分类器的概率校准简介

代码实现[Python]

# -*- coding: utf-8 -*- 
print(__doc__)

# Author: Mathieu Blondel 
#         Alexandre Gramfort 
#         Balazs Kegl 
#         Jan Hendrik Metzen 
# License: BSD Style.

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm

from sklearn.datasets import make_blobs
from sklearn.naive_bayes import GaussianNB
from sklearn.metrics import brier_score_loss
from sklearn.calibration import CalibratedClassifierCV
from sklearn.model_selection import train_test_split


n_samples = 50000
n_bins = 3  # use 3 bins for calibration_curve as we have 3 clusters here

# Generate 3 blobs with 2 classes where the second blob contains
# half positive samples and half negative samples. Probability in this
# blob is therefore 0.5.
centers = [(-5, -5), (0, 0), (5, 5)]
X, y = make_blobs(n_samples=n_samples, n_features=2, cluster_std=1.0,
                  centers=centers, shuffle=False, random_state=42)

y[:n_samples // 2] = 0
y[n_samples // 2:] = 1
sample_weight = np.random.RandomState(42).rand(y.shape[0])

# 为校准切分训练集和测试集
X_train, X_test, y_train, y_test, sw_train, sw_test = \
    train_test_split(X, y, sample_weight, test_size=0.9, random_state=42)

# 未校准的高斯朴素贝叶斯
clf = GaussianNB()
clf.fit(X_train, y_train)  # GaussianNB itself does not support sample-weights
prob_pos_clf = clf.predict_proba(X_test)[:, 1]

# 使用等渗校准的高斯朴素贝叶斯
clf_isotonic = CalibratedClassifierCV(clf, cv=2, method='isotonic')
clf_isotonic.fit(X_train, y_train, sw_train)
prob_pos_isotonic = clf_isotonic.predict_proba(X_test)[:, 1]

# 使用sigmoid校准(S校准)的高斯朴素贝叶斯
clf_sigmoid = CalibratedClassifierCV(clf, cv=2, method='sigmoid')
clf_sigmoid.fit(X_train, y_train, sw_train)
prob_pos_sigmoid = clf_sigmoid.predict_proba(X_test)[:, 1]

print("Brier scores: (the smaller the better)")

clf_score = brier_score_loss(y_test, prob_pos_clf, sw_test)
print("No calibration: %1.3f" % clf_score)

clf_isotonic_score = brier_score_loss(y_test, prob_pos_isotonic, sw_test)
print("With isotonic calibration: %1.3f" % clf_isotonic_score)

clf_sigmoid_score = brier_score_loss(y_test, prob_pos_sigmoid, sw_test)
print("With sigmoid calibration: %1.3f" % clf_sigmoid_score)

# #############################################################################
# 绘制数据和预测的概率
plt.figure()
y_unique = np.unique(y)
colors = cm.rainbow(np.linspace(0.0, 1.0, y_unique.size))
for this_y, color in zip(y_unique, colors):
    this_X = X_train[y_train == this_y]
    this_sw = sw_train[y_train == this_y]
    plt.scatter(this_X[:, 0], this_X[:, 1], s=this_sw * 50,
                c=color[np.newaxis, :],
                alpha=0.5, edgecolor='k',
                label="Class %s" % this_y)
plt.legend(loc="best")
plt.title("Data")

plt.figure()
order = np.lexsort((prob_pos_clf, ))
plt.plot(prob_pos_clf[order], 'r', label='No calibration (%1.3f)' % clf_score)
plt.plot(prob_pos_isotonic[order], 'g', linewidth=3,
         label='Isotonic calibration (%1.3f)' % clf_isotonic_score)
plt.plot(prob_pos_sigmoid[order], 'b', linewidth=3,
         label='Sigmoid calibration (%1.3f)' % clf_sigmoid_score)
plt.plot(np.linspace(0, y_test.size, 51)[1::2],
         y_test[order].reshape(25, -1).mean(1),
         'k', linewidth=3, label=r'Empirical')
plt.ylim([-0.05, 1.05])
plt.xlabel("Instances sorted according to predicted probability "
           "(uncalibrated GNB)")
plt.ylabel("P(y=1)")
plt.legend(loc="upper left")
plt.title("Gaussian naive Bayes probabilities")

plt.show()

代码执行

代码运行时间大约:0分0.108秒。
运行代码输出的文本内容如下:

Brier scores: (the smaller the better)
No calibration: 0.104
With isotonic calibration: 0.084
With sigmoid calibration: 0.109

运行代码输出的图片内容如下:

源码下载

• Python版源码文件: plot_calibration.py
• Jupyter Notebook版源码文件: plot_calibration.ipynb

参考资料

• Probability calibration of classifiers