机器学习sklearn（84）：算法实例（41）分类（20）朴素贝叶斯（三） 不同分布下的贝叶斯（二） 概率类模型的评估指标
1 布里尔分数Brier Score
from sklearn.metrics import brier_score_loss #注意，第一个参数是真实标签，第二个参数是预测出的概率值 #在二分类情况下，接口predict_proba会返回两列，但SVC的接口decision_function却只会返回一列 #要随时注意，使用了怎样的概率分类器，以辨别查找置信度的接口，以及这些接口的结构 brier_score_loss(Ytest, prob[:,1], pos_label=1) #我们的pos_label与prob中的索引一致，就可以查看这个类别下的布里尔分数是多少
布里尔分数可以用于任何可以使用predict_proba接口调用概率的模型，我们来探索一下在我们的手写数字数据集上，逻辑回归，SVC和我们的高斯朴素贝叶斯的效果如何：
from sklearn.metrics import brier_score_loss brier_score_loss(Ytest,prob[:,8],pos_label=8) from sklearn.svm import SVC from sklearn.linear_model import LogisticRegression as LR logi = LR(C=1., solver='lbfgs',max_iter=3000,multi_class="auto").fit(Xtrain,Ytrain) svc = SVC(kernel = "linear",gamma=1).fit(Xtrain,Ytrain) brier_score_loss(Ytest,logi.predict_proba(Xtest)[:,1],pos_label=1) #由于SVC的置信度并不是概率，为了可比性，我们需要将SVC的置信度“距离”归一化，压缩到[0,1]之间 svc_prob = (svc.decision_function(Xtest) - svc.decision_function(Xtest).min())/(svc.decision_function(Xtest).max() - svc.decision_function(Xtest).min()) brier_score_loss(Ytest,svc_prob[:,1],pos_label=1)
如果将每个分类器每个标签类别下的布里尔分数可视化：
import pandas as pd name = ["Bayes","Logistic","SVC"] color = ["red","black","orange"] df = pd.DataFrame(index=range(10),columns=name) for i in range(10): df.loc[i,name[0]] = brier_score_loss(Ytest,prob[:,i],pos_label=i) df.loc[i,name[1]] = brier_score_loss(Ytest,logi.predict_proba(Xtest) [:,i],pos_label=i) df.loc[i,name[2]] = brier_score_loss(Ytest,svc_prob[:,i],pos_label=i) for i in range(df.shape[1]): plt.plot(range(10),df.iloc[:,i],c=color[i]) plt.legend() plt.show() df
2 对数似然函数Log Loss
from sklearn.metrics import log_loss log_loss(Ytest,prob) log_loss(Ytest,logi.predict_proba(Xtest)) log_loss(Ytest,svc_prob)
3 可靠曲线Reliability Curve
1. 导入需要的库和模块
import numpy as np import matplotlib.pyplot as plt from sklearn.datasets import make_classification as mc from sklearn.naive_bayes import GaussianNB from sklearn.svm import SVC from sklearn.linear_model import LogisticRegression as LR from sklearn.metrics import brier_score_loss from sklearn.model_selection import train_test_split
2. 创建数据集
X, y = mc(n_samples=100000,n_features=20 #总共20个特征 ,n_classes=2 #标签为2分类 ,n_informative=2 #其中两个代表较多信息 ,n_redundant=10 #10个都是冗余特征 ,random_state=42) #样本量足够大，因此使用1%的样本作为训练集 Xtrain, Xtest, Ytrain, Ytest = train_test_split(X, y ,test_size=0.99 ,random_state=42) Xtrain np.unique(Ytrain)
3. 建立模型，绘制图像
gnb = GaussianNB() gnb.fit(Xtrain,Ytrain) y_pred = gnb.predict(Xtest) prob_pos = gnb.predict_proba(Xtest)[:,1] #我们的预测概率 - 横坐标 #Ytest - 我们的真实标签 - 横坐标 #在我们的横纵表坐标上，概率是由顺序的（由小到大），为了让图形规整一些，我们要先对预测概率和真实标签按照预测 概率进行一个排序，这一点我们通过DataFrame来实现 df = pd.DataFrame({"ytrue":Ytest[:500],"probability":prob_pos[:500]}) df df = df.sort_values(by="probability") df.index = range(df.shape[0]) df #紧接着我们就可以画图了 fig = plt.figure() ax1 = plt.subplot() ax1.plot([0, 1], [0, 1], "k:", label="Perfectly calibrated") #得做一条对角线来对比呀 ax1.plot(df["probability"],df["ytrue"],"s-",label="%s (%1.3f)" % ("Bayes", clf_score)) ax1.set_ylabel("True label") ax1.set_xlabel("predcited probability") ax1.set_ylim([-0.05, 1.05]) ax1.legend() plt.show()
