二元分类器中的阈值
Threshold values in binary classifiers
我试图了解 decision_function 和 predict_proba 在二进制分类器中的用法，并遇到了 precision_recall_curve
中的阈值
现在给出decision_function计算到超平面的距离，predict_proba给出数据点属于某个组的概率。
precision_recall_curve returns 具有不同阈值的阈值数组。
如果阈值是这些数据点分类的概率，那么阈值如何取负值或小于0或大于1的值。
另外，我们用什么来微调我们的二元分类器？ decision_function 或 predict_proba ?
示例：
from sklearn.metrics import precision_recall_curve
precision, recall, thresholds = precision_recall_curve(y_test, y_scores_lr)
closest_zero = np.argmin(np.abs(thresholds))
closest_zero_p = precision[closest_zero]
closest_zero_r = recall[closest_zero]
print('Thresholds are',thresholds)
这里的阈值为
Thresholds are [ -4.04847662 -3.93819545 -3.48628627 -3.44776445 -3.33892603
-2.5783356 -2.37746137 -2.34718536 -2.30446832 -2.15792885
-2.03386685 -1.87131487 -1.7495844 -1.72691524 -1.68712543
-1.47668716 -1.33979401 -1.3051061 -1.08033549 -0.57099832
0.13088342 0.17583273 0.47631823 0.6418365 1.00422797
1.33670725 1.68203683 1.69861005 1.87908244 2.18989765
2.43420944 2.55168221 3.71752409 3.80620565 4.21070117
4.25093438 4.30966876 4.31558393 4.55321241 4.57143325
4.93002949 5.23271557 5.73378353 6.12856799 6.55341039
6.86404167 6.92400179 7.22184672 7.37403798 7.80959453
8.26212674 8.3930213 8.45858117 9.84572083 9.87342932
10.201736 11.20681116 11.4821926 11.55476419 11.68009017
13.26095216 14.73832302 16.02811865]
所以如果它们是概率值，它们怎么不在 0 到 1 的范围内，这些 decision_function 值还是其他值？
precision_recall_curve 为您提供二进制 class 运算符在特定阈值下的精度和召回值。这假设您正在查看某个 class 的概率。拟合后，您可以通过 predict_proba(self, X) 函数获得概率。每个 class 一个概率。对于二进制 classifier，这当然是两个 classes。这与 predict(self, X) 形成对比，它本质上让您知道某些 class 的概率是否为 > 0.5，然后 returns 是否为 class。我猜您想做的是以理想的方式选择此阈值（默认情况下为 0.5）以优化 f 分数、召回率或精度。这可以通过使用上面提到的 precision_recall_curve 函数来实现。
下面的例子展示了它是如何完成的。
import numpy as np
from sklearn.linear_model import LogisticRegression
from sklearn.datasets import load_iris
from sklearn.metrics import precision_recall_curve
X, y = load_iris(return_X_y=True)
# reduce multiclass to binary problem, i.e. class 0 or 1 (class 2 starts at index 100)
X = X[0:100]
y = y[0:100]
lr = LogisticRegression(random_state=0).fit(X, y)
y_test_hat = lr.predict_proba(X)
# just look at probabilities for class 1
y_test_hat_class_1 = y_test_hat[:,1]
precisions, recalls, thresholds = precision_recall_curve(y, y_test_hat_class_1)
f_scores = np.nan_to_num((2 * precisions * recalls) / (precisions + recalls))
for p, r, f, t in zip(precisions, recalls, f_scores, thresholds):
print('Using threshold={} as decision boundary, we reach '
'precision={}, recall={}, and f-score={}'.format(t, p, r, f))
f_max_index = np.argmax(f_scores)
max_f_score = f_scores[f_max_index]
max_f_score_threshold = thresholds[f_max_index]
print('The threshold for the max f-score is {}'.format(max_f_score_threshold))
导致：
Using threshold=0.8628645363798557 as decision boundary, we reach precision=1.0, recall=1.0, and f-score=1.0
Using threshold=0.9218669507660147 as decision boundary, we reach precision=1.0, recall=0.98, and f-score=0.98989898989899
Using threshold=0.93066642297958 as decision boundary, we reach precision=1.0, recall=0.96, and f-score=0.9795918367346939
Using threshold=0.9332685743944795 as decision boundary, we reach precision=1.0, recall=0.94, and f-score=0.9690721649484536
Using threshold=0.9395382533408563 as decision boundary, we reach precision=1.0, recall=0.92, and f-score=0.9583333333333334
Using threshold=0.9640718757241656 as decision boundary, we reach precision=1.0, recall=0.9, and f-score=0.9473684210526316
Using threshold=0.9670374623286897 as decision boundary, we reach precision=1.0, recall=0.88, and f-score=0.9361702127659575
Using threshold=0.9687934720210198 as decision boundary, we reach precision=1.0, recall=0.86, and f-score=0.924731182795699
Using threshold=0.9726392263137621 as decision boundary, we reach precision=1.0, recall=0.84, and f-score=0.9130434782608696
Using threshold=0.973775627114333 as decision boundary, we reach precision=1.0, recall=0.82, and f-score=0.9010989010989011
Using threshold=0.9740474969329987 as decision boundary, we reach precision=1.0, recall=0.8, and f-score=0.888888888888889
Using threshold=0.9741603105458991 as decision boundary, we reach precision=1.0, recall=0.78, and f-score=0.8764044943820225
Using threshold=0.9747085542467909 as decision boundary, we reach precision=1.0, recall=0.76, and f-score=0.8636363636363636
Using threshold=0.974749494774799 as decision boundary, we reach precision=1.0, recall=0.74, and f-score=0.8505747126436781
Using threshold=0.9769993303678443 as decision boundary, we reach precision=1.0, recall=0.72, and f-score=0.8372093023255813
Using threshold=0.9770140294088295 as decision boundary, we reach precision=1.0, recall=0.7, and f-score=0.8235294117647058
Using threshold=0.9785921201646789 as decision boundary, we reach precision=1.0, recall=0.68, and f-score=0.8095238095238095
Using threshold=0.9786461690308931 as decision boundary, we reach precision=1.0, recall=0.66, and f-score=0.7951807228915663
Using threshold=0.9789411518223052 as decision boundary, we reach precision=1.0, recall=0.64, and f-score=0.7804878048780487
Using threshold=0.9796555988114017 as decision boundary, we reach precision=1.0, recall=0.62, and f-score=0.7654320987654321
Using threshold=0.9801649093623934 as decision boundary, we reach precision=1.0, recall=0.6, and f-score=0.7499999999999999
Using threshold=0.9805566289582609 as decision boundary, we reach precision=1.0, recall=0.58, and f-score=0.7341772151898733
Using threshold=0.9808560894443067 as decision boundary, we reach precision=1.0, recall=0.56, and f-score=0.717948717948718
Using threshold=0.982400866419342 as decision boundary, we reach precision=1.0, recall=0.54, and f-score=0.7012987012987013
Using threshold=0.9828790909959155 as decision boundary, we reach precision=1.0, recall=0.52, and f-score=0.6842105263157895
Using threshold=0.9828854909335458 as decision boundary, we reach precision=1.0, recall=0.5, and f-score=0.6666666666666666
Using threshold=0.9839851081942663 as decision boundary, we reach precision=1.0, recall=0.48, and f-score=0.6486486486486487
Using threshold=0.9845312460821358 as decision boundary, we reach precision=1.0, recall=0.46, and f-score=0.6301369863013699
Using threshold=0.9857012993403023 as decision boundary, we reach precision=1.0, recall=0.44, and f-score=0.6111111111111112
Using threshold=0.9879940756602601 as decision boundary, we reach precision=1.0, recall=0.42, and f-score=0.5915492957746479
Using threshold=0.9882223190984861 as decision boundary, we reach precision=1.0, recall=0.4, and f-score=0.5714285714285715
Using threshold=0.9889482842475497 as decision boundary, we reach precision=1.0, recall=0.38, and f-score=0.5507246376811594
Using threshold=0.9892545856218082 as decision boundary, we reach precision=1.0, recall=0.36, and f-score=0.5294117647058824
Using threshold=0.9899303560728386 as decision boundary, we reach precision=1.0, recall=0.34, and f-score=0.5074626865671642
Using threshold=0.9905455482163618 as decision boundary, we reach precision=1.0, recall=0.32, and f-score=0.48484848484848486
Using threshold=0.9907019104721698 as decision boundary, we reach precision=1.0, recall=0.3, and f-score=0.4615384615384615
