隐马尔科夫模型 介绍 HMM python代码

#HMM Forward algorithm  

#input  Matrix A,B vector pi  

import  numpy as np  

A=np.array([[0.5,0.2,0.3],[0.3,0.5,0.2],[0.2,0.3,0.5]])
B=np.array([[0.5,0.5],[0.4,0.6],[0.7,0.3]])
O=np.array([0 ,1, 0])#T=3
#O=np.array([1 ,0, 1])#T=3
pi=np.array([0.2,0.4,0.4])  

N=3#N kind state
M=2#M kind of observation
T=3  

#initialize:  

Aerfa=np.zeros((3,3),np.float)
for i in range(N):
    Aerfa[0,i]=pi[i]*B[i,O[0]]  

#Recursion:
for t in range(T-1):
    for i in range(N):
        for j in range(N):
            Aerfa[t+1,i]+=Aerfa[t,j]*A[j,i]
        Aerfa[t+1,i]*=B[i,O[t+1]]  

#compute P(O|lamda) and termination
P=0
for i in range(N):
    P+=Aerfa[T-1,i]#begin with 0 so T-1  

print P  

#backward  

#initialize:
Beta=np.zeros((T,N),np.float)
print Beta
for i in range(N):
    Beta[T-1,i]=1  

#recursion:
for t in range(T-2,-1,-1):
    for i in range(N):
        for j in range(N):
            Beta[t,i]+=A[i,j]*B[j,O[t+1]]*Beta[t+1,j]  

#termination:
P_back=0
for i in range(N):
    P_back+=pi[i]*B[i,O[0]]*Beta[0,i]  

print P_back  

参考文献：统计学习方法，李航。

下一篇将介绍：问题3的具体解决方法为维比特算法（biterbi) algorithm

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