HMM Basic problem 1 1.Initialization a1(1)=7D(二1|x) 2. Induction: Repeat for t=1:T ()=∑a(p(x X 3. Termination :水7 (O|A)=∑a() of the computation of a ()in terms of a ttice of observations t, and states j HMM Basic Problem 2 Viterbi Decoding: Same principle as forward algorithm with an extra term iNitialization tErmination 6()=xp(=1|x) P=maxi(i) 1≤isX v1()=0 arg ma 6(O)] 2)Induction 4)Back tracking 6(0)=max-(1p(x1|x,a)p(|x) x=v1+1(x+1) v, (i)=arg max8_()p(x; Ixj, aHMM Basic Problem 1 )|()( 1 i 1 i α i = π )|(),|()()( 1 || 1 1 it X j t t tij i j x + = + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ α = ∑α ∑= = || 1 )()|( X i t αλ i 3) Termination 4) Back tracking HMM Basic Problem 2 ● algorithm, with an extra term 1) Initialization 2) Induction 0)( )|()( 1 1 1 = = i i i i ψ δ π [ ] )( [ ),|()( ] )|(),|()(max)( 1 ||1 1 ||1 t jji Xj t t itjji Xj t i j i j − − = = ψ δ δ δ [ ] [ ])( )(max ||1 * ||1 x i P i T T T δ δ ∗ = = )( * 11 * = ttt ++ ψ xx 1. Initialization 2. Induction: Repeat for t=1:T 3. Termination: x z p z p a x x p O p Viterbi Decoding: Same principle as forward x z p max arg a x x p x z p a x x p ≤≤ ≤≤ max arg X i X i ≤≤ ≤≤ Implementation of the computation of (j) in terms of a lattice of observations t, and states j. Observation, t 1 1 2 State 2 3 T N at