fig = plt.figure() ax1 = plt.subplot() ax1.plot([0, 1], [0, 1], "k:", label="Perfectly calibrated") ax1.scatter(df["probability"],df["ytrue"],s=10) ax1.set_ylabel("True label") ax1.set_xlabel("predcited probability") ax1.set_ylim([-0.05, 1.05]) ax1.legend() plt.show()
4. 使用可靠性曲线的类在贝叶斯上绘制一条校准曲线
from sklearn.calibration import calibration_curve #从类calibiration_curve中获取横坐标和纵坐标 trueproba, predproba = calibration_curve(Ytest, prob_pos ,n_bins=10 #输入希望分箱的个数 ) fig = plt.figure() ax1 = plt.subplot() ax1.plot([0, 1], [0, 1], "k:", label="Perfectly calibrated") ax1.plot(predproba, trueproba,"s-",label="%s (%1.3f)" % ("Bayes", clf_score)) ax1.set_ylabel("True probability for class 1") ax1.set_xlabel("Mean predcited probability") ax1.set_ylim([-0.05, 1.05]) ax1.legend() plt.show()
5. 不同的n_bins取值下曲线如何改变？
fig, axes = plt.subplots(1,3,figsize=(18,4)) for ind,i in enumerate([3,10,100]): ax = axes[ind] ax.plot([0, 1], [0, 1], "k:", label="Perfectly calibrated") trueproba, predproba = calibration_curve(Ytest, prob_pos,n_bins=i) ax.plot(predproba, trueproba,"s-",label="n_bins = {}".format(i)) ax1.set_ylabel("True probability for class 1") ax1.set_xlabel("Mean predcited probability") ax1.set_ylim([-0.05, 1.05]) ax.legend() plt.show()
6. 建立更多模型
name = ["GaussianBayes","Logistic","SVC"] gnb = GaussianNB() logi = LR(C=1., solver='lbfgs',max_iter=3000,multi_class="auto") svc = SVC(kernel = "linear",gamma=1)
7. 建立循环，绘制多个模型的概率校准曲线
fig, ax1 = plt.subplots(figsize=(8,6)) ax1.plot([0, 1], [0, 1], "k:", label="Perfectly calibrated") for clf, name_ in zip([gnb,logi,svc],name): clf.fit(Xtrain,Ytrain) y_pred = clf.predict(Xtest) #hasattr(obj,name)：查看一个类obj中是否存在名字为name的接口，存在则返回True if hasattr(clf, "predict_proba"): prob_pos = clf.predict_proba(Xtest)[:,1] else: # use decision function prob_pos = clf.decision_function(Xtest) prob_pos = (prob_pos - prob_pos.min()) / (prob_pos.max() - prob_pos.min()) #返回布里尔分数 clf_score = brier_score_loss(Ytest, prob_pos, pos_label=y.max()) trueproba, predproba = calibration_curve(Ytest, prob_pos,n_bins=10) ax1.plot(predproba, trueproba,"s-",label="%s (%1.3f)" % (name_, clf_score)) ax1.set_ylabel("True probability for class 1") ax1.set_xlabel("Mean predcited probability") ax1.set_ylim([-0.05, 1.05]) ax1.legend() ax1.set_title('Calibration plots (reliability curve)') plt.show()
4 预测概率的直方图
fig, ax2 = plt.subplots(figsize=(8,6)) for clf, name_ in zip([gnb,logi,svc],name): clf.fit(Xtrain,Ytrain) y_pred = clf.predict(Xtest) #hasattr(obj,name)：查看一个类obj中是否存在名字为name的接口，存在则返回True if hasattr(clf, "predict_proba"): prob_pos = clf.predict_proba(Xtest)[:,1] else: # use decision function prob_pos = clf.decision_function(Xtest) prob_pos = (prob_pos - prob_pos.min()) / (prob_pos.max() - prob_pos.min()) ax2.hist(prob_pos ,bins=10 ,label=name_ ,histtype="step" #设置直方图为透明 ,lw=2 #设置直方图每个柱子描边的粗细 ) ax2.set_ylabel("Distribution of probability") ax2.set_xlabel("Mean predicted probability") ax2.set_xlim([-0.05, 1.05]) ax2.set_xticks([0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1]) ax2.legend(loc=9) plt.show()
5 校准可靠性曲线
1. 包装函数
