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实现用例为李航统计学习方法第177页例10.2

import numpy as np'''   用numpy实现隐马尔科夫模型的概率计算，即已知三元模型λ=（A,B,π）和观测序列O，计算在模型λ下观测序列O出现的概率P(O|λ)''''''一，定义模型的三要素''''''状态的集合'''def status_gener(status_len:int):    status_list = []    for status_index in range(status_len):        status_list.append(status_len)    return status_list'''观测的集合'''obs_list = np.array(["红", "白", "红"])'''时刻数'''T = 3'''初始取哪个盒子的概率分布'''init_prob_dist = np.array([0.2,0.4,0.4]) '''状态转移概率分布'''state_tran_prob = np.array([[0.5, 0.2, 0.3],                                [0.3, 0.5, 0.2],                                [0.2, 0.3, 0.5]])'''观测概率分布'''obs_prob_dist =  np.array([[0.5, 0.5],                           [0.4, 0.6],                           [0.7, 0.3]])'''二，利用前向算法计算''''''初值计算'''def init_value_calcu(obs_list, obs_prob_dist, init_prob_dist): # 3个形参分别为观测序列、观测概率分布、初始状态概率分布    if obs_list[0] == "红":        obs_prob_dist_col = obs_prob_dist[:,0]  # 取出每一时刻取出某个盒子后拿出红球的概率    elif obs_list[0] == "白":        obs_prob_dist_col = obs_prob_dist[:,1]  #  取出每一时刻取出某个盒子后拿出白球的概率    init_value = init_prob_dist * obs_prob_dist_col # 初始取哪个盒子的概率分布*每一时刻取出某个盒子后拿出白或红球的概率         return init_value'''递推计算'''def recur_calcu(obs_list, state_tran_prob):    # print(len(state_tran_prob))    init_state_value = init_value_calcu(obs_list, obs_prob_dist, init_prob_dist)    # print(init_state_value)    a = 0    time_num = len(state_tran_prob)    for obs_id in obs_list[1:]:        state = np.array([])        for time_num_id in range(time_num):            if a < 1:                prob_value = np.cumsum(init_state_value * state_tran_prob[:, time_num_id], axis=0)[-1]                state = np.append(state, prob_value)            else:                prob_value = np.cumsum(state_value * state_tran_prob[:, time_num_id], axis=0)[-1]                state = np.append(state, prob_value)        if obs_id == "红":            state_value = state * obs_prob_dist[:, 0]        elif obs_id == "白":            state_value = state * obs_prob_dist[:, 1]        a += 1    final_value = np.cumsum(state_value, axis=0)[-1]    return final_value  if __name__ == "__main__":    print(recur_calcu(obs_list, state_tran_prob))

Done！