### Convex Risk Exegesis

This semester, I have been going to the statistics department's reading group
on
learning theory,
even though it meets at the unholy hour of 9 am on Thursdays. (Naturally, I
learned about it from Kris.) Since the end of
September, we've been reading a single paper, Peter Bartlett, Michael Jordan (no, no,
the *important* one) and Jon McAuliffe's "Convexity,
Classification and Risk Bounds" [abstract, pdf]. Moved by
some perverse impulse, I volunteered to present Theorem 3 in this paper, and
did so on October 9th.

This was most instructive. My explanation of what was going on in this
theorem and its proof, which occupy two pages of large type, took me three days
to write, ran to five densely-printed RevTeX pages, and went on for a full hour
and a half. (I am told that this kind of compression ratio is typical of
papers written for the Annals of
Statistics.) In the (highly unlikely) that you, Dear Reader, would
also like to understand that theorem, you can find my notes via the
reading-group's web-page.
(While there, you should really read Moulinath Banerjee's notes on covering
numbers and VC dimension; these aren't involved in that theorem, but they're
very important, and Mouli explains them well.)

I bring this up now because this week we had our final meeting on the paper,
covering theorem 17, which is where they (at last!) get actual learning rates.
We convinced ourselves that the proof was invalid, though the result may well
be correct. (For want of a log, the bound was lost, etc.) This felt good, not
because I like to see my betters stumble, but because I've finally become able
to *see* what was happening in a proof like that, at least through the
point where it went off the rails. I couldn't have done that a few years ago.
It wasn't exactly a "your journey to the dark side is now complete" moment, but
certainly it wasn't the kind of thing I was trained for by any means...

We're not sure what to read next; suggestions?

Enigmas of
Chance

Posted at November 20, 2004 17:03 | permanent link