樸素貝葉斯是直接衡量標簽和特征之間的概率關系的有監督學習算法

分類原理：通過某對象的先驗概率，利用貝葉斯公式計算出其后驗概率，即該對象屬于某一類的概率，選擇具有最大后驗概率的類作為該對象的類。

import pandas as pd import numpy as np from sklearn.datasets import load_breast_cancer, load_wine from sklearn.model_selection import train_test_split from sklearn.naive_bayes import GaussianNB from sklearn.naive_bayes import MultinomialNB from sklearn.naive_bayes import BernoulliNB from sklearn.naive_bayes import ComplementNB cancer = load_breast_cancer() data_train, data_test, target_train, target_test = train_test_split(cancer.data, cancer.target, test_size=0.2, random_state=0)

樸素貝葉斯

樸素貝葉斯法假設：在分類確定的條件下，用于分類的特征是條件獨立的。

樸素貝葉斯學習的參數是先驗概率和條件概率，通常采用極大似然估計這兩種概率

高斯樸素貝葉斯

假設特征的條件概率分布滿足高斯分布

sklearn.naive_bayes.GaussianNB

class sklearn.naive_bayes.GaussianNB(*, priors=None, var_smoothing=1e-09)

prior：類的先驗概率，如果不指定，則自行根據數據計算先驗概率

var_smoothing：浮點數，默認1e-9

GaussianNB_model = GaussianNB() GaussianNB_model.fit(data_train, target_train) train_score = GaussianNB_model.score(data_train, target_train) print('train score:',train_score) test_score = GaussianNB_model.score(data_test, target_test) print('test score:',test_score)

多項式樸素貝葉斯

假設特征的條件概率分布滿足多項式分布

sklearn.naive_bayes.MultinomialNB

class?sklearn.naive_bayes.MultinomialNB(*,?alpha=1.0,?fit_prior=True,?class_prior=None)

alpha：浮點數，用于指定α的值

fit_prior：bool，如果為True，則不學習概率值，代以均勻分布

class_prior：數組，指定每個分類的先驗概率

MultiomiaNB_model = MultinomialNB() MultiomiaNB_model.fit(data_train, target_train) train_score = MultiomiaNB_model.score(data_train, target_train) print('train score:',train_score) test_score = MultiomiaNB_model.score(data_test, target_test) print('test score:',test_score)

繪制準確率與學習率的學習曲線

def test_MultinomialNB_alpha(*data):'''測試 MultinomialNB 的預測性能隨 alpha 參數的影響:param data: 可變參數。它是一個元組，這里要求其元素依次為：訓練樣本集、測試樣本集、訓練樣本的標記、測試樣本的標記:return: None'''X_train,X_test,y_train,y_test=dataalphas=np.logspace(-2,5,num=200)train_scores=[]test_scores=[]for alpha in alphas:cls=MultinomialNB(alpha=alpha)cls.fit(X_train,y_train)train_scores.append(cls.score(X_train,y_train))test_scores.append(cls.score(X_test, y_test))## 繪圖fig=plt.figure()ax=fig.add_subplot(1,1,1)ax.plot(alphas,train_scores,label="Training Score")ax.plot(alphas,test_scores,label="Testing Score")ax.set_xlabel(r"$\alpha$")ax.set_ylabel("score")ax.set_ylim(0,1.0)ax.set_title("MultinomialNB")ax.set_xscale("log")plt.show()

伯努利貝葉斯分類器

假設特征的條件概率分布滿足二項分布

sklearn.naive_bayes.BernoulliNB

class?sklearn.naive_bayes.BernoulliNB(*,?alpha=1.0,?binarize=0.0,?fit_prior=True,?class_prior=None)

alpha=1.0：浮點數，α值

binarize：將特征二值化的閾值

處理二項分布的樸素貝葉斯，需要先對數據二值化

BernoulliNB_model = BernoulliNB() BernoulliNB_model.fit(data_train, target_train) train_score = BernoulliNB_model.score(data_train, target_train) print('train score:',train_score) test_score = BernoulliNB_model.score(data_test, target_test) print('test score:',test_score)

測試 BernoulliNB 的預測性能隨 binarize 參數的影響

作為經驗值，可以將binarize取（所有特征中的最小值 + 所有特征中的最大值）/ 2

def test_BernoulliNB_binarize(*data):'''測試 BernoulliNB 的預測性能隨 binarize 參數的影響:param data: 可變參數。它是一個元組，這里要求其元素依次為：訓練樣本集、測試樣本集、訓練樣本的標記、測試樣本的標記:return: None'''X_train,X_test,y_train,y_test=datamin_x=min(np.min(X_train.ravel()),np.min(X_test.ravel()))-0.1max_x=max(np.max(X_train.ravel()),np.max(X_test.ravel()))+0.1binarizes=np.linspace(min_x,max_x,endpoint=True,num=100)train_scores=[]test_scores=[]for binarize in binarizes:cls=BernoulliNB(binarize=binarize)cls.fit(X_train,y_train)train_scores.append(cls.score(X_train,y_train))test_scores.append(cls.score(X_test, y_test))## 繪圖fig=plt.figure()ax=fig.add_subplot(1,1,1)ax.plot(binarizes,train_scores,label="Training Score")ax.plot(binarizes,test_scores,label="Testing Score")ax.set_xlabel("binarize")ax.set_ylabel("score")ax.set_ylim(0,1.0)ax.set_xlim(min_x-1,max_x+1)ax.set_title("BernoulliNB")ax.legend(loc="best")plt.show()test_BernoulliNB_binarize(data_train,data_test,target_train,target_test) # 調用 test_BernoulliNB_alpha

補集樸素貝葉斯

sklearn.naive_bayes.ComplementNB

class?sklearn.naive_bayes.ComplementNB(*,?alpha=1.0,?fit_prior=True,?class_prior=None,?norm=False)

多項式樸素貝葉斯算法的改進，可以用于捕捉少數類

ComplementNB_model = ComplementNB() ComplementNB_model.fit(data_train, target_train) train_score = ComplementNB_model.score(data_train, target_train) print('train score:',train_score) test_score = ComplementNB_model.score(data_test, target_test) print('test score:',test_score)

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