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I am using Scikit-learn RFECV to select most significant features for a logistic regression using a Cross Validation. Assume X is a [n,x] dataframe of features, and y represents the response variable:
from sklearn.pipeline import make_pipeline
from sklearn.grid_search import GridSearchCV
from sklearn.cross_validation import StratifiedKFold
from sklearn import preprocessing
from sklearn.feature_selection import RFECV
import sklearn
import sklearn.linear_model as lm
import sklearn.grid_search as gs
# Create a logistic regression estimator
logreg = lm.LogisticRegression()
# Use RFECV to pick best features, using Stratified Kfold
rfecv = RFECV(estimator=logreg, cv=StratifiedKFold(y, 3), scoring='roc_auc')
# Fit the features to the response variable
rfecv.fit(X, y)
# Put the best features into new df X_new
X_new = rfecv.transform(X)
#
pipe = make_pipeline(preprocessing.StandardScaler(), lm.LogisticRegression())
# Define a range of hyper parameters for grid search
C_range = 10.**np.arange(-5, 1)
penalty_options = ['l1', 'l2']
skf = StratifiedKFold(y, 3)
param_grid = dict(logisticregression__C=C_range, logisticregression__penalty=penalty_options)
grid = GridSearchCV(pipe, param_grid, cv=skf, scoring='roc_auc')
grid.fit(X_new, y)
Two questions:
a) Is this the correct process for feature, hyper-parameter selection and fitting?
b) Where can I find the fitted coefficients for the selected features?
356
Is this the correct process for feature selection? This is ONE of the many ways of feature selection. Recursive feature elimination is an automated approach to this, others are listed in scikit.learn documentation. They have different pros and cons, and usually feature selection is best achieved by also involving common sense and trying models with different features. RFE is a quick way of selecting a good set of features, but does not necessarily give you the ultimately best. By the way, you don't need to build your StratifiedKFold separately. If you just set the cv parameter to cv=3, both RFECV and GridSearchCV will automatically use StratifiedKFold if the y values are binary or multiclass, which I'm assuming is most likely the case since you are using LogisticRegression. You can also combine
# Fit the features to the response variable rfecv.fit(X, y) # Put the best features into new df X_new X_new = rfecv.transform(X) into
X_new = rfecv.fit_transform(X, y) Is this the correct process for hyper-parameter selection? GridSearchCV is basically an automated way of systematically trying a whole set of combinations of model parameters and picking the best among these according to some performance metric. It's a good way of finding well-suited parameters, yes.
Is this the correct process for fitting? Yes, this is a valid way of fitting the model. When you call grid.fit(X_new, y), it makes a grid of LogisticRegression estimators (each with a set of parameters that are tried) and fits each of them. It will keep the one with the best performance under grid.best_estimator_, the parameters of this estimator in grid.best_params_ and the performance score for this estimator under grid.best_score_. It will return itself, and not the best estimator. Remember that with incoming new X values that you will use the model to predict on, you have to apply the transform with the fitted RFECV model. So, you can actually add this step to the pipeline as well.
Where can I find the fitted coefficients for the selected features? The grid.best_estimator_ attribute is a LogisticRegression object with all this information, so grid.best_estimator_.coef_ has all the coefficients (and grid.best_estimator_.intercept_ is the intercept). Note that to be able to get this grid.best_estimator_, the refit parameter on GridSearchCV needs to be set to True, but this is the default anyway.
178
Essentially, you need to do a train-validation-test split for your sample data. Where train set is used to tuned your normal params, validation set for tuning hyperparameters in grid search, and test set for performance evaluation. Here is one way to do this.
