周志华《机器学习》课后习题（第七章）：贝叶斯分类

import numpy as np
import pandas as pd
from sklearn.utils.multiclass import type_of_target
from collections import namedtuple
def train_nb(X, y):
    m, n = X.shape
    p1 = (len(y[y == '是']) + 1) / (m + 2)  # 拉普拉斯平滑
    p1_list = []  # 用于保存正例下各属性的条件概率
    p0_list = []
    X1 = X[y == '是']
    X0 = X[y == '否']
    m1, _ = X1.shape
    m0, _ = X0.shape
    for i in range(n):
        xi = X.iloc[:, i]
        p_xi = namedtuple(X.columns[i], ['is_continuous', 'conditional_pro'])  # 用于储存每个变量的情况
        is_continuous = type_of_target(xi) == 'continuous'
        xi1 = X1.iloc[:, i]
        xi0 = X0.iloc[:, i]
        if is_continuous:  # 连续值时，conditional_pro 储存的就是 [mean, var] 即均值和方差
            xi1_mean = np.mean(xi1)
            xi1_var = np.var(xi1)
            xi0_mean = np.mean(xi0)
            xi0_var = np.var(xi0)
            p1_list.append(p_xi(is_continuous, [xi1_mean, xi1_var]))
            p0_list.append(p_xi(is_continuous, [xi0_mean, xi0_var]))
        else:  # 离散值时直接计算各类别的条件概率
            unique_value = xi.unique()  # 取值情况
            nvalue = len(unique_value)  # 取值个数
            xi1_value_count = pd.value_counts(xi1)[unique_value].fillna(0) + 1  # 计算正样本中，该属性每个取值的数量，并且加1，即拉普拉斯平滑
            xi0_value_count = pd.value_counts(xi0)[unique_value].fillna(0) + 1
            p1_list.append(p_xi(is_continuous, np.log(xi1_value_count / (m1 + nvalue))))
            p0_list.append(p_xi(is_continuous, np.log(xi0_value_count / (m0 + nvalue))))
    return p1, p1_list, p0_list
def predict_nb(x, p1, p1_list, p0_list):
    n = len(x)
    x_p1 = np.log(p1)
    x_p0 = np.log(1 - p1)
    for i in range(n):
        p1_xi = p1_list[i]
        p0_xi = p0_list[i]
        if p1_xi.is_continuous:
            mean1, var1 = p1_xi.conditional_pro
            mean0, var0 = p0_xi.conditional_pro
            x_p1 += np.log(1 / (np.sqrt(2 * np.pi) * var1) * np.exp(- (x[i] - mean1) ** 2 / (2 * var1 ** 2)))
            x_p0 += np.log(1 / (np.sqrt(2 * np.pi) * var0) * np.exp(- (x[i] - mean0) ** 2 / (2 * var0 ** 2)))
        else:
            x_p1 += p1_xi.conditional_pro[x[i]]
            x_p0 += p0_xi.conditional_pro[x[i]]
    if x_p1 > x_p0:
        return '是'
    else:
        return '否'
if __name__ == '__main__':
    data_path = r'C:\Users\hanmi\Documents\xiguabook\watermelon3_0_Ch.csv'
    data = pd.read_csv(data_path, index_col=0)
    X = data.iloc[:, :-1]
    y = data.iloc[:, -1]
    p1, p1_list, p0_list = train_nb(X, y)
    x_test = X.iloc[0, :]   # 书中测1 其实就是第一个数据
    print(predict_nb(x_test, p1, p1_list, p0_list))

'''
目前仅拿西瓜数据集测试过，运行正常，其他数据未测试
'''
import numpy as np
import pandas as pd
from sklearn.utils.multiclass import type_of_target
class AODE(object):
    def __init__(self, m):
        self.m_hat = m
        self.m = None
        self.n = None
        self.unique_y = None
        self.n_class = None
        self.is_continuous = None
        self.unique_values = None
        self.total_p = None
    def predict(self, X):
        X = np.array(X)
        if self.total_p == None:
            raise Exception('you have to fit first before predict.')
