Scikit-learn Ridge classifier: extracting class probabilities

Question

I'm currently using sklearn's Ridge classifier, and am looking to ensemble this classifier with classifiers from sklearn and other libraries. In order to do this, it would be ideal to extract the probability that a given input belongs to each class in a list of classes. Currently, I'm zipping the classes with the output of model.decision_function(x), but this returns the distance from the hyperplane as opposed to a straightforward probability. These distance values vary from around -1 to around 1.

distances = dict(zip(clf.classes_, clf.decision_function(x)[0]))  

How can I convert these distances to a more concrete set of probabilities (a series of positive values that sum to 1)? I'm looking for something like clf.predict_proba() that is implemented for the SVC in sklearn.

Answer 1

The solutions provided here didn't work for me. I think the softmax function is the correct solution, so I extended RidgeClassifierCV class with a predict_proba method similar to LogisticRegressionCV

from sklearn.utils.extmath import softmax
class RidgeClassifierCVwithProba(RidgeClassifierCV):
    def predict_proba(self, X):
        d = self.decision_function(X)
        d_2d = np.c_[-d, d]
        return softmax(d_2d)

Answer 2

Further exploration lead to using the softmax function.

d = clf.decision_function(x)[0]
probs = np.exp(d) / np.sum(np.exp(d))

This guarantees a 0-1 bounded distribution that sums to 1.

Answer 3

A little look at the source code of predict shows that decision_function is in fact the logit-transform of the actual class probabilities, i.e., if decision funciton is f, then the class probability of class 1 is exp(f) / (1 + exp(f)). This translates to following check in the sklearn source:

    scores = self.decision_function(X)
    if len(scores.shape) == 1:
        indices = (scores > 0).astype(np.int)
    else:
        indices = scores.argmax(axis=1)
    return self.classes_[indices]

If you observe this check, it tells you that if decision function is greater than zero, then predict class 1, otherwise predict class 0 - a classical logit approach.

So, you will have to turn the decision function into something like:

d = clf.decision_function(x)[0]
probs = numpy.exp(d) / (1 + numpy.exp(d))

And then take appropriate zip etc.