We have for all t dpxt xt ph xt xt pxt xt px1t

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Unformatted text preview: x<t ) qt ph (xt |qt )ph (qt |x<t ) (5.76) p(x1:t ) log p(xt |x<t ) ph (xt |qx<t ) (5.77) p(x1:t ) log = p(xt |x<t ) p(xt |x<t ) (5.78) x1:t = x1:t (5.79) =0 Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-80 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Cont. Proof: Suff conds for HMMs Generative Accuracy ... cont. It then follows, using the above equation, that: 0= t D(p(Xt |X<t )||ph (Xt |X<t )) = p(x1:t ) log t x1:t p(x1:T ) log = x1:T p(xt |x<t ) = ph (xt |x<t ) (5.80) p(x1:T ) log t t p(xt |x<t ) = t ph (xt |x<t ) x x1:T p(x1:T ) log 1:T p(xt |x<t ) (5.81) ph (xt |x<t ) p(x1:T ) ph (x1:T ) (5.82) = D(p(X1:T )||ph (X1:T )) (5.83) Strong conditions H (Qt |X<t ) = 0, not likely to happen in practice. Is this really what we need for an HMM, generative accuracy? We’ll address this again soon. Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-81 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Mealy vs. Moore Machines Mealy vs. Moore finite state automata: Input Symbol State Logic Input Symbol Output Symbol State Memory Prof. Jeff Bilmes Output Symbol Logic EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 Logic Memory page 5-82 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Mealy vs. Moore Machines Mealy vs. Moore finite state automata: Input Symbol State Logic Input Symbol Output Symbol State Memory Output Symbol Logic Logic Memory Moore machine has only one possible output for each state — the output is a function only of the current state. Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-82 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Mealy vs. Moore Machines Mealy vs. Moore finite state automata: Input Symbol State Logic Input Symbol Output Symbol State Memory Output Symbol Logic Logic Memory Moore machine has only one possible output for each state — the output is a function only of the current state. Mealy machine has only one possible output for each state-input pair — given current state, the input determines both the next state and the current output. Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan 25th, 2013 page 5-82 (of 232) HMMs Trellis Other HMM queries MPE Sampling What HMMs can do Summary Scratch Mealy vs. Moore Machines Mealy vs. Moore finite state automata: Input Symbol State Logic Input Symbol Output Symbol State Memory Output Symbol Logic Logic Memory Moore machine has only one possible output for each state — the output is a function only of the current state. Mealy machine has only one possible output for each state-input pair — given current state, the input determines both the next state and the current output. Mealy machine: given a current state, and a next state (determined by input), there is an output. Prof. Jeff Bilmes EE596A/Winter 2013/DGMs – Lecture 5 - Jan...
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