mealy arcs is shown as input:output and means “null” Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-84 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Mealy vs. Moore HMMs Graphical model for Moore-HMM: as we have seen it (Qt is a parent of Xt for each t. y1 y2 y3 y4 y5 y1 y2 y3 y4 y5 x1 x2 x3 x4 x5 x1 x2 x3 x4 x5 Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-85 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Mealy vs. Moore HMMs Graphical model for Moore-HMM: as we have seen it (Qt is a parent of Xt for each t. y1 y2 y3 y4 y5 y1 y2 y3 y4 y5 x1 x2 x3 x4 x5 x1 x2 x3 x4 x5 Graphical model for Mealy-HMM: Xt has two parents, either (Qt−1 , Qt ) or (Qt , Qt+1 ). y1 y2 y3 y4 y5 y1 y2 y3 y4 y5 x1 x2 x3 x4 x5 x1 x2 x3 x4 x5 Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-85 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Mealy vs. Moore HMMs Mealy and Moore HMMs are equivalent in that they correspond to the same class of probability distributions. Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-86 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Mealy vs. Moore HMMs Mealy and Moore HMMs are equivalent in that they correspond to the same class of probability distributions. Mealy → Moore conversion: cluster adjacent variables in the graphical model. Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-86 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Mealy vs. Moore HMMs Mealy and Moore HMMs are equivalent in that they correspond to the same class of probability distributions. Mealy → Moore conversion: cluster adjacent variables in the graphical model. More → Mealy conversion: Use a separate arc for each possible output with observation randomness applied to the arc. Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-86 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Mealy vs. Moore HMMs Mealy and Moore HMMs are equivalent in that they correspond to the same class of probability distributions. Mealy → Moore conversion: cluster adjacent variables in the graphical model. More → Mealy conversion: Use a separate arc for each possible output with observation randomness applied to the arc. It is sometimes more efficient, in terms of number of states, to specify a language in terms of a Mealy HMM (see parenthesis matching example in the readings). Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-86 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Sources for Today’s Lecture Probability and Random Processes, Grimmett/Stirzaker, 3rd Ed, 2001. “doc.pdf” sections 8.1 - 8.3 Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-87 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Scratch Paper Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-88 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Scratch Paper Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-89 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Scratch Paper Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-90 (of 232)...
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