predict: add support for -b2 (softmax probs) and -b3 (raw scores)

[cheusov]

Add support for softmax probabilities (-b2) and raw scores (-b3) to "predict" executable.

[cjlin1]

Sorry we don't add such things unless experiments have been done to show that in general the prob obtained via this is better than the one currently provided in liblinear. Liblinear uses one vs rest rather than maxent for multiclass, so the theoretically sound way is some settings to combine several binary prob outputs..
See appendix L of
https://www.csie.ntu.edu.tw/~cjlin/papers/liblinear.pdf
Thanks

[cheusov]

I know how liblinear works internally, but I still don't understand what exactly prevents you from converting raw scores (distances from hyperplane) to probability with a help of softmax. There are a lot of applications where the use of [0..1] probabilities is just more convenient than arbitrary real numbers. IMHO it would be nice to have a command-line option for this.

Any way, what about "-b 3" (or analog) for outputing raw scores?

[cheusov]

It seems to me you understood my patch incorrectly. What I proposed is an extension to existing functionality, not replacing the existing one. Also note that "use softmax eq in predict_probability func #20" pull request have nothing in common with what I proposed.