隐马尔可夫模型学习小记——forward算法

#-*-coding:utf-8-*-
__author__ = ‘ZhangHe‘
def forward(N,M,A,B,P,observed):
    p = 0.0
    #观察到的状态数目
    LEN = len(observed)
    #中间概率LEN*M
    Q = [([0]*N) for i in range(LEN)]
    #第一个观察到的状态,状态的初始概率乘上隐藏状态到观察状态的条件概率。
    for j in range(N):
        Q[0][j] = P[j]*B[j][observation.index(observed[0])]
    #第一个之后的状态，首先从前一天的每个状态，转移到当前状态的概率求和，然后乘上隐藏状态到观察状态的条件概率。
    for i in range(1,LEN):
        for j in range(N):
            sum = 0.0
            for k in range(N):
                sum += Q[i-1][k]*A[k][j]
            Q[i][j] = sum * B[j][observation.index(observed[i])]
    for i in range(N):
        p += Q[LEN-1][i]
    return p
# 3 种隐藏层状态:sun cloud rain
hidden = []
hidden.append(‘sun‘)
hidden.append(‘cloud‘)
hidden.append(‘rain‘)
N = len(hidden)
# 4 种观察层状态:dry dryish damp soggy
observation = []
observation.append(‘dry‘)
observation.append(‘damp‘)
observation.append(‘soggy‘)
M = len(observation)
# 初始状态矩阵（1*N第一天是sun，cloud，rain的概率）
P = (0.3,0.3,0.4)
# 状态转移矩阵A（N*N 隐藏层状态之间互相转变的概率）
A=((0.2,0.3,0.5),(0.1,0.5,0.4),(0.6,0.1,0.3))
# 混淆矩阵B（N*M 隐藏层状态对应的观察层状态的概率）
B=((0.1,0.5,0.4),(0.2,0.4,0.4),(0.3,0.6,0.1))
#假设观察到一组序列为observed，输出HMM模型（N，M，A，B，P）产生观察序列observed的概率
observed = [‘dry‘]
print forward(N,M,A,B,P,observed)
observed = [‘damp‘]
print forward(N,M,A,B,P,observed)
observed = [‘dry‘,‘damp‘]
print forward(N,M,A,B,P,observed)
observed = [‘dry‘,‘damp‘,‘soggy‘]
print forward(N,M,A,B,P,observed)