Short Notes on Variational Bounds with Rescaled Terms

 

Screen Shot 2016-07-03 at 7.04.44 PM

Screen Shot 2016-06-27 at 9.33.00 PM

Screen Shot 2016-06-27 at 5.24.41 PM

Screen Shot 2016-06-27 at 7.40.55 PM

 

Screen Shot 2016-06-27 at 7.39.02 PM

 

Screen Shot 2016-06-27 at 9.36.50 PM

 

Screen Shot 2016-06-27 at 6.21.05 PM

You can get the pdf of this post here.

For a quick intro to variational approximations, checkout the posts below:

Advertisