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朴素贝叶斯属于生成模型，学习数据概率分布P(X,Y)，然后求后验概率P(Y|X)。对条件概率分布作条件独立性假设。
模型：贝叶斯定理
策略：后验概率最大化（等价于期望风险最小化）
算法：略
朴素贝叶斯在进行概率估计时有两种方式：基于最大似然估计、基于贝叶斯估计。朴素贝叶斯可以进一步扩展成贝叶斯网络
import numpy as npdef Train(X_train,Y_train,feature):global class_num,labelclass_num=2label=[1,-1]feature_len=3feature=[[1,'S'],[2,'M'],[3,'L']]prior_probability=np.zeros(class_num)conditional_probability=np.zeros((class_num,feature_len,2))pos,neg=0,0for i in range(len(Y_train)):if Y_train[i] == 1:pos+= 1else:neg += 1##计算出P(Y)prior_probability[0]=pos/len(X_train)prior_probability[1]=neg/len(X_train)##统计P(X1,X2|Y)，假设X1与X2相互独立，计算P(X1,X2|Y)=P(X1|Y)*P(X2|Y),所以统计X1,X2不同取值对应的不同Y的数量for i in range(class_num):for j in range(feature_len):for k in range(len(Y_train)):if Y_train[k]==label[i]:if X_train[k][0]==feature[j][0]:conditional_probability[i][j][0]+=1if X_train[k][1]==feature[j][1]:conditional_probability[i][j][1]+=1class_label_num=[pos,neg]
##计算P(X1,X2|Y)for i in range(class_num):for j in range(feature_len):conditional_probability[i][j][0]/=class_label_num[i]conditional_probability[i][j][1]/=class_label_num[i]return prior_probability,conditional_probabilitydef Predict(X_test,prior_probability,conditional_probability,feature):result=np.zeros(len(label))for i in range(class_num):fea0,fea1=0,0for j in range(len(feature)):if feature[j][0]==X_test[0]:fea0=conditional_probability[i][j][0]if feature[j][1]==X_test[1]:fea1=conditional_probability[i][j][1]result[i]=fea0*fea1*prior_probability[i]result=np.vstack([result,label])return result
def main():X_train=[[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']]Y_train = [-1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1]feature = [[1, 'S'],[2, 'M'],[3, 'L']]testset = [2, 'S']prior_probability, conditional_probability = Train(X_train, Y_train, feature)result = Predict(testset, prior_probability, conditional_probability, feature)print(result)if __name__ == '__main__':main()
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