scikit-learn：3.3. Model evaluation: quantifying the quality of predictions

參考：http://scikit-learn.org/stable/modules/model_evaluation.html#scoring-parameter

三种方法评估模型的预測质量：

• Estimator score method: Estimators都有 score method作为默认的评估标准，不属于本节内容。详细參考不同estimators的文档。

• Scoring parameter: Model-evaluation toolsusing cross-validation (such
  as cross_validation.cross_val_score and grid_search.GridSearchCV)
  rely on an internal scoring strategy. 本节讨论The
  scoring parameter: defining model evaluation rules.（參考第一小节）
• Metric functions: The metrics module 能较全面评价预測质量，本节讨论Classification
  metrics, Multilabel
  ranking metrics, Regression
  metrics and Clustering
  metrics.（參考二、三、四、五小节）

最后介绍 Dummy estimators 。提供随机推測的策略，能够作为预測质量评价的baseline。

（參考第六小节）

See also

For “pairwise” metrics, between samples and not estimators or predictions, see the Pairwise
metrics, Affinities and Kernels section.

详细内容有时间再写。。

。

1、

The scoring parameter: defining model evaluation rules

Model selection and evaluation using tools, such as grid_search.GridSearchCV and cross_validation.cross_val_score,
take a scoring parameter
that controls what metric they apply to the estimators evaluated.

1）提前定义的标准

全部的scorer都是越大越好。因此mean_absolute_error and mean_squared_error（測量预測点离模型的距离）是负值。

Scoring	Function	Comment
Classification
‘accuracy’	metrics.accuracy_score
‘average_precision’	metrics.average_precision_score
‘f1’	metrics.f1_score	for binary targets
‘f1_micro’	metrics.f1_score	micro-averaged
‘f1_macro’	metrics.f1_score	macro-averaged
‘f1_weighted’	metrics.f1_score	weighted average
‘f1_samples’	metrics.f1_score	by multilabel sample
‘log_loss’	metrics.log_loss	requires predict_proba support
‘precision’ etc.	metrics.precision_score	suffixes apply as with ‘f1’
‘recall’ etc.	metrics.recall_score	suffixes apply as with ‘f1’
‘roc_auc’	metrics.roc_auc_score
Clustering
‘adjusted_rand_score’	metrics.adjusted_rand_score
Regression
‘mean_absolute_error’	metrics.mean_absolute_error
‘mean_squared_error’	metrics.mean_squared_error
‘median_absolute_error’	metrics.median_absolute_error
‘r2’	metrics.r2_score

给个样例：

>>> from sklearn import svm, cross_validation, datasets
>>> iris = datasets.load_iris()
>>> X, y = iris.data, iris.target
>>> model = svm.SVC()
>>> cross_validation.cross_val_score(model, X, y, scoring='wrong_choice')
Traceback (most recent call last):
ValueError: 'wrong_choice' is not a valid scoring value. Valid options are ['accuracy', 'adjusted_rand_score', 'average_precision', 'f1', 'f1_macro', 'f1_micro', 'f1_samples', 'f1_weighted', 'log_loss', 'mean_absolute_error', 'mean_squared_error', 'median_absolute_error', 'precision', 'precision_macro', 'precision_micro', 'precision_samples', 'precision_weighted', 'r2', 'recall', 'recall_macro', 'recall_micro', 'recall_samples', 'recall_weighted', 'roc_auc']
>>> clf = svm.SVC(probability=True, random_state=0)
>>> cross_validation.cross_val_score(clf, X, y, scoring='log_loss')
array([-0.07..., -0.16..., -0.06...])

3）自己定义scoring标准

following two rules:

• It can be called with parameters (estimator, X, y),
  where estimator is the model that should be evaluated, X is
  validation data, and y is the ground truth target for X (in
  the supervised case) or None (in the unsupervised case).
• It returns a floating point number that quantifies the estimator prediction
  quality on X, with reference to y.
  Again, by convention higher numbers are better, so if your scorer returns loss, that value should be negated.

2、

Classification metrics

The sklearn.metrics module
implements several loss, score, and utility functions to measure classification performance.

