sklearn LogisticRegression and changing the default threshold for classification

Question

I am using LogisticRegression from the sklearn package, and have a quick question about classification. I built a ROC curve for my classifier, and it turns out that the optimal threshold for my training data is around 0.25. I'm assuming that the default threshold when creating predictions is 0.5. How can I change this default setting to find out what the accuracy is in my model when doing a 10-fold cross-validation? Basically, I want my model to predict a '1' for anyone greater than 0.25, not 0.5. I've been looking through all the documentation, and I can't seem to get anywhere.

Thanks in advance for your help.

Answer 1

That is not a built-in feature. You can "add" it by wrapping the LogisticRegression class in your own class, and adding a threshold attribute which you use inside a custom predict() method.

However, some cautions:

1. The default threshold is actually 0. LogisticRegression.decision_function() returns a signed distance to the selected separation hyperplane. If you are looking at predict_proba(), then you are looking at logit() of the hyperplane distance with a threshold of 0.5. But that's more expensive to compute.
2. By selecting the "optimal" threshold like this, you are utilizing information post-learning, which spoils your test set (i.e., your test or validation set no longer provides an unbiased estimate of out-of-sample error). You may therefore be inducing additional over-fitting unless you choose the threshold inside a cross-validation loop on your training set only, then use it and the trained classifier with your test set.
3. Consider using class_weight if you have an unbalanced problem rather than manually setting the threshold. This should force the classifier to choose a hyperplane farther away from the class of serious interest.

Answer 2

I would like to give a practical answer

from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import accuracy_score, confusion_matrix, recall_score, roc_auc_score, precision_score

X, y = make_classification(
    n_classes=2, class_sep=1.5, weights=[0.9, 0.1],
    n_features=20, n_samples=1000, random_state=10
)

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.33, random_state=42)

clf = LogisticRegression(class_weight="balanced")
clf.fit(X_train, y_train)
THRESHOLD = 0.25
preds = np.where(clf.predict_proba(X_test)[:,1] > THRESHOLD, 1, 0)

pd.DataFrame(data=[accuracy_score(y_test, preds), recall_score(y_test, preds),
                   precision_score(y_test, preds), roc_auc_score(y_test, preds)], 
             index=["accuracy", "recall", "precision", "roc_auc_score"])

By changing the THRESHOLD to 0.25, one can find that recall and precision scores are decreasing. However, by removing the class_weight argument, the accuracy increases but the recall score falls down. Refer to the @accepted answer

Answer 3

Special case: one-dimensional logistic regression

The value separating the regions where a sample X is labeled as 1 and where it is labeled 0 is calculated using the formula:

from scipy.special import logit
thresh = 0.1
val = (logit(thresh)-clf.intercept_)/clf.coef_[0]

Thus, the predictions can be calculated more directly with

preds = np.where(X>val, 1, 0)

Answer 4

For the sake of completeness, I would like to mention another way to elegantly generate predictions based on scikit's probability computations using binarize:

import numpy as np
from sklearn.preprocessing import binarize

THRESHOLD = 0.25

# This probabilities would come from logistic_regression.predict_proba()
y_logistic_prob =  np.random.uniform(size=10)

predictions = binarize(y_logistic_prob.reshape(-1, 1), THRESHOLD).ravel()

Furthermore, I agree with the considerations that Andreus makes, specially 2 and 3. Be sure to keep an eye for them.