樸素貝葉斯法實際上學習到生成數(shù)據(jù)的機制，所以屬于生成模型。條件獨立假設(shè)等于說是用于分類的特征在類確定的條件下都是條件獨立的。這一假設(shè)使樸素貝葉斯法變得簡單，但是有時會犧牲一定的分類準確率。
樸素貝葉斯算法（naive Bayes algorithm）

樸素貝葉斯算法

code

# 樸素貝葉斯
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

    # 數(shù)學期望
    @staticmethod
    def mean(X):
        return sum(X) / float(len(X))

    # 標準差（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)))

    # 概率密度函數(shù)
    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

    # 處理X_train
    def summarize(self, train_data):
        summaries = [(self.mean(i), self.stdev(i)) for i in zip(*train_data)]
        return summaries

    # 分類別求出數(shù)學期望和標準差
    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!'

    # 計算概率
    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

    # 類別
    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))

# 實例化
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]])