2013/3/25 Paolo Losi <paolo.l...@gmail.com>:
> My 2 cents ...
>
> The problem is that penalized (l1 o l2) single class Logistic Regression is
> not
> well calibrated to start with.
> In other terms: the penalization param value that optimizes classification
> accuracy is not
> guaranteed to be the one that maximizes probability estimation accuracy.
>
> Optimizing a cross validated probability estimation loss
> (like log-likelihood or brier scorer) might be better but again
> you are using a single parameter (the penalization value) to obtain two
> goals:
> - preventing overfitting by controlling model parsimony
> - having a well calibrated estimate of log likelihood
>
> I'd suggest tuning the penalization parameter in order to get the best
> classification accuracy,
> then run out of bag calibration on the score function
> (standard logistic regression if n_sample <  500/1000, isotonic otherwise)
>
> Then I'm +1 with Mathieu on simple normalization of the one-class
> probabilities

I am also +1 a simple short term solution while still keeping longer
terms goal for
- proper multinomial penalized LR on one hand,
- tooling for calibrating arbitrary decision functions in general (not
just penalized LR) using isotonic regression for both binary class and
multiclass with one-vs-rest re-normalization) on the other hand.

--
Olivier
http://twitter.com/ogrisel - http://github.com/ogrisel

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