def plot_calib(models,name,Xtrain,Xtest,Ytrain,Ytest,n_bins=10): import matplotlib.pyplot as plt from sklearn.metrics import brier_score_loss from sklearn.calibration import calibration_curve fig, (ax1, ax2) = plt.subplots(1, 2,figsize=(20,6)) ax1.plot([0, 1], [0, 1], "k:", label="Perfectly calibrated") for clf, name_ in zip(models,name): clf.fit(Xtrain,Ytrain) y_pred = clf.predict(Xtest) #hasattr(obj,name)：查看一个类obj中是否存在名字为name的接口，存在则返回True if hasattr(clf, "predict_proba"): prob_pos = clf.predict_proba(Xtest)[:,1] else: # use decision function prob_pos = clf.decision_function(Xtest) prob_pos = (prob_pos - prob_pos.min()) / (prob_pos.max() - prob_pos.min()) #返回布里尔分数 clf_score = brier_score_loss(Ytest, prob_pos, pos_label=y.max()) trueproba, predproba = calibration_curve(Ytest, prob_pos,n_bins=n_bins) ax1.plot(predproba, trueproba,"s-",label="%s (%1.3f)" % (name_, clf_score)) ax2.hist(prob_pos, range=(0, 1), bins=n_bins, label=name_,histtype="step",lw=2) ax2.set_ylabel("Distribution of probability") ax2.set_xlabel("Mean predicted probability") ax2.set_xlim([-0.05, 1.05]) ax2.legend(loc=9) ax2.set_title("Distribution of probablity") ax1.set_ylabel("True probability for class 1") ax1.set_xlabel("Mean predcited probability") ax1.set_ylim([-0.05, 1.05]) ax1.legend() ax1.set_title('Calibration plots(reliability curve)') plt.show()
2. 设实例化模型，设定模型的名字
from sklearn.calibration import CalibratedClassifierCV name = ["GaussianBayes","Logistic","Bayes+isotonic","Bayes+sigmoid"] gnb = GaussianNB() models = [gnb ,LR(C=1., solver='lbfgs',max_iter=3000,multi_class="auto") #定义两种校准方式 ,CalibratedClassifierCV(gnb, cv=2, method='isotonic') ,CalibratedClassifierCV(gnb, cv=2, method='sigmoid')]
3. 基于函数进行绘图
plot_calib(models,name,Xtrain,Xtest,Ytrain,Ytest)
4. 基于校准结果查看精确性的变化
gnb = GaussianNB().fit(Xtrain,Ytrain) gnb.score(Xtest,Ytest) brier_score_loss(Ytest,gnb.predict_proba(Xtest)[:,1],pos_label = 1) gnbisotonic = CalibratedClassifierCV(gnb, cv=2, method='isotonic').fit(Xtrain,Ytrain) gnbisotonic.score(Xtest,Ytest) brier_score_loss(Ytest,gnbisotonic.predict_proba(Xtest)[:,1],pos_label = 1)
5. 试试看对于SVC，哪种校准更有效呢？
name_svc = ["SVC","Logistic","SVC+isotonic","SVC+sigmoid"] svc = SVC(kernel = "linear",gamma=1) models_svc = [svc ,LR(C=1., solver='lbfgs',max_iter=3000,multi_class="auto") #依然定义两种校准方式 ,CalibratedClassifierCV(svc, cv=2, method='isotonic') ,CalibratedClassifierCV(svc, cv=2, method='sigmoid')] plot_calib(models_svc,name_svc,Xtrain,Xtest,Ytrain,Ytest)
name_svc = ["SVC","SVC+isotonic","SVC+sigmoid"] svc = SVC(kernel = "linear",gamma=1) models_svc = [svc ,CalibratedClassifierCV(svc, cv=2, method='isotonic') ,CalibratedClassifierCV(svc, cv=2, method='sigmoid')] for clf, name in zip(models_svc,name_svc): clf.fit(Xtrain,Ytrain) y_pred = clf.predict(Xtest) if hasattr(clf, "predict_proba"): prob_pos = clf.predict_proba(Xtest)[:, 1] else: prob_pos = clf.decision_function(Xtest) prob_pos = (prob_pos - prob_pos.min()) / (prob_pos.max() - prob_pos.min()) clf_score = brier_score_loss(Ytest, prob_pos, pos_label=y.max()) score = clf.score(Xtest,Ytest) print("{}:".format(name)) print(" Brier:{:.4f}".format(clf_score)) print(" Accuracy:{:.4f}".format(score))