习题10.3

习题10.3

  在习题10.1中，试用维特比算法求最优路径。

Q = [1, 2, 3]
V = ['红', '白']
A = [[0.5, 0.2, 0.3], [0.3, 0.5, 0.2], [0.2, 0.3, 0.5]]
B = [[0.5, 0.5], [0.4, 0.6], [0.7, 0.3]]
O = ['红', '白', '红', '白']
PI = [[0.2, 0.4, 0.4]]
HMM = HiddenMarkov()
HMM.viterbi(Q, V, A, B, O, PI)

delta1(1) = pi1 b1(o1) = 0.20 0.50 = 0.10
psis1(1) = 0
delta1(2) = pi2 b2(o1) = 0.40 0.40 = 0.16
psis1(2) = 0
delta1(3) = pi3 b3(o1) = 0.40 0.70 = 0.28
psis1(3) = 0
delta2(1) = max[delta1(j)aj1]b1(o2) = 0.06 0.50 = 0.02800
psis2(1) = argmax[delta1(j)aj1] = 2
delta2(2) = max[delta1(j)aj2]b2(o2) = 0.08 0.60 = 0.05040
psis2(2) = argmax[delta1(j)aj2] = 2
delta2(3) = max[delta1(j)aj3]b3(o2) = 0.14 0.30 = 0.04200
psis2(3) = argmax[delta1(j)aj3] = 2
delta3(1) = max[delta2(j)aj1]b1(o3) = 0.02 0.50 = 0.00756
psis3(1) = argmax[delta2(j)aj1] = 1
delta3(2) = max[delta2(j)aj2]b2(o3) = 0.03 0.40 = 0.01008
psis3(2) = argmax[delta2(j)aj2] = 1
delta3(3) = max[delta2(j)aj3]b3(o3) = 0.02 0.70 = 0.01470
psis3(3) = argmax[delta2(j)aj3] = 2
delta4(1) = max[delta3(j)aj1]b1(o4) = 0.00 0.50 = 0.00189
psis4(1) = argmax[delta3(j)aj1] = 0
delta4(2) = max[delta3(j)aj2]b2(o4) = 0.01 0.60 = 0.00302
psis4(2) = argmax[delta3(j)aj2] = 1
delta4(3) = max[delta3(j)aj3]b3(o4) = 0.01 * 0.30 = 0.00220
psis4(3) = argmax[delta3(j)aj3] = 2
i4 = argmax[deltaT(i)] = 2
i3 = psis4(i4) = 2
i2 = psis3(i3) = 2
i1 = psis2(i2) = 3
最优路径是： 3->2->2->2