predict_proba and probA_ / probB_ do not match in SVC #19588

Not a probability calibration expert but my understanding by browsing the references below is that it seems like a genuine problem indeed. I will try to take a closer look, but for now I ran out of steam in the libsvm C code which is not that easy to follow.

• SVC doc: https://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.html and extremely quickly the reference paper http://citeseer.ist.psu.edu/viewdoc/download?doi=10.1.1.41.1639&rep=rep1&type=pdf mentioned there
• probability calibration doc: https://scikit-learn.org/stable/modules/calibration.html#sigmoid

I think the missing detail is that the decision_value in the documentation refers to the internal decision value used by LIBSVM, not necessarily the value returned by scikit-learn's model.decision_function(X).

probA_ and probB_ are learned during LIBSVM's internal cross-validation, and predict_proba() uses the corresponding internal decision values when applying Platt scaling.

So this:

1 / (1 + np.exp(
    model.decision_function(X) * model.probA_[0] + model.probB_[0]
))

doesn't exactly reproduce predict_proba() because you're applying the calibration parameters to a different decision value.

Therefore, there isn't simply a missing - or another term in the sigmoid. To reproduce predict_proba() exactly, you'd need to reproduce LIBSVM's internal probability-prediction procedure.

In short: the formula is correct, but model.decision_function(X) is not the same decision_value used internally by LIBSVM for probability calibration.