Using threshold=0.9911493537429485 as decision boundary, we reach precision=1.0, recall=0.28, and f-score=0.43750000000000006
Using threshold=0.9914230947944308 as decision boundary, we reach precision=1.0, recall=0.26, and f-score=0.41269841269841273
Using threshold=0.9915673581329265 as decision boundary, we reach precision=1.0, recall=0.24, and f-score=0.3870967741935484
Using threshold=0.9919835313724615 as decision boundary, we reach precision=1.0, recall=0.22, and f-score=0.36065573770491804
Using threshold=0.9925274516087134 as decision boundary, we reach precision=1.0, recall=0.2, and f-score=0.33333333333333337
Using threshold=0.9926276253093826 as decision boundary, we reach precision=1.0, recall=0.18, and f-score=0.3050847457627119
Using threshold=0.9930234956465036 as decision boundary, we reach precision=1.0, recall=0.16, and f-score=0.2758620689655173
Using threshold=0.9931758599517743 as decision boundary, we reach precision=1.0, recall=0.14, and f-score=0.24561403508771928
Using threshold=0.9935881899997894 as decision boundary, we reach precision=1.0, recall=0.12, and f-score=0.21428571428571425
Using threshold=0.9946684285206863 as decision boundary, we reach precision=1.0, recall=0.1, and f-score=0.18181818181818182
Using threshold=0.9960976336416663 as decision boundary, we reach precision=1.0, recall=0.08, and f-score=0.14814814814814814
Using threshold=0.996289803123931 as decision boundary, we reach precision=1.0, recall=0.06, and f-score=0.11320754716981131
Using threshold=0.9975518299472802 as decision boundary, we reach precision=1.0, recall=0.04, and f-score=0.07692307692307693
Using threshold=0.998322588642525 as decision boundary, we reach precision=1.0, recall=0.02, and f-score=0.0392156862745098
The threshold for the max f-score is 0.8628645363798557
此示例还会计算您用于最大化 f 分数的阈值。
有关 decision_function 的更多信息，请参阅 this answer 上的统计信息。
我试图了解 decision_function 和 predict_proba 在二进制分类器中的用法，并遇到了 precision_recall_curve
现在给出decision_function计算到超平面的距离，predict_proba给出数据点属于某个组的概率。
precision_recall_curve returns 具有不同阈值的阈值数组。
如果阈值是这些数据点分类的概率，那么阈值如何取负值或小于0或大于1的值。
另外，我们用什么来微调我们的二元分类器？ decision_function 或 predict_proba ?
示例：
from sklearn.metrics import precision_recall_curve
precision, recall, thresholds = precision_recall_curve(y_test, y_scores_lr)
closest_zero = np.argmin(np.abs(thresholds))
closest_zero_p = precision[closest_zero]
closest_zero_r = recall[closest_zero]
print('Thresholds are',thresholds)
这里的阈值为
Thresholds are [ -4.04847662 -3.93819545 -3.48628627 -3.44776445 -3.33892603
-2.5783356 -2.37746137 -2.34718536 -2.30446832 -2.15792885
-2.03386685 -1.87131487 -1.7495844 -1.72691524 -1.68712543
-1.47668716 -1.33979401 -1.3051061 -1.08033549 -0.57099832
0.13088342 0.17583273 0.47631823 0.6418365 1.00422797
1.33670725 1.68203683 1.69861005 1.87908244 2.18989765
2.43420944 2.55168221 3.71752409 3.80620565 4.21070117
4.25093438 4.30966876 4.31558393 4.55321241 4.57143325
4.93002949 5.23271557 5.73378353 6.12856799 6.55341039
6.86404167 6.92400179 7.22184672 7.37403798 7.80959453
8.26212674 8.3930213 8.45858117 9.84572083 9.87342932
10.201736 11.20681116 11.4821926 11.55476419 11.68009017
13.26095216 14.73832302 16.02811865]
所以如果它们是概率值，它们怎么不在 0 到 1 的范围内，这些 decision_function 值还是其他值？
precision_recall_curve 为您提供二进制 class 运算符在特定阈值下的精度和召回值。这假设您正在查看某个 class 的概率。拟合后，您可以通过 predict_proba(self, X) 函数获得概率。每个 class 一个概率。对于二进制 classifier，这当然是两个 classes。这与 predict(self, X) 形成对比，它本质上让您知道某些 class 的概率是否为 > 0.5，然后 returns 是否为 class。我猜您想做的是以理想的方式选择此阈值（默认情况下为 0.5）以优化 f 分数、召回率或精度。这可以通过使用上面提到的 precision_recall_curve 函数来实现。
下面的例子展示了它是如何完成的。
import numpy as np
from sklearn.linear_model import LogisticRegression
