朴素贝叶斯算法（naive Bayes）是基于贝叶斯定理与特征条件独立假设的分类算法，在机器学习众多算法中，它实现简单、效率高，但代价是往往要牺牲一定的分类准确率。
从模型的分类上来讲，朴素贝叶斯算法属于概率模型（或生成模型），即它学习到的是数据生成的机制。详见笔记第一章 1.2.2
1、关于条件独立性假设
2、定义数据集
数据集
特征空间
3、假设空间
从贝叶斯定理推出假设函数
4、目标函数（最大似然估计）
5、优化算法
手写 naive Bayes 算法
# -*- coding: utf-8 -*-
from __future__ import (absolute_import, division, print_function)
import numpy as np
import pandas as pd
import scipy.spatial.distance as dist
from scipy.stats import norm
from sklearn.utils import shuffle
from sklearn.model_selection import train_test_split
#import random as rd
#import matplotlib.pyplot as plt
from sklearn.preprocessing import StandardScaler
from sklearn.datasets import load_iris
class NaiveBayesModel(object):
def __init__(self, x_train, y_train, x_test):
self.x_train = x_train
self.y_train = y_train
self.x_test = x_test
self.N, self.n = x_train.shape
def prior_probs(self):
'''计算标记值的先验概率(含拉普拉斯平滑)： 本案设为三分类问题'''
labels, labels_count = np.unique(self.y_train, return_counts=True)
label_0, label_1, label_2 = labels[0], labels[1], labels[2]
prior_probs_0, prior_probs_1, prior_probs_2 = (labels_count + 1) / (labels_count.sum() + self.n)
# 类别标记
label_dict = {"label_0": label_0,
"label_1": label_1,
"label_2": label_2}
# 类别标记对应的先验概率
prior_probs_dict = {"prior_probs_0": prior_probs_0,
"prior_probs_1": prior_probs_1,
"prior_probs_2": prior_probs_2}
return label_dict, prior_probs_dict
def likelihood_probs(self, label):
'''计算每个样本的似然概率(含拉普拉斯平滑)'''
# 初始化似然概率数组
likeli_probs_array = np.array([])
# 行循环
for i in range(len(self.x_test)):
# 初始化似然概率的联合分布
likeli_probs_res = 1.0
# 列循环
for j in range(self.n):
val = self.x_test.iloc[i, j]
# 若字段取值为分类变量，则计算条件概率，加拉普拉斯平滑
if isinstance(val, str):
fen_zi = len(self.x_train.loc[(self.x_train.iloc[:, j] == val) &
(y_train == label)]) + 1
fen_mu = sum(self.y_train == label) + self.n
likeli_probs = fen_zi / fen_mu
# 若字段取值为连续变量，则依据正态分布计算条件概率密度
elif isinstance(val, float):
vals = x_train[self.y_train == label].iloc[:, j]
mean = np.mean(vals)
std = np.std(vals)
likeli_probs = norm.pdf(val, mean, std)
else:
raise TypeError("Type must be as str or float.")
# 计算似然概率的联合分布
likeli_probs_res *= likeli_probs
# 保持似然概率
likeli_probs_array = np.append(likeli_probs_array, likeli_probs_res)
return likeli_probs_array
def predict(self, prior_probs_0, prior_probs_1, prior_probs_2,
likeli_probs_array_0, likeli_probs_array_1, likeli_probs_array_2):
'''模型预测, 计算后验概率, 取最大化'''
posterior_probs_0 = (prior_probs_0 * likeli_probs_array_0).reshape(-1, 1)
posterior_probs_1 = (prior_probs_1 * likeli_probs_array_1).reshape(-1, 1)
posterior_probs_2 = (prior_probs_2 * likeli_probs_array_2).reshape(-1, 1)
posterior_probs = np.concatenate([posterior_probs_0,
posterior_probs_1,
posterior_probs_2], axis=1)
# 最大后验概率
y_pred = np.argmax(posterior_probs, axis=1)
return y_pred
def get_score(self, y_true, y_pred):
'''模型评估'''
score = sum(y_true == y_pred) / len(y_true)
return score
if __name__ == "__main__":
# 读取数据
iris = load_iris()
dataSet = pd.DataFrame(iris.data, columns=iris.feature_names)
dataSet.columns = ["sepal_length", "sepal_width", "petal_length", "petal_width"]
# 构造三分类变量
dataSet["sepal_length_mult"] = pd.cut(dataSet.sepal_length, bins=3,
right=True, include_lowest=True,
labels=["low", "med", "high"])
dataSet["sepal_width_mult"] = pd.cut(dataSet.sepal_width, bins=3,
right=True, include_lowest=True,
labels=["low", "med", "high"])
# 构造二分类变量
dataSet["petal_length_bina"] = pd.cut(dataSet.petal_length, bins=2,
right=True, include_lowest=True,
labels=["small", "big"])
dataSet["petal_width_mult"] = pd.cut(dataSet.petal_width, bins=2,
right=True, include_lowest=True,
labels=["small", "big"])
# 标记值
dataSet["label"] = iris.target
# 洗牌
dataSet = shuffle(dataSet) # , random_state=0
x = dataSet.iloc[:, 0:8]
y = dataSet.iloc[:, 8]
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.1)
# 手写模型
model = NaiveBayesModel(x_train, y_train, x_test)
label_dict, prior_probs_dict = model.prior_probs()
label_0 = label_dict.get("label_0")
label_1 = label_dict.get("label_1")
label_2 = label_dict.get("label_2")
prior_probs_0 = prior_probs_dict.get("prior_probs_0")
prior_probs_1 = prior_probs_dict.get("prior_probs_1")
prior_probs_2 = prior_probs_dict.get("prior_probs_2")
likeli_probs_array_0 = model.likelihood_probs(label=label_0)
likeli_probs_array_1 = model.likelihood_probs(label=label_1)
likeli_probs_array_2 = model.likelihood_probs(label=label_2)
y_pred = model.predict(prior_probs_0, prior_probs_1, prior_probs_2,
likeli_probs_array_0, likeli_probs_array_1, likeli_probs_array_2)
score = model.get_score(y_test, y_pred)
print(f"NaiveBayesModel 预测准确率：{score}")
NaiveBayesModel 预测准确率：0.9333333333333333
网友评论