SVM, SMM, and the kernel trick

Today I gave a talk (and led an informal discussion) on the fundamental concept of support vector machine, support measure machine, and the kernel trick at the Center for Cosmology and Particle Physics (CCPP), NYU. Most of the audiences are astronomers who know very little about SVM and kernel methods, but they eventually seemed to understand the concept very quickly. I am quite impressed.

The highlight of the day seemed to be the discussion on the benefits of the kernel trick. David Hogg (NYU), who organized this talk for me, pointed out many interesting insights of kernel and how one can apply this technique in astronomy. In fact, he seemed to be very excited about the idea of kernel trick. David also pointed out that the distance metric we used in SMM for quasar target selection looks like the Chi-square, which is nice because this is naturally the case when comparing two Gaussian distributions. Moreover, Jonathan Goodman (NYU), who is a mathematician, also gave some insights about kernel function and Mercer's theorem. He was also curious about the different between SMM on distributions and SVM on infinitely many samples drawn from distributions, which was one of the most fundamental questions we addressed in our NIPS2012 paper.

At the end of the talk, I explained very briefly how one can use SMM for quasar target selection. The quasar target selection is essentially a classification problem in which one is interested in detecting a quasar, which looks very much like a star.


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