March 20th, 2010

beartato phd

(no subject)

Regarding the current research project, one of the interesting dangling threads leading off into unknown (at least unknown to me) territory has to do with metrics on the space of probability distributions. The one I am considering right now is just

d(p1, p2) = max_{x : τ} | ln( p1(x) / p2(x) ) |

for p1, p2 : τ → [0,1] being probability distributions on τ. This captures the "worst case multiplicative difference" in the probability that p1 might assign to an event compared to p2, and so it's just right for getting a handle on differential privacy.

But Katrina, while we were chatting the other day, pointed me towards the Lévy-Prokhorov metric and the Fréchet metric, which both look really interesting as well. Not sure what they mean for me yet. Fréchet, as it turns out, was an esperantist, and wrote entire papers in the language. Then again, mathematicians as a rule would not blink an eye at the apparent near-futility of writing paper that is only readable by a very select minority.