隐马尔可夫模型（向前算法和维特比算法演示）----python

样例：

观测序列：【A,B,A,B】 （代码中用1，2，1，2代表）

# 隐马尔可夫模型代码演示
def main():
    pos = [[0.4, 0.6, 0], [0, 0.8, 0.2],[0, 0, 1]]  # 状态转化

    A = [0.7,0.3]
    B = [0.4,0.6]
    C = [0.8,0.2]
    gcgl = [A,B,C] # 观测概率
    guance = [1,2,1,2] # 观测序列
    N = len(pos)  # 状态数
    len_g = len(guance) # 观测序列长度
    dp = [[0 for i in range(len_g)]for i in range(N)]
    dp[0][0] = A[0]
    dp[1][0] = 0
    for j in range(1,len_g):
        for i in range(N):
            for k in range(N):      # 上一时刻的状态
                dp[i][j] += dp[k][j - 1] * pos[k][i] * gcgl[i][guance[j] - 1]
    ans = 0
    for i in range(N):
        ans += dp[i][len_g - 1]
        print(dp[i])
    print("观测序列出现概率：" , ans)

    # 维特比算法
    fai = [[0 for i in range(len_g)]for i in range(N)]     # 上一最佳状态存储
    dpv = [[0 for i in range(len_g)]for i in range(N)]
    dpv[0][0] = A[0]
    dpv[1][0] = 0
    fai[0][0] = -1
    for j in range(1,len_g):
        for i in range(N):
            flag = 0
            max1 = 0
            for k in range(N):      # 上一时刻的状态
                if max1 < dpv[k][j - 1] * pos[k][i] * gcgl[i][guance[j] - 1]:
                    max1 = dpv[k][j - 1] * pos[k][i] * gcgl[i][guance[j] - 1]
                    flag = k
            dpv[i][j] = max1
            fai[i][j] = flag    # 上一最佳来源

    maxpos = 0
    maxpoint = 0
    for i in range(N):
        if maxpoint < dpv[i][len_g - 1]:
            maxpos = i
            maxpoint = dpv[i][len_g - 1]

    i = maxpos
    j = len_g - 1
    best = []
    best.append(i)
    while fai[i][j] != -1:
        best.append(fai[i][j])
        i = fai[i][j]
        j -= 1
    best.reverse()
    for i in range(len(best)):
        best[i] += 1
    print("最佳出现状态序列：",best)



if __name__ == '__main__':
    main()

运行结果：