        result = pd.DataFrame(np.zeros((X.shape[0], self.unique_y.shape[0])), columns=self.unique_y)
        for i in self.total_p.keys():
            result += self._spode_predict(X, self.total_p[i], i)
        return self.unique_y[np.argmax(result.values, axis=1)]
    def fit(self, X, y):
        X = np.array(X)
        self.m, self.n = X.shape
        self.unique_y = np.unique(y)
        self.n_class = self.unique_y.size
        # 这里转为list, 是因为貌似type_of_target 有bug, 只有在pd.Series类型的时候才能解析为'continuous',
        # 在这里转为array类型后解析为 'unknown'了
        is_continuous = pd.DataFrame(X).apply(lambda x: (type_of_target(x.tolist()) == 'continuous'))
        self.is_continuous = is_continuous
        unique_values = {}  # 离散型字段的各取值
        for i in is_continuous[~is_continuous].index:
            unique_values[i] = np.unique(X[:, i])
        self.unique_values = unique_values
        # 获取可以作为父节点的属性索引，这里在论文中取值为30; 但在西瓜书中由于样本很少, 所有直接取0就好
        parent_attribute_index = self._get_parent_attribute(X)
        total_p = {}
        for i in parent_attribute_index:
            p = self._spode_fit(X, y, i)
            total_p[i] = p
        self.total_p = total_p
        return self
    def _spode_fit(self, X, y, xi_index):
        p = pd.DataFrame(columns=self.unique_y, index=self.unique_values[xi_index])  # 储存各取值下的条件概率
        nunique_xi = self.unique_values[xi_index].size  # 当前属性的取值数量
        pc_xi_denominator = self.m + self.n_class * nunique_xi  # 计算 p(c, xi) 的分母 |D| + N * N_i
        for c in self.unique_y:
            for xi in self.unique_values[xi_index]:
                p_list = []  # 储存y取值为c, Xi取值为xi下各个条件概率p(xj|c, xi)和先验概率p(c, xi)
                c_xi = (X[:, xi_index] == xi) & (y == c)
                X_c_xi = X[c_xi, :]  # y 取值 为c, Xi 取值为xi 的所有数据
                pc_xi = (X_c_xi.shape[0] + 1) / pc_xi_denominator  # p(c, xi)
                # 实际上这里在j = i时, 个人理解应该是可以跳过不计算的，因为p(xi|c, xi) = 1, 在计算中都是一样的但这里为了方便实现，就没有跳过了。
                for j in range(self.n):
                    if self.is_continuous[j]:  # 字段为连续值, 假设服从高斯分布, 保存均值和方差
                        # 这里因为样本太少。有时候会出现X_c_xi为空或者只有一个数据的情况, 如何是离散值，依然可以计算;
                        # 但是连续值的情况下,np.mean会报warning, 只有一个数据时,方差为0
                        # 所有这时, 均值和方差以类别样本来替代。
                        if X_c_xi.shape[0] <= 1:
                            p_list.append([np.mean(X[y == c, j]), np.var(X[y == c, j])])
                        else:
                            p_list.append([np.mean(X_c_xi[:, j]), np.var(X_c_xi[:, j])])
                    else:
                        # 计算 p(xj|c, xi)
                        condi_proba_of_xj = (pd.value_counts(X_c_xi[:, j])[self.unique_values[j]].fillna(0) + 1) / (
                                X_c_xi.shape[0] + self.unique_values[j].size)
                        p_list.append(np.log(condi_proba_of_xj))
                p_list.append(np.log(pc_xi))  # p(c, xi)在最后的位置
                p.loc[xi, c] = p_list
        return p
    def _spode_predict(self, X, p, xi_index):
        assert X.shape[1] == self.n
        xi = X[:, xi_index]
        result = pd.DataFrame(np.zeros((X.shape[0], p.shape[1])), columns=self.unique_y)  # 储存每个样本为不同类别的对数概率值
        for value in p.index:  # 为了可以使用pandas的索引功能, 对于要预测的X值, 每一次循环求同一取值下样本的条件概率和
            xi_value = xi == value
            X_split = X[xi_value, :]
            for c in p.columns:
                p_list = p.loc[value, c]  # 储存p(xj|c, xi) 和 p(c, xi)的列表
                for j in range(self.n):  # 遍历所有的条件概率, 将对应的条件概率相加
                    if self.is_continuous[j]:
                        mean_, var_ = p_list[j]
                        result.loc[xi_value, c] += (
                                -np.log(np.sqrt(2 * np.pi) * var_) - (X_split[:, j] - mean_) ** 2 / (2 * var_ ** 2))
                    else:
                        result.loc[xi_value, c] += p_list[j][X_split[:, j]].values
                result.loc[xi_value, c] += p_list[-1]  # 最后加上p(c, xi)
        return result
    def _get_parent_attribute(self, X):
        '''
        基于属性下各取值的样本数量，决定哪些属性可以作为父属性。
        关于连续值的处理，在《机器学习》书中也没有提及，AODE的原论文也没有提及如何处理连续值，
        考虑到若将连续值x_j作为父属性时，如何求解p(x_i|c, x_j)条件概率会比较麻烦(可以通过贝叶斯公式求解)，
        此外AODE本身就是要将取值样本数量低于m的属性去除的，从这个角度来说，连续值就不能作为父属性了。
        所以这里连续值不作为父属性
        :param X:
        :return:
        '''
        enough_quantity = pd.DataFrame(X).apply(
            lambda x: (type_of_target(x.tolist()) != 'continuous') & (pd.value_counts(x) > self.m_hat).all())
        return enough_quantity[enough_quantity].index.tolist()
if __name__ == '__main__':
    data_path = r'C:\Users\hanmi\Documents\xiguabook\watermelon3_0_Ch.csv'
    data = pd.read_csv(data_path, index_col=0)
    X = data.iloc[:, :-1]
    y = data.iloc[:, -1]
    aode = AODE(0)
    print(aode.fit(X, y).predict(X.iloc[[0], :]))