from sklearn.datasets import load_iris
from sklearn.metrics import precision_recall_curve
X, y = load_iris(return_X_y=True)
# reduce multiclass to binary problem, i.e. class 0 or 1 (class 2 starts at index 100)
X = X[0:100]
y = y[0:100]
lr = LogisticRegression(random_state=0).fit(X, y)
y_test_hat = lr.predict_proba(X)
# just look at probabilities for class 1
y_test_hat_class_1 = y_test_hat[:,1]
precisions, recalls, thresholds = precision_recall_curve(y, y_test_hat_class_1)
f_scores = np.nan_to_num((2 * precisions * recalls) / (precisions + recalls))
for p, r, f, t in zip(precisions, recalls, f_scores, thresholds):
print('Using threshold={} as decision boundary, we reach '
'precision={}, recall={}, and f-score={}'.format(t, p, r, f))
f_max_index = np.argmax(f_scores)
max_f_score = f_scores[f_max_index]
max_f_score_threshold = thresholds[f_max_index]
print('The threshold for the max f-score is {}'.format(max_f_score_threshold))
导致：
Using threshold=0.8628645363798557 as decision boundary, we reach precision=1.0, recall=1.0, and f-score=1.0
Using threshold=0.9218669507660147 as decision boundary, we reach precision=1.0, recall=0.98, and f-score=0.98989898989899
Using threshold=0.93066642297958 as decision boundary, we reach precision=1.0, recall=0.96, and f-score=0.9795918367346939
Using threshold=0.9332685743944795 as decision boundary, we reach precision=1.0, recall=0.94, and f-score=0.9690721649484536
Using threshold=0.9395382533408563 as decision boundary, we reach precision=1.0, recall=0.92, and f-score=0.9583333333333334
Using threshold=0.9640718757241656 as decision boundary, we reach precision=1.0, recall=0.9, and f-score=0.9473684210526316
Using threshold=0.9670374623286897 as decision boundary, we reach precision=1.0, recall=0.88, and f-score=0.9361702127659575
Using threshold=0.9687934720210198 as decision boundary, we reach precision=1.0, recall=0.86, and f-score=0.924731182795699
Using threshold=0.9726392263137621 as decision boundary, we reach precision=1.0, recall=0.84, and f-score=0.9130434782608696
Using threshold=0.973775627114333 as decision boundary, we reach precision=1.0, recall=0.82, and f-score=0.9010989010989011
Using threshold=0.9740474969329987 as decision boundary, we reach precision=1.0, recall=0.8, and f-score=0.888888888888889
Using threshold=0.9741603105458991 as decision boundary, we reach precision=1.0, recall=0.78, and f-score=0.8764044943820225
Using threshold=0.9747085542467909 as decision boundary, we reach precision=1.0, recall=0.76, and f-score=0.8636363636363636
Using threshold=0.974749494774799 as decision boundary, we reach precision=1.0, recall=0.74, and f-score=0.8505747126436781
Using threshold=0.9769993303678443 as decision boundary, we reach precision=1.0, recall=0.72, and f-score=0.8372093023255813
Using threshold=0.9770140294088295 as decision boundary, we reach precision=1.0, recall=0.7, and f-score=0.8235294117647058
Using threshold=0.9785921201646789 as decision boundary, we reach precision=1.0, recall=0.68, and f-score=0.8095238095238095
Using threshold=0.9786461690308931 as decision boundary, we reach precision=1.0, recall=0.66, and f-score=0.7951807228915663
Using threshold=0.9789411518223052 as decision boundary, we reach precision=1.0, recall=0.64, and f-score=0.7804878048780487
Using threshold=0.9796555988114017 as decision boundary, we reach precision=1.0, recall=0.62, and f-score=0.7654320987654321
Using threshold=0.9801649093623934 as decision boundary, we reach precision=1.0, recall=0.6, and f-score=0.7499999999999999
Using threshold=0.9805566289582609 as decision boundary, we reach precision=1.0, recall=0.58, and f-score=0.7341772151898733