from sklearn.datasets import make_classification from sklearn.pipeline import make_pipeline from sklearn.grid_search import GridSearchCV from sklearn.cross_validation import StratifiedKFold from sklearn.preprocessing import StandardScaler from sklearn.feature_selection import RFECV from sklearn.linear_model import LogisticRegression from sklearn.metrics import classification_report import pandas as pd # simulate some artifical data so that I can show you the result of each intermediate step # 1000 obs, X dim 1000-by-100, 2 different y labels with unbalanced weights X, y = make_classification(n_samples=1000, n_features=100, n_informative=5, n_classes=2, weights=[0.1, 0.9]) X.shape Out[78]: (1000, 100) y.shape Out[79]: (1000,) # Nested Cross-Validation, this returns an train/test index interator split = StratifiedKFold(y, n_folds=5, shuffle=True, random_state=1) # to take a look at the split, you will see it has 5 tuples list(split) # the 1st fold train_index = list(split)[0][0] Out[80]: array([ 0, 1, 2, ..., 997, 998, 999]) test_index = list(split)[0][1] Out[81]: array([ 5, 12, 17, ..., 979, 982, 984]) # let's play with just one iteration for now # your pipe pipe = make_pipeline(StandardScaler(), LogisticRegression()) # set up params params_space = dict(logisticregression__C=10.0**np.arange(-5,1), logisticregression__penalty=['l1', 'l2'], logisticregression__class_weight=[None, 'auto']) # apply your grid search only in train data but with a futher cv step # so original train set has [gscv_train, gscv_validation] where the latter is used to tune hyperparameters # all performance is still evaluated in a separated held-out 'test' set grid = GridSearchCV(pipe, params_space, cv=StratifiedKFold(y[train_index], n_folds=3), scoring='roc_auc') # fit the data on train set grid.fit(X[train_index], y[train_index]) # to get the params of your estimator, call your gscv grid.best_estimator_ Out[82]: Pipeline(steps=[('standardscaler', StandardScaler(copy=True, with_mean=True, with_std=True)), ('logisticregression', LogisticRegression(C=0.10000000000000001, class_weight=None, dual=False, fit_intercept=True, intercept_scaling=1, max_iter=100, multi_class='ovr', penalty='l1', random_state=None, solver='liblinear', tol=0.0001, verbose=0))]) # the performance in validation set grid.grid_scores_ Out[83]: [mean: 0.50000, std: 0.00000, params: {'logisticregression__C': 1.0000000000000001e-05, 'logisticregression__class_weight': None, 'logisticregression__penalty': 'l1'}, mean: 0.87975, std: 0.01753, params: {'logisticregression__C': 1.0000000000000001e-05, 'logisticregression__class_weight': None, 'logisticregression__penalty': 'l2'}, mean: 0.50000, std: 0.00000, params: {'logisticregression__C': 1.0000000000000001e-05, 'logisticregression__class_weight': 'auto', 'logisticregression__penalty': 'l1'}, mean: 0.87985, std: 0.01746, params: {'logisticregression__C': 1.0000000000000001e-05, 'logisticregression__class_weight': 'auto', 'logisticregression__penalty': 'l2'}, mean: 0.50000, std: 0.00000, params: {'logisticregression__C': 0.0001, 'logisticregression__class_weight': None, 'logisticregression__penalty': 'l1'}, mean: 0.88033, std: 0.01707, params: {'logisticregression__C': 0.0001, 'logisticregression__class_weight': None, 'logisticregression__penalty': 'l2'}, mean: 0.50000, std: 0.00000, params: {'logisticregression__C': 0.0001, 'logisticregression__class_weight': 'auto', 'logisticregression__penalty': 'l1'}, mean: 0.87975, std: 0.01732, params: {'logisticregression__C': 0.0001, 'logisticregression__class_weight': 'auto', 'logisticregression__penalty': 'l2'}, mean: 0.50000, std: 0.00000, params: {'logisticregression__C': 0.001, 'logisticregression__class_weight': None, 'logisticregression__penalty': 'l1'}, mean: 0.88245, std: 0.01732, params: {'logisticregression__C': 0.001, 'logisticregression__class_weight': None, 'logisticregression__penalty': 'l2'}, mean: 0.50000, std: 0.00000, params: {'logisticregression__C': 0.001, 'logisticregression__class_weight': 'auto', 'logisticregression__penalty': 'l1'}, mean: 0.87955, std: 0.01686, params: {'logisticregression__C': 0.001, 'logisticregression__class_weight': 'auto', 'logisticregression__penalty': 'l2'}, mean: 0.50000, std: 0.00000, params: {'logisticregression__C': 0.01, 'logisticregression__class_weight': None, 'logisticregression__penalty': 'l1'}, mean: 0.88746, std: 0.02318, params: {'logisticregression__C': 0.01, 'logisticregression__class_weight': None, 'logisticregression__penalty': 'l2'}, mean: 0.50000, std: 0.00000, params: {'logisticregression__C': 0.01, 'logisticregression__class_weight': 'auto', 'logisticregression__penalty': 'l1'}, mean: 0.87990, std: 0.01634, params: {'logisticregression__C': 0.01, 'logisticregression__class_weight': 'auto', 'logisticregression__penalty': 'l2'}, mean: 0.94002, std: 0.02959, params: {'logisticregression__C': 0.10000000000000001, 'logisticregression__class_weight': None, 'logisticregression__penalty': 'l1'}, mean: 0.87419, std: 0.02174, params: {'logisticregression__C': 0.10000000000000001, 'logisticregression__class_weight': None, 'logisticregression__penalty': 'l2'}, mean: 0.93508, std: 0.03101, params: {'logisticregression__C': 0.10000000000000001, 'logisticregression__class_weight': 'auto', 'logisticregression__penalty': 'l1'}, mean: 0.87091, std: 0.01860, params: {'logisticregression__C': 0.10000000000000001, 'logisticregression__class_weight': 'auto', 'logisticregression__penalty': 'l2'}, mean: 0.88013, std: 0.03246, params: {'logisticregression__C': 1.0, 'logisticregression__class_weight': None, 'logisticregression__penalty': 'l1'}, mean: 0.85247, std: 0.02712, params: {'logisticregression__C': 1.0, 'logisticregression__class_weight': None, 'logisticregression__penalty': 'l2'}, mean: 0.88904, std: 0.02906, params: {'logisticregression__C': 1.0, 'logisticregression__class_weight': 'auto', 'logisticregression__penalty': 'l1'}, mean: 0.85197, std: 0.02097, params: {'logisticregression__C': 1.0, 'logisticregression__class_weight': 'auto', 'logisticregression__penalty': 'l2'}] # or the best score among them grid.best_score_ Out[84]: 0.94002188482393367 # now after finishing training the estimator, we now predict in test set y_pred = grid.predict(X[test_index]) # since LogisticRegression is probability based model, we have the luxury to get the propability for each obs y_pred_probs = grid.predict_proba(X[test_index]) Out[87]: array([[ 0.0632, 0.9368], [ 0.0236, 0.9764], [ 0.0227, 0.9773], ..., [ 0.0108, 0.9892], [ 0.2903, 0.7097], [ 0.0113, 0.9887]]) # to get evaluation result, print(classification_report(y[test_index], y_pred)) precision recall f1-score support 0 0.93 0.59 0.72 22 1 0.95 0.99 0.97 179 avg / total 0.95 0.95 0.95 201 # to put all things together with the nested cross-validation # generate a pandas dataframe to store prediction probability kfold_df = pd.DataFrame(0.0, index=np.arange(len(y)), columns=unique(y)) report = [] # to store classificaiton report split = StratifiedKFold(y, n_folds=5, shuffle=True, random_state=1) for train_index, test_index in split: grid = GridSearchCV(pipe, params_space, cv=StratifiedKFold(y[train_index], n_folds=3), scoring='roc_auc') grid.fit(X[train_index], y[train_index]) y_pred_probs = grid.predict_proba(X[test_index]) kfold_df.iloc[test_index, :] = y_pred_probs y_pred = grid.predict(X[test_index]) report.append(classification_report(y[test_index], y_pred)) # your result print(kfold_df) Out[88]: 0 1 0 0.1710 0.8290 1 0.0083 0.9917 2 0.2049 0.7951 3 0.0038 0.9962 4 0.0536 0.9464 5 0.0632 0.9368 6 0.1243 0.8757 7 0.1150 0.8850 8 0.0796 0.9204 9 0.4096 0.5904 .. ... ... 990 0.0505 0.9495 991 0.2128 0.7872 992 0.0270 0.9730 993 0.0434 0.9566 994 0.8078 0.1922 995 0.1452 0.8548 996 0.1372 0.8628 997 0.0127 0.9873 998 0.0935 0.9065 999 0.0065 0.9935 [1000 rows x 2 columns] for r in report: print(r) for r in report: print(r) precision recall f1-score support 0 0.93 0.59 0.72 22 1 0.95 0.99 0.97 179 avg / total 0.95 0.95 0.95 201 precision recall f1-score support 0 0.86 0.55 0.67 22 1 0.95 0.99 0.97 179 avg / total 0.94 0.94 0.93 201 precision recall f1-score support 0 0.89 0.38 0.53 21 1 0.93 0.99 0.96 179 avg / total 0.93 0.93 0.92 200 precision recall f1-score support 0 0.88 0.33 0.48 21 1 0.93 0.99 0.96 178 avg / total 0.92 0.92 0.91 199 precision recall f1-score support 0 0.88 0.33 0.48 21 1 0.93 0.99 0.96 178 avg / total 0.92 0.92 0.91 199 If you love us? 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