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--- code:model_selection [2015/10/05 13:25]
asa created
+++ code:model_selection [2015/10/05 15:01]
asa
@@ Line 20: / Line 20: @@
 </code>
+The simplest form of model evaluation uses a validation/test set:
+<code python>
+In [9]: X_train, X_test, y_train, y_test = cross_validation.train_test_split(X, y, test_size=0.4, random_state=0)
+In [10]: classifier = svm.SVC(kernel='linear', C=1).fit(X_train, y_train)
+In [11]: classifier.score(X_test, y_test)
+Out[11]: 0.7592592592592593
+</code>
+Next, let'd perform cross-validation:
+<code python>
+In [18]: cross_validation.cross_val_score(classifier, X, y, cv=5, scoring='accuracy')
+Out[18]: array([ 0.7962963 ,  0.83333333,  0.88888889,  0.83333333,  0.83333333])
+In [19]:
+In [19]: # you can obtain accuracy for other metrics, such as area under the roc curve:
+In [20]: cross_validation.cross_val_score(classifier, X, y, cv=5, scoring='roc_auc')
+Out[20]: array([ 0.89166667,  0.89166667,  0.95833333,  0.87638889,  0.91388889])
+In [21]:
+In [21]: # you can also obtain the predictions by cross-validation and then compute the accuracy:
+In [22]: y_predict = cross_validation.cross_val_predict(classifier, X, y, cv=5)
+In [23]: metrics.accuracy_score(y, y_predict)
+Out[23]: 0.83703703703703702
+</code>
+H ere's an alternative way of doing cross-validation.
+<code python>
+In [25]: # first divide the data into folds:
+In [26]: cv = cross_validation.StratifiedKFold(y, 5)
+In [27]: # now use these folds:
+In [28]: print cross_validation.cross_val_score(classifier, X, y, cv=cv, scoring='roc_auc')
+[ 0.89166667  0.89166667  0.95833333  0.87638889  0.91388889]
+In [29]: # you can see how examples were divided into folds by looking at the test_folds attribute:
+In [30]: print cv.test_folds
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2
+2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
+2 2 2 2 2 2 2 2 2 2 2 3 3 2 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
+3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4
+4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
+4 4 4 4 4 4 4 4 4 4]
+In [31]: # hmm... perhaps we should shuffle things a bit...
+In [32]: cv = cross_validation.StratifiedKFold(y, 5, shuffle=True)
+In [33]: print cv.test_folds
+[0 1 1 2 0 1 4 3 4 3 2 0 2 3 2 3 2 0 4 1 1 3 4 1 1 4 1 4 4 2 2 3 0 2 3 1 4
+3 2 0 2 0 1 3 2 0 0 2 3 0 4 2 0 4 3 4 1 1 0 3 2 4 3 2 3 1 1 1 1 4 3 1 1
+2 2 3 3 1 4 2 1 0 2 1 0 2 4 1 0 3 2 3 1 2 2 1 1 0 4 1 3 0 1 1 3 3 0 3 3
+2 0 2 0 2 4 0 1 0 4 4 1 1 0 4 0 1 4 4 3 1 3 3 2 4 3 4 2 4 3 4 1 4 2 0 3
+3 3 0 0 0 4 3 4 2 3 0 1 1 0 0 4 0 4 1 4 0 0 0 0 3 3 0 4 4 2 0 3 3 0 1 2
+2 3 2 1 3 4 4 4 1 1 4 2 1 0 3 1 2 0 0 0 0 2 3 4 3 2 0 0 4 1 3 2 2 0 1 2
+2 4 0 2 1 1 0 4 4 1 4 4 3 4 2 3 3 1 4 2 1 4 1 3 2 1 3 2 1 3 1 3 0 2 2 0
+4 2 2 4 3 3 0 2 0 2]
+In [34]: # if you run division into folds multiple times you will get a different answer:
