I was a fool enough to miss most of Eric's course. Well, just one lecture out of two, technically. But still. Though it wasn't much of my fault either: that Saturday had been reserved long time ago.
So, I listened to his talk last Wednesday which wasn't exactly impressive, then missed the first lecture on MC, and today finally arrived for his last lecture which was really cool. He's a great reader!
Now, I'm to remind you that I don't know much about measures and probabilities, it's not my field. So most of the stuff that I found cool might in fact be quite trivial. But here are things that were new to me and seemed cool:
- Hamiltonian paths are closed. For this reason when doing HMC we got to be taking random lengths lest our iterations end up just where they begin
- Total Variation is actually a norm on measures which is dual to -norm on functions! Really lovely. And quite useful, because I couldn't persuade myself to try and really read the definition of TV for along time now. You know, analytic definitions always make you feel disrespected -- it is as if the author didn't care enough to pre-process his idea into a form convenient enough to be taken as an apparent geometrical truth.
- There exists a coupling formulation for TV: For measures there exist -valued random variables (on some prob. space) such that
- We've also covered Dobrushin coefficient.
- We've even applied Banach's fixed-point theorem! Felt like I was home. Not all this stochastic-differential-rubbish that they don't care to define signatures of!