003_训练学习朴素贝叶斯分类器，确定类标记y

# 计算先验概率 P(Y)
def prior_prob(list_Y):
    probs = {}
    for c in set(list_Y):
        probs[c] = Y.count(c)/len(list_Y)
    return probs

# 计算条件概率 P(X_i = v | Y=c) 使用拉普拉斯平滑
def conditional_prob(X, list_Y, values):
    probs = {}
    setY = set(list_Y)
    for c in setY:
        probs[c] = {}
        idxc = []
        for i, y in enumerate(list_Y):
            if y == c:
                idxc.append(i)
        n_c = len(idxc)
        for v in values:
            count = 0
            for i in idxc:
                if X[i] == v:
                    count += 1
            # 拉普拉斯平滑
            probs[c][v] = (count + 1)/(n_c + len(values))
    return probs


# 预测函数
def predict(x):
    results = {}
    for c in P_Y:
        prob = P_Y[c] * P_X1_Y[c][x[0]] * P_X2_Y[c][x[1]]
        results[c] = prob
    # 返回概率最大类别
    return max(results, key=results.get)


# 训练数据
X1 = [1,1,1,1,1,2,2,2,2,2,3,3,3,3,3]
X2 = ['S','M','M','S','S','S','S','M','M','L','L','L','M','M','L']
Y  = [-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,-1]

# 特征的取值集合
A1 = [1,2,3]
A2 = ['S','M','L']

P_Y = prior_prob(Y)
P_X1_Y = conditional_prob(X1, Y, A1)
P_X2_Y = conditional_prob(X2, Y, A2)

# 测试样本
x_test = (3,'M')
y_pred = predict(x_test)
print("样本 {} 的预测类别为: {}".format(x_test, y_pred))