Approximating Free Energies

Merry Christmas all!

By now, I hope all machine learners are convinced of the importance of variational methods for approximated inference and learning in general. Specially given the fast increase in popularity of those methods (NIPS15, NIPS14).

As a follow up of my posts on partition functions ( part1, part2 and part3 ), I was inspired by a couple of papers this last NIPS ( paper1, paper2 ) to expand/review a little more the methods for approximating partition functions and free energies in statistical mechanics.



The full pdf of this post can be found here.




Partition Functions and Higher-order Jensen Inequalities (3/3)

When trying to compute variational bounds (as derived in the previous post), a naive attempt to approximate the involved expectations (e.g. using a Taylor expansion) may destroy the bound.

This is where the Higher-order Jensen-Feynman inequality comes in. It allows us to do a higher-order polynomial expansion without destroying the variational bound.

Screen Shot 2015-12-14 at 5.03.40 PM


Screen Shot 2015-12-12 at 4.42.41 PM