ing model on two-dimensional toy dataset encoding not only the predicted outcome but also how certain the classifier is provides additional information howeverin this visualizationit is hard to make out the boundary between the two classes predicting probabilities the output of predict_proba is probability for each classand is often more easily understood than the output of decision_function it is always of shape (n_samples for binary classificationin[ ]print("shape of probabilities{}format(gbrt predict_proba(x_testshape)out[ ]shape of probabilities( the first entry in each row is the estimated probability of the first classand the second entry is the estimated probability of the second class because it is probabilitythe output of predict_proba is always between and and the sum of the entries for both classes is always in[ ]show the first few entries of predict_proba print("predicted probabilities:\ {}formatgbrt predict_proba(x_test[: ])) supervised learning