朴素贝叶斯法的参数估计——极大似然估计及其Python实现
统计学习方法——朴素贝叶斯法原理
1. 朴素贝叶斯法的极大似然估计
2. 朴素贝叶斯极大似然学习及分类算法
算法过程：
2. Python实现
def priorProbability(labelList): # 计算先验概率
labelSet = set(labelList) # 得到类别的值
labelCountDict = {} # 利用一个字典来存储训练集中各个类别的实例数
for label in labelList:
if label not in labelCountDict:
labelCountDict[label] = 0
labelCountDict[label] += 1
priorProbabilityDict = {}
for label in labelSet: # 计算不同的类别对应的先验概率
priorProbabilityDict[label] = labelCountDict[label]/len(labelList)
return priorProbabilityDict
def conditionProbability(dataSet,labelList): # 计算条件概率
dimNum = len(dataSet[0]) # 得到特征数
characterVal = []
# 利用一个数组来存储训练数据集中不同特征的不同特征值。
# 每一个不同特征的特征值都要需要另一个数组来存储，这样 characterVal实际上是一个二维数组
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 = [] # 数组来存储最后的所有的条件概率
labelSet = list(set(labelList))
for dim in range(dimNum): # 学习条件概率，需要计算K*S1*...*Sj个概率
tempMemories = {} # 对于每一个特征，利用一个字点来存储这个特征所有的取值对应的条件概率
for val in characterVal[dim]:
for label in labelSet:
labelCount = 0 # 记录每一类的个数
mixCount = 0 # 记录当前特征值为这个数，且类别为这个类别的实例个数
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/labelCount
# key表示哪一个特征值和类别，键表示对应的条件概率
probability.append(tempMemories) # 计算完一个特征，填充一个
return probability # 返回条件概率
def naiveBayes(x,dataSet,labelList): # 贝叶斯分类
priorProbabilityDict = priorProbability(labelList)
probability = conditionProbability(dataSet,labelList)
bayesProbability = {} # 计算所有类所对应的后验概率
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)# 排序
return result[0][0]# 返回后验概率最大的类
dataSet = ([[1,"s"],[1,"m"],[1,"m"],[1,"s"],[1,"s"],[2,"s"],[2,"m"],[2,"m"],
[2,"l"],[2,"l"],[3,"l"],[3,"m"],[3,"m"],[3,"l"],[3,"l"]])
labelList = [-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,-1]
print(naiveBayes([2,"s"],dataSet,labelList))
## 返回结果为-1，即归为-1类。