Some of these are restricted to the binary classification case:

matthews_corrcoef(y_true, y_pred)	Compute the Matthews correlation coefficient (MCC) for binary classes
precision_recall_curve(y_true, probas_pred)	Compute precision-recall pairs for different probability thresholds
roc_curve(y_true, y_score[, pos_label, ...])	Compute Receiver operating characteristic (ROC)

Others also work in the multiclass case:

confusion_matrix(y_true, y_pred[, labels])	Compute confusion matrix to evaluate the accuracy of a classification
hinge_loss(y_true, pred_decision[, labels, ...])	Average hinge loss (non-regularized)

Some also work in the multilabel case:

accuracy_score(y_true, y_pred[, normalize, ...])	Accuracy classification score.
classification_report(y_true, y_pred[, ...])	Build a text report showing the main classification metrics
f1_score(y_true, y_pred[, labels, ...])	Compute the F1 score, also known as balanced F-score or F-measure
fbeta_score(y_true, y_pred, beta[, labels, ...])	Compute the F-beta score
hamming_loss(y_true, y_pred[, classes])	Compute the average Hamming loss.
jaccard_similarity_score(y_true, y_pred[, ...])	Jaccard similarity coefficient score
log_loss(y_true, y_pred[, eps, normalize, ...])	Log loss, aka logistic loss or cross-entropy loss.
precision_recall_fscore_support(y_true, y_pred)	Compute precision, recall, F-measure and support for each class
precision_score(y_true, y_pred[, labels, ...])	Compute the precision
recall_score(y_true, y_pred[, labels, ...])	Compute the recall
zero_one_loss(y_true, y_pred[, normalize, ...])	Zero-one classification loss.

And some work with binary and multilabel (but not multiclass) problems:

average_precision_score(y_true, y_score[, ...])	Compute average precision (AP) from prediction scores
roc_auc_score(y_true, y_score[, average, ...])	Compute Area Under the Curve (AUC) from prediction scores

In the following sub-sections, we will describe each of those functions, preceded by some notes on common API and metric definition.

2）accuracy score：

The accuracy_score function
computes the accuracy,
默认是计算预測正确的比例，假设设置normalize=False。计算预測正确的绝对数量。给个样例就明确：

>>> import numpy as np
>>> from sklearn.metrics import accuracy_score
>>> y_pred = [0, 2, 1, 3]
>>> y_true = [0, 1, 2, 3]
>>> accuracy_score(y_true, y_pred)
0.5
>>> accuracy_score(y_true, y_pred, normalize=False)
2

对于multilabel classification，仅仅有所有的labels所有预測对。该sample才算预測对。

给个样例就明确：

>>> accuracy_score(np.array([[0, 1], [1, 1]]), np.ones((2, 2)))
0.5

再參考：

• See Test
  with permutations the significance of a classification score for an example of accuracy score usage using permutations of the dataset.

3）confusion
matrix：

The confusion_matrix function
evaluates classification accuracy by computing the confusion
matrix. 给个样例：

>>> from sklearn.metrics import confusion_matrix
>>> y_true = [2, 0, 2, 2, 0, 1]
>>> y_pred = [0, 0, 2, 2, 0, 2]
>>> confusion_matrix(y_true, y_pred)
array([[2, 0, 0],
       [0, 0, 1],
       [1, 0, 2]])

（注意：纵轴是true label，横轴是predict label）

再參考：

• See Confusion
  matrix for an example of using a confusion matrix to evaluate classifier output quality.
• See Recognizing
  hand-written digits for an example of using a confusion matrix to classify hand-written digits.
• See Classification
  of text documents using sparse features for an example of using a confusion matrix to classify text documents.

4）classification
report：

The classification_report function
builds a text report showing the main classification metrics. 给个样例：

>>> from sklearn.metrics import classification_report
>>> y_true = [0, 1, 2, 2, 0]
>>> y_pred = [0, 0, 2, 2, 0]
>>> target_names = ['class 0', 'class 1', 'class 2']
>>> print(classification_report(y_true, y_pred, target_names=target_names))
             precision    recall  f1-score   support

    class 0       0.67      1.00      0.80         2
    class 1       0.00      0.00      0.00         1
    class 2       1.00      1.00      1.00         2

avg / total       0.67      0.80      0.72         5

再參考：

• See Recognizing
  hand-written digits for an example of classification report usage for hand-written digits.
• See Classification
  of text documents using sparse features for an example of classification report usage for text documents.
• See Parameter
  estimation using grid search with cross-validation for an example of classification report usage for grid search with nested cross-validation.

