To be specific, let's consider Support Vector Machines.

In the 1 vs all case, one has $n$ binary classifiers where $n$ is the number of classes. In each classifier one has two labels 0, 1 and for a given test data set, one can predict $\rm Prob(0)$ and $\rm Prob(1)$.

But how to compute prediction probability $\rm Prob(i)$ of a given test data point in class $i=1,2,\cdots,n$.

In sklearn, it seems that ${\rm Prob}(i) = {\rm Prob}(1;i)/\sum_{j=1}^n {\rm Prob}(1;j)$. How to interpret it?

In the 1 vs 1 case, one has $n(n-1)$ binary classifiers. Then how to compute prediction probability of classes from binary classifiers?


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