Iain Murray: "Introduction to MCMC for Deep Learning"

Graduate Summer School 2012: Deep Learning, Feature Learning
"Introduction to MCMC for Deep Learning"
Iain Murray, University of Edinburgh
Institute for Pure and Applied Mathematics, UCLA
July 26, 2012
For more information: www.ipam.ucla.edu/programs/su...

[@dannydk6]

This has to be the clearest explanation of MCMC I could find online. Thank you!

[@tempvariable]

50:00 Auxiliary Variables
52:00 Swendsen Wang
55:00 Hamiltonian Monte Carlo

[@marcuschiu8615]

38:28 What does he mean by valid in "MCMC T is valid"? like T is a stationary distribution?

[@dermitdembrot3091]

Has anyone looked at the exercise at 16:00 ? Could it be that the right-hand side should read
sum P* / sum Q* instead of sum w* ? Otherwise I'd have to think it through more thoroughly.

[@muhong9636]

From my understanding, the w* = P*/Q*. And he normalized the w* divided by sum w* making up to 1.

[@dermitdembrot3091]

@@muhong9636 thanks for your reply. As you say, w* = P*/Q*. Therefore sum w* = sum P*/Q*. I thought it maybe should read sum P* / sum Q* instead, but I just found out that the version in the slides makes it even easier. Here's my proof:
1/S sum w*
= 1/S sum P*/Q*
-> E_Q[P*/Q*] (for S->infinity)
= E_P[ Q/P P*/Q*]
= E_P[ ZP/ZQ Q*/P* P*/Q*]
= ZP/ZQ

[@muhong9636]

@@dermitdembrot3091 Thanks for sharing👍