HMM原理介绍 示例 python代码实现

下面使用李航博士书上的例子说明：



























对步骤（3）进行推导



下面给出简单的例子和前向算法的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