Probability estimate from soft margin SVMs

[sbgaucho]

Apologies if this has already been covered either in the forums or in a lecture, but I don't recall it in any lecture and couldn't find anything in the forum.

It seems to me that it would be nice after using SVM to get a probability estimate that a given x (particularly for out of sample x's) corresponds to y=1. For noisy but non linearly separable data it seems like it would be ideal to combine the probabilistic output of a logistic regression with the power of SVM. I googled this and found a couple presentations/references, but it doesn't seem like there is a clear-cut answer. Am I way off base? If not what is the simplest/easiest direction to go in terms of learning about and implementing such a thing? Is it easiest just to use something like libsvm or weka?

Thanks

[htlin]

Originally Posted by sbgaucho

Apologies if this has already been covered either in the forums or in a lecture, but I don't recall it in any lecture and couldn't find anything in the forum.

It seems to me that it would be nice after using SVM to get a probability estimate that a given x (particularly for out of sample x's) corresponds to y=1. For noisy but non linearly separable data it seems like it would be ideal to combine the probabilistic output of a logistic regression with the power of SVM. I googled this and found a couple presentations/references, but it doesn't seem like there is a clear-cut answer. Am I way off base? If not what is the simplest/easiest direction to go in terms of learning about and implementing such a thing? Is it easiest just to use something like libsvm or weka?

Thanks

SVM with probabilistic outputs is useful for some applications. The most popular technique was proposed from Platt. The technique basically runs a variant of logistic regression to post-process the outputs of SVM. An earlier work of myself improves Platt's proposed algorithm from an optimization perspective:

http://www.csie.ntu.edu.tw/~htlin/pa.../plattprob.pdf

Hope this helps.

[yaser]

A related question asked by email

Can you please tell me if the following would be a good idea for post-processing after performing SVM: use the same z-space but instead of maximizing the margin, use logistic regression (in z space) and also allow the width of the logistic function to be a free parameter (let the cross-entropy be the objective function and use gradient descent). The solution from SVM could be used as the initial guess. Would this be a good idea (ie. improve the SVM result)?

and the answer from htlin (my colleague Professor Hsuan-Tien Lin):

Post-processing the outputs of SVM by logistic regression formulation has been explored for getting probabilistic (soft) outputs from SVMs. The formulation comes with two parameters: the width (scaling) of the SVM output as you suggest, and an additional "bias" term. You can check

http://www.csie.ntu.edu.tw/~htlin/pa.../plattprob.pdf

and the earlier work of John Platt for some additional information. Hope this helps.