纯numpy写朴素贝叶斯模型

朴素贝叶斯学习到生成数据的机制，属于生成模型。
学习过程：模型思想，根据数据集计算出联合分布概率，即计算先验概率和条件概率
如何计算：可利用极大时然估计，或者贝叶斯估计
预测过程：根据后验概率进行预测
为什么可以这样预测？
证明：将样本分配到后验概率最大的类中等价于期望风险最小化

import numpy as np
from collections import Counter

class Navie_Bayes():
    def __init__(self):
        self.lmbda = 0.2
        self.p_y = {}
        self.p_x0_y = {}
        self.p_x1_y = {}
        
    def fit(self, X, Y):
        y_counts = Counter(Y)
        class_number = len(y_counts.keys())
        for i in y_counts.keys():
            self.p_y[i] =  (y_counts[i] + self.lmbda)/(X.shape[0] + class_number * self.lmbda)
        
        x0_counts = Counter(X[:,0])
        x1_counts = Counter(X[:,1])
        for x, y in zip(X, Y):
            self.p_x0_y[(x[0],y)] = (x0_counts[x[0]] + self.lmbda) / (y_counts[y] + class_number * self.lmbda)
            self.p_x1_y[(x[1],y)] = (x1_counts[x[1]] + self.lmbda) / (y_counts[y] + class_number * self.lmbda)
            
    def predict(self, new_x):
        p0 = self.p_y[-1] * self.p_x0_y[(new_x[0],-1)] * self.p_x1_y[(new_x[1],-1)]
        p1 = self.p_y[1] * self.p_x0_y[(new_x[0],1)] * self.p_x1_y[(new_x[1],1)]
        if p0 > p1:
            return -1
        else:
            return 1
        
if __name__ == '__main__':
    X = np.array([[1,'S'],[1,'M'],[1,'M'],[2,'S'],[2,'M'],[2,'M'],[2,'L'],[2,'L'],[3,'L'],[3,'M'],[3,'M'],[3,'L'],[3,'L']])
    y = np.array([-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,-1])
    navies_bayes = Navie_Bayes()
    navies_bayes.fit(X, y)
    x_new = np.array([2,'S'])
    y_pred = navies_bayes.predict(x_new)
    print('My Navie_Bayes predict %d' %y_pred)