Using threshold=0.9808560894443067 as decision boundary, we reach precision=1.0, recall=0.56, and f-score=0.717948717948718
Using threshold=0.982400866419342 as decision boundary, we reach precision=1.0, recall=0.54, and f-score=0.7012987012987013
Using threshold=0.9828790909959155 as decision boundary, we reach precision=1.0, recall=0.52, and f-score=0.6842105263157895
Using threshold=0.9828854909335458 as decision boundary, we reach precision=1.0, recall=0.5, and f-score=0.6666666666666666
Using threshold=0.9839851081942663 as decision boundary, we reach precision=1.0, recall=0.48, and f-score=0.6486486486486487
Using threshold=0.9845312460821358 as decision boundary, we reach precision=1.0, recall=0.46, and f-score=0.6301369863013699
Using threshold=0.9857012993403023 as decision boundary, we reach precision=1.0, recall=0.44, and f-score=0.6111111111111112
Using threshold=0.9879940756602601 as decision boundary, we reach precision=1.0, recall=0.42, and f-score=0.5915492957746479
Using threshold=0.9882223190984861 as decision boundary, we reach precision=1.0, recall=0.4, and f-score=0.5714285714285715
Using threshold=0.9889482842475497 as decision boundary, we reach precision=1.0, recall=0.38, and f-score=0.5507246376811594
Using threshold=0.9892545856218082 as decision boundary, we reach precision=1.0, recall=0.36, and f-score=0.5294117647058824
Using threshold=0.9899303560728386 as decision boundary, we reach precision=1.0, recall=0.34, and f-score=0.5074626865671642
Using threshold=0.9905455482163618 as decision boundary, we reach precision=1.0, recall=0.32, and f-score=0.48484848484848486
Using threshold=0.9907019104721698 as decision boundary, we reach precision=1.0, recall=0.3, and f-score=0.4615384615384615
Using threshold=0.9911493537429485 as decision boundary, we reach precision=1.0, recall=0.28, and f-score=0.43750000000000006
Using threshold=0.9914230947944308 as decision boundary, we reach precision=1.0, recall=0.26, and f-score=0.41269841269841273
Using threshold=0.9915673581329265 as decision boundary, we reach precision=1.0, recall=0.24, and f-score=0.3870967741935484
Using threshold=0.9919835313724615 as decision boundary, we reach precision=1.0, recall=0.22, and f-score=0.36065573770491804
Using threshold=0.9925274516087134 as decision boundary, we reach precision=1.0, recall=0.2, and f-score=0.33333333333333337
Using threshold=0.9926276253093826 as decision boundary, we reach precision=1.0, recall=0.18, and f-score=0.3050847457627119
Using threshold=0.9930234956465036 as decision boundary, we reach precision=1.0, recall=0.16, and f-score=0.2758620689655173
Using threshold=0.9931758599517743 as decision boundary, we reach precision=1.0, recall=0.14, and f-score=0.24561403508771928
Using threshold=0.9935881899997894 as decision boundary, we reach precision=1.0, recall=0.12, and f-score=0.21428571428571425
Using threshold=0.9946684285206863 as decision boundary, we reach precision=1.0, recall=0.1, and f-score=0.18181818181818182
Using threshold=0.9960976336416663 as decision boundary, we reach precision=1.0, recall=0.08, and f-score=0.14814814814814814
Using threshold=0.996289803123931 as decision boundary, we reach precision=1.0, recall=0.06, and f-score=0.11320754716981131
Using threshold=0.9975518299472802 as decision boundary, we reach precision=1.0, recall=0.04, and f-score=0.07692307692307693
Using threshold=0.998322588642525 as decision boundary, we reach precision=1.0, recall=0.02, and f-score=0.0392156862745098
The threshold for the max f-score is 0.8628645363798557
此示例还会计算您用于最大化 f 分数的阈值。
有关 decision_function 的更多信息，请参阅 this answer 上的统计信息。