Controlling the threshold in Logistic Regression in Scikit Learn

Question

I am using the LogisticRegression() method in scikit-learn on a highly unbalanced data set. I have even turned the class_weight feature to auto.

I know that in Logistic Regression it should be possible to know what is the threshold value for a particular pair of classes.

Is it possible to know what the threshold value is in each of the One-vs-All classes the LogisticRegression() method designs?

I did not find anything in the documentation page.

Does it by default apply the 0.5 value as threshold for all the classes regardless of the parameter values?

Answer 1

Yes, Sci-Kit learn is using a threshold of P>=0.5 for binary classifications. I am going to build on some of the answers already posted with two options to check this:

One simple option is to extract the probabilities of each classification using the output from model.predict_proba(test_x) segment of the code below along with class predictions (output from model.predict(test_x) segment of code below). Then, append class predictions and their probabilities to your test dataframe as a check.

As another option, one can graphically view precision vs. recall at various thresholds using the following code.

### Predict test_y values and probabilities based on fitted logistic 
regression model

pred_y=log.predict(test_x) 

probs_y=log.predict_proba(test_x) 
  # probs_y is a 2-D array of probability of being labeled as 0 (first 
  column of 
  array) vs 1 (2nd column in array)

from sklearn.metrics import precision_recall_curve
precision, recall, thresholds = precision_recall_curve(test_y, probs_y[:, 
1]) 
   #retrieve probability of being 1(in second column of probs_y)
pr_auc = metrics.auc(recall, precision)

plt.title("Precision-Recall vs Threshold Chart")
plt.plot(thresholds, precision[: -1], "b--", label="Precision")
plt.plot(thresholds, recall[: -1], "r--", label="Recall")
plt.ylabel("Precision, Recall")
plt.xlabel("Threshold")
plt.legend(loc="lower left")
plt.ylim([0,1])

Answer 2

There is a little trick that I use, instead of using model.predict(test_data) use model.predict_proba(test_data). Then use a range of values for thresholds to analyze the effects on the prediction;

pred_proba_df = pd.DataFrame(model.predict_proba(x_test))
threshold_list = [0.05,0.1,0.15,0.2,0.25,0.3,0.35,0.4,0.45,0.5,0.55,0.6,0.65,.7,.75,.8,.85,.9,.95,.99]
for i in threshold_list:
    print ('\n******** For i = {} ******'.format(i))
    Y_test_pred = pred_proba_df.applymap(lambda x: 1 if x>i else 0)
    test_accuracy = metrics.accuracy_score(Y_test.as_matrix().reshape(Y_test.as_matrix().size,1),
                                           Y_test_pred.iloc[:,1].as_matrix().reshape(Y_test_pred.iloc[:,1].as_matrix().size,1))
    print('Our testing accuracy is {}'.format(test_accuracy))

    print(confusion_matrix(Y_test.as_matrix().reshape(Y_test.as_matrix().size,1),
                           Y_test_pred.iloc[:,1].as_matrix().reshape(Y_test_pred.iloc[:,1].as_matrix().size,1)))

Best!

Answer 3

Logistic regression chooses the class that has the biggest probability. In case of 2 classes, the threshold is 0.5: if P(Y=0) > 0.5 then obviously P(Y=0) > P(Y=1). The same stands for the multiclass setting: again, it chooses the class with the biggest probability (see e.g. Ng's lectures, the bottom lines).

Introducing special thresholds only affects in the proportion of false positives/false negatives (and thus in precision/recall tradeoff), but it is not the parameter of the LR model. See also the similar question.