predict_proba and probA_ / probB_ do not match in SVC

[marketmind-schuster]

According to the sklearn Help page:

Platt scaling uses the logistic function 1 / (1 + exp(decision_value * probA_ + probB_)) where probA_ and probB_ are learned from the dataset [2].

now, if I try a simple SVC example

import numpy as np
from sklearn.datasets import load_digits
from sklearn.svm import SVC

X, y = load_digits(return_X_y=True)

mask = (y == 0) | (y == 1)
X = X[mask, :]
y = y[mask]  # make a binary classification problem

model = SVC(probability=True)
model.fit(X,y)

If I use predict_proba to get all probabilities, this leads to

import pandas as pd
pd.DataFrame(model.predict_proba(X)).iloc[:,1]

0     0.00143866
1     0.99998592
2     0.00469432
3     0.99741052
4     0.00264468

while using the formula from above leads to a different result

pd.DataFrame(1/(1+(np.exp(model.decision_function(X) * model.probA_ + model.probB_)))).iloc[:,0]

0     0.00116055
1     0.99732754
2     0.00377729
3     0.99679562
4     0.00213140

What am I missing here? How does the formular need to be changed to make the results match with predict_proba?

Thanks for your help!

[lesteve]

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