朴素贝叶斯法实际上学习到生成数据的机制，所以属于生成模型。条件独立假设等于说是用于分类的特征在类确定的条件下都是条件独立的。这一假设使朴素贝叶斯法变得简单，但是有时会牺牲一定的分类准确率。
朴素贝叶斯算法（naive Bayes algorithm）
朴素贝叶斯算法
算法中(1) 的来源为朴素贝叶斯法的极大似然估计，（2）为联合概率分布和后验概率分布推导。如果看不懂推导，我可以写出来。基本上书上都写得很详细，个人建议仔细推导。
code
# 朴素贝叶斯
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
import math
def create_data():
iris = load_iris()
df = pd.DataFrame(iris.data, columns=iris.feature_names)
df['label'] = iris.target
df.columns = ['sepal length', 'sepal width', 'petal length', 'petal width', 'label']
data = np.array(df.iloc[:100, :])
# print(data)
return data[:,:-1], data[:,-1]
X, y = create_data()
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3)
class NaiveBayes:
def __init__(self):
self.model = None
# 数学期望
@staticmethod
def mean(X):
return sum(X) / float(len(X))
# 标准差（方差）
def stdev(self, X):
avg = self.mean(X)
return math.sqrt(sum([pow(x-avg, 2) for x in X]) / float(len(X)))
# 概率密度函数
def gaussian_probability(self, x, mean, stdev):
exponent = math.exp(-(math.pow(x-mean,2)/(2*math.pow(stdev,2))))
return (1 / (math.sqrt(2*math.pi) * stdev)) * exponent
# 处理X_train
def summarize(self, train_data):
summaries = [(self.mean(i), self.stdev(i)) for i in zip(*train_data)]
return summaries
# 分类别求出数学期望和标准差
def fit(self, X, y):
labels = list(set(y))
data = {label:[] for label in labels}
for f, label in zip(X, y):
data[label].append(f)
self.model = {label: self.summarize(value) for label, value in data.items()}
return 'gaussianNB train done!'
# 计算概率
def calculate_probabilities(self, input_data):
# summaries:{0.0: [(5.0, 0.37),(3.42, 0.40)], 1.0: [(5.8, 0.449),(2.7, 0.27)]}
# input_data:[1.1, 2.2]
probabilities = {}
for label, value in self.model.items():
probabilities[label] = 1
for i in range(len(value)):
mean, stdev = value[i]
probabilities[label] *= self.gaussian_probability(input_data[i], mean, stdev)
return probabilities
# 类别
def predict(self, X_test):
# {0.0: 2.9680340789325763e-27, 1.0: 3.5749783019849535e-26}
label = sorted(self.calculate_probabilities(X_test).items(), key=lambda x: x[-1])[-1][0]
return label
def score(self, X_test, y_test):
right = 0
for X, y in zip(X_test, y_test):
label = self.predict(X)
if label == y:
right += 1
return right / float(len(X_test))
# 实例化
model = NaiveBayes()
model.fit(X_train, y_train)
print(model.predict([4.4, 3.2, 1.3, 0.2]))
sklearn
from sklearn.naive_bayes import GaussianNB
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
def create_data():
iris = load_iris()
df = pd.DataFrame(iris.data, columns=iris.feature_names)
df['label'] = iris.target
df.columns = ['sepal length', 'sepal width', 'petal length', 'petal width', 'label']
data = np.array(df.iloc[:100, :])
# print(data)
return data[:,:-1], data[:,-1]
X, y = create_data()
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3)
clf = GaussianNB()
clf.fit(X_train, y_train)
clf.score(X_test,y_test)
clf.predict([[4.4, 3.2, 1.3, 0.2]])
