朴素贝叶斯法的参数估计——贝叶斯估计及其Python实现

统计学习方法——朴素贝叶斯法原理

1. 贝叶斯估计

1.1 为什么要用贝叶斯估计（极大似然的缺点）

1.2 贝叶斯估计原理

贝叶斯估计的算法过程合极大似然估计的算法过程一模一样，代码也几乎一模一样，只是加了一个λ。

2. Python代码

def priorProbability(labelList,Lambda):  # 加入一个lambda
    labelSet = set(labelList)
    labelCountDict = {}
    for label in labelList:
        if label not in labelCountDict:
            labelCountDict[label] = 0
        labelCountDict[label] += 1
    priorProbabilityDict = {}
    for label in labelSet:
        priorProbabilityDict[label] = (labelCountDict[label]+Lambda)/(len(labelList)+len(labelSet)*Lambda)
    return priorProbabilityDict
def conditionProbability(dataSet,labelList,Lambda):
    dimNum = len(dataSet[0])
    characterVal = []
    for i in range(dimNum):
        temp = []
        for j in range(len(dataSet)):
            if dataSet[j][i] not in temp:
                temp.append(dataSet[j][i])
        characterVal.append(temp)
    probability = []
    labelSet = list(set(labelList))
    for dim in range(dimNum):
        tempMemories = {}
        for val in characterVal[dim]:
            for label in labelSet:
                labelCount = 0
                mixCount = 0
                for i in range(len(labelList)):
                    if labelList[i] == label:
                        labelCount += 1
                        if dataSet[i][dim] == val:
                            mixCount += 1
                tempMemories[str(val) + "|" + str(label)] = (mixCount+Lambda)/(labelCount+len(characterVal[dim])*Lambda)
        probability.append(tempMemories)
    return probability
def naiveBayes(x,dataSet,labelList,Lambda):
    priorProbabilityDict = priorProbability(labelList,Lambda)
    probability = conditionProbability(dataSet,labelList,Lambda)
    bayesProbability = {}
    labelSet = list(set(labelList))
    for label in labelSet:
        tempProb = priorProbabilityDict[label]
        for dim in range(len(x)):
            tempProb *= probability[dim][str(x[dim])+"|"+str(label)]
        bayesProbability[label] = tempProb
    result = sorted(bayesProbability.items(),key= lambda x:x[1],reverse=True)
    return result[0][0]