牛刀小試利使用Python利用維特比算法解決經典隱馬爾科夫鏈問題

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以下是解決李航的《統計學習方法》中例10.2（盒子和綵球問題）的Python代碼實現。Csdn對Word文檔編輯的矩陣顯示支持得不太好，算法思路請通過以下鏈接下載查看。

# -*- coding: UTF-8 -*-
"""
   維特比算法實現：解決盒子與球顏色問題
   KaiwiiHo
"""
import numpy as np

if __name__ == '__main__':
    """
    狀態（盒子序號）Q：1,2,3
    觀察值（球的顏色）V：紅，白
    訓練集產生的模型參數（A,B,π）
    """
    stateTransition = np.array([0.5,0.2,0.3,0.3,0.5,0.2,0.2,0.3,0.5]).reshape(3,3)#狀態間轉移概率矩陣A
    stateToObservationTransition = np.array([0.5,0.5,0.4,0.6,0.7,0.3]).reshape(3,2)#狀態轉移觀察概率矩陣B
    startState = np.array([0.2,0.4,0.4])#狀態初始化概率π
    """
       觀察結果O:"red","white","red",對應序號爲：0,1,0
    """
    observation = np.array([0,1,0])
    """
       迭代計算
    """
    resMaxProbability = []#記錄在當前時刻出現當前觀察值時，出現某狀態的最大概率。
    resMaxState = []#爲出現某狀態的最大概率時，上一時刻的狀態值。
    obs_index = 0
    for obs in observation:
        if obs_index == 0:
            #初始化狀態
            curProbability = startState*stateToObservationTransition[:,observation[obs_index]]
            resMaxProbability.append(curProbability)
        else:
            previewMaxProbability = resMaxProbability[obs_index-1]
            curProbability = []
            curState = []
            for item in range(len(stateTransition)):
                temp = stateTransition[:,item]*previewMaxProbability
                curProbability.append(np.max(temp))
                curState.append(np.argmax(temp))
            curProbability = curProbability*stateToObservationTransition[:,observation[obs_index]]
            resMaxProbability.append(curProbability)
            resMaxState.append(curState)
        obs_index = obs_index + 1
    print(resMaxProbability)
    print("=================")
    print(resMaxState)
    """
    回溯
    """
    resState = []#推理所得的狀態序列
    resMaxProbabilityLen = len(resMaxProbability)
    lastMaxState = np.argmax(resMaxProbability[resMaxProbabilityLen-1])
    resState.append(lastMaxState)
    curMaxProbabilityState = lastMaxState
    print(lastMaxState)
    for index in range(resMaxProbabilityLen-1):
        curMaxProbabilityState = resMaxState[resMaxProbabilityLen-2-index][curMaxProbabilityState]
        resState.append(curMaxProbabilityState)

    print("結果是：%s" % resState)