+In [35]: cv = cross_validation.StratifiedKFold(y, 5, shuffle=True)
+In [36]: print cv.test_folds
+[3 0 2 2 0 2 2 4 1 4 0 2 3 4 2 0 4 0 3 3 4 0 2 0 4 4 0 1 4 4 3 4 1 2 3 3 1
+1 4 4 4 0 0 4 2 0 0 2 0 1 3 1 0 3 4 0 3 0 4 1 1 2 4 2 0 2 3 1 0 3 0 1 2
+2 4 0 0 0 1 4 3 2 2 4 3 1 3 2 0 2 0 0 3 2 1 2 4 4 0 0 4 2 1 4 3 0 4 3 4
+4 0 0 4 2 1 4 4 3 4 1 1 3 0 2 2 3 1 2 3 1 0 4 1 4 1 3 1 3 3 4 4 1 0 0 0
+4 3 1 2 2 3 0 3 2 4 3 2 2 3 0 3 1 0 4 2 3 0 2 4 3 0 4 3 4 3 3 0 3 1 2 2
+3 4 1 0 4 3 4 0 0 0 3 2 2 1 3 4 4 2 3 4 3 2 1 3 0 4 0 1 3 1 2 2 2 2 0 3
+1 1 2 0 1 4 1 1 1 2 2 1 2 3 3 1 4 4 3 4 2 0 2 2 1 1 1 2 0 3 0 2 1 1 3 1
+1 0 1 3 4 4 2 1 1 1]
+In [37]: # if you want to consistently get the same division into folds:
+In [38]: cv = cross_validation.StratifiedKFold(y, 5, shuffle=True, random_state=0)
+In [39]: # this sets the seed for the random number generator.
+</code>
+Let's do grid search for the optimal set of parameters:
+<code python>
+In [40]: from sklearn.grid_search import GridSearchCV
+In [41]: Cs = np.logspace(-2, 3, 6)
+In [42]: classifier = GridSearchCV(estimator=svm.LinearSVC(), param_grid=dict(C=Cs) )
+In [43]: classifier.fit(X, y)
+Out[43]:
+GridSearchCV(cv=None, error_score='raise',
+       estimator=LinearSVC(C=1.0, class_weight=None, dual=True, fit_intercept=True,
+     intercept_scaling=1, loss='squared_hinge', max_iter=1000,
+     multi_class='ovr', penalty='l2', random_state=None, tol=0.0001,
+     verbose=0),
+       fit_params={}, iid=True, loss_func=None, n_jobs=1,
+       param_grid={'C': array([  1.00000e-02,   1.00000e-01,   1.00000e+00,   1.00000e+01,
+.00000e+02,   1.00000e+03])},
+       pre_dispatch='2*n_jobs', refit=True, score_func=None, scoring=None,
+       verbose=0)
+In [44]:
+In [44]: # print the best accuracy, classifier and parameters:
+In [45]: print classifier.best_score_
+.844444444444
+In [46]: print classifier.best_estimator_
+LinearSVC(C=1.0, class_weight=None, dual=True, fit_intercept=True,
+     intercept_scaling=1, loss='squared_hinge', max_iter=1000,
+     multi_class='ovr', penalty='l2', random_state=None, tol=0.0001,
+     verbose=0)
+In [47]: print classifier.best_params_
+{'C': 1.0}
+n [48]: # performing nested cross validation:
+In [49]: print  cross_validation.cross_val_score(classifier, X, y, cv=5)
+[ 0.7962963   0.81481481  0.88888889  0.83333333  0.83333333]
+In [50]: # if we want to do grid search over multiple parameters:
+In [51]: param_grid = [
+   ....:   {'C': [1, 10, 100, 1000], 'kernel': ['linear']},
+   ....:   {'C': [1, 10, 100, 1000], 'gamma': [0.001, 0.0001], 'kernel': ['rbf']},
+   ....:  ]
+In [52]: classifier = GridSearchCV(estimator=svm.SVC(), param_grid=param_grid)
+In [53]: print cross_validation.cross_val_score(classifier, X, y, cv=5)
+[ 0.7962963   0.83333333  0.88888889  0.7962963   0.87037037]
+</code>

CS545 fall 2016

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