以下的一些不经常使用，简单列出来。不做过多解释和翻译：

5）hamming
loss：

If  is
the predicted value for the -th
label of a given sample,  is
the corresponding true value, and  is
the number of classes or labels, then the Hamming loss  between
two samples is defined as:

6）jaccard
similarity coefficient score：

The Jaccard similarity coefficient of the -th samples,
with a ground truth label set  and predicted label set ,
is defined as

7）precision、recall、f-measures：

Several functions allow you to analyze the precision, recall and F-measures score:

average_precision_score(y_true, y_score[, ...])	Compute average precision (AP) from prediction scores
f1_score(y_true, y_pred[, labels, ...])	Compute the F1 score, also known as balanced F-score or F-measure
fbeta_score(y_true, y_pred, beta[, labels, ...])	Compute the F-beta score
precision_recall_curve(y_true, probas_pred)	Compute precision-recall pairs for different probability thresholds
precision_recall_fscore_support(y_true, y_pred)	Compute precision, recall, F-measure and support for each class
precision_score(y_true, y_pred[, labels, ...])	Compute the precision
recall_score(y_true, y_pred[, labels, ...])	Compute the recall

Note that the precision_recall_curve function
is restricted to the binary case. The average_precision_score function
works only in binary classification and multilabel indicator format.

8）hinge loss：

9）log loss：

10）matthews
correlation coefficient：

11）receiver
operating characteristic（ROC）：

12）zero one loss：

3、

Multilabel ranking metrics

In multilabel learning, each sample can have any number of ground truth labels associated with it. The goal is to give
high scores and better rank to the ground truth labels.

1）coverage error：

2）label ranking average precision：

4、

Regression metrics

The sklearn.metrics module
implements several loss, score, and utility functions to measure regression performance.

Some of those have been enhanced to handle the multioutput case: mean_absolute_error, mean_squared_error, median_absolute_error and r2_score.

1）explained variance score：

If  is
the estimated target output,  the
corresponding (correct) target output, and  is Variance,
the square of the standard deviation, then the explained variance is estimated as follow:

2）mean absolute error：

If  is
the predicted value of the -th
sample, and  is
the corresponding true value, then the mean absolute error (MAE) estimated over  is
defined as

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3）mean squared error：

If  is
the predicted value of the -th
sample, and  is
the corresponding true value, then the mean squared error (MSE) estimated over  is
defined as

4）R^2 score、the coefficient of determination：

If  is
the predicted value of the -th
sample and  is
the corresponding true value, then the score R² estimated over  is
defined as

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5、

Clustering metrics

The sklearn.metrics module
implements several loss, score, and utility functions. For more information see the Clustering
performance evaluation section for instance clustering, and Biclustering
evaluation for biclustering.

6、Dummy estimators

对于supervised learning。使用随机产生的结果作为baseline是非常easy的对照。

DummyClassifier提供了产生随机结果的简单的策略：

• stratified generates random predictions by respecting the training set class distribution.

• most_frequent always predicts the most frequent label in the training set.

• uniform generates predictions uniformly at random.

• constant always predicts a constant label that is provided by the user.（A
  major motivation of this method is F1-scoring, when the positive class is in the minority.）

Note that with all these strategies, the predict method completely ignores the input data!

给个简单样例：

first let’s create an imbalanced dataset:

>>>

>>> from sklearn.datasets import load_iris
>>> from sklearn.cross_validation import train_test_split
>>> iris = load_iris()
>>> X, y = iris.data, iris.target
>>> y[y != 1] = -1
>>> X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)

Next, let’s compare the accuracy of SVC and most_frequent:

>>>

>>> from sklearn.dummy import DummyClassifier
>>> from sklearn.svm import SVC
>>> clf = SVC(kernel='linear', C=1).fit(X_train, y_train)
>>> clf.score(X_test, y_test)
0.63...
>>> clf = DummyClassifier(strategy='most_frequent',random_state=0)
>>> clf.fit(X_train, y_train)
DummyClassifier(constant=None, random_state=0, strategy='most_frequent')
>>> clf.score(X_test, y_test)
0.57...

We see that SVC doesn’t do much better than a dummy classifier. Now, let’s change the kernel:

>>>

>>> clf = SVC(kernel='rbf', C=1).fit(X_train, y_train)
>>> clf.score(X_test, y_test)
0.97...

同理，对于回归问题：

DummyRegressor also
implements four simple rules of thumb for regression:

• mean always predicts the mean of the training targets.
• median always predicts the median of the training targets.
• quantile always predicts a user provided quantile of the training targets.
• constant always predicts a constant value that is provided by the user.

In all these strategies, the predict method completely ignores the input data.