Probabilistic Output from AVA (Multi-class) Classifier

What is the typical method for creating a probabilistic output from an All-vs-All or One-vs-All multi-class classifier? For example, if my problem has 3 classes (Class1, Class2, Class3) and I build an AVA classifier, then I have a classifier for:

• Class1 vs Class2 ($f_{12}(x)$)
• Class1 vs Class3 ($f_{13}(x)$)
• Class2 vs Class3 ($f_{23}(x)$)

Then, the classification is simply:

$$f(x)=\text{argmax}_{i} \sum_j f_{ij}(x)$$

However, we have no probability output of the class label (as with binary class logistic regression). In other words, how does one typically compute $p(y=Class1|x)$, $p(y=Class2|x)$, $p(y=Class3|x)$.

• Any progress here? – viyps Jul 30 '14 at 6:09