Rényi Entropy and Free Energy

I want to keep telling you about information geometry… but I got sidetracked into thinking about something slightly different, thanks to some fascinating discussions here at the CQT.

There are a lot of people interested in entropy here, so some of us ? Oscar Dahlsten, Mile Gu, Elisabeth Rieper, Wonmin Son and me ? decided to start meeting more or less regularly. I call it the Entropy Club. I’m learning a lot of wonderful things, and I hope to tell you about them someday. But for now, here’s a little idea I came up with, triggered by our conversations:

? John Baez, Rnyi entropy and free energy.

In 1960, Alfred Rnyi defined a generalization of the usual Shannon entropy that depends on a parameter. If \$latex p\$ is a probability distribution on a finite set, its Rnyi entropy of order \$latex beta\$ is defined to be

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Kernels Part 1: What is an RBF Kernel? Really?

My first blog on machine learning is to discuss a pet peeve I have about working in the industry, namely why not to apply an RBF kernel to text classification tasks.

I wrote this as a follow up to a Quora Answer on the subject:

http://www.quora.com/Machine-Learning/How-does-one-decide-on-which-kernel-to-choose-for-an-SVM-RBF-vs-linear-vs-poly-kernel

I will eventually re-write this entry once I get better at Latex.  For now, refer to

Smola, Scholkopf, and Muller, The connection between regularization operators and support vector kernels  http://cbio.ensmp.fr/~jvert/svn/bibli/local/Smola1998connection.pdf

I expand on one point–why not to use Radial Basis Function (RBF) Kernels for Text Classification.  I encountered this  while a consultant a few years ago eBay, where not one but 3 of the teams (local, German, and Indian) were all doing this, with no success  They are were treating a multi-class text classification problem using an SVM with an RBF Kernel.  What is worse, they were claiming the RBF calculations…

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