I have read Alexandru Niculescu-Mizil and Rich Caruana's paper "[Obtaining Calibrated Probabilities from Boosting][1]" and the discussion in [this][2] thread. However, I am still having trouble understanding and implementing **logistic** or **Platt's scaling** to calibrate the output of my multi-class boosting classifier (gentle-boost with decision stumps).

I am somewhat familiar with generalized linear models, and I think I understand how the logistic and Platt's calibration methods work in the binary case, but am not sure I know how to extend the method described in the paper to the multi-class case.

The classifier I am using outputs the following: 

 -  $f_{ij}$ = Number of votes that the classifier casts for class $j$ for the sample $i$ that is being classified
 -  $y_i$ = Estimated class 

At this point I have the following questions:

**Q1:** Do I need to use a multinomial logit to estimate probabilities? or can I still do this with logistic regression (e.g. in a *1-vs-all* fashion)?

**Q2:** How could I define the intermediate target variables in Platt's scaling for the multi-class case?

**Q3:** I understand this might be a lot to ask, but would anybody be willing to sketch out the pseudo-code to this problem? (on a more practical level, I am interested in a solution in Matlab).


  [1]: http://aaaipress.org/Papers/Workshops/2007/WS-07-05/WS07-05-006.pdf
  [2]: http://stats.stackexchange.com/questions/5196/why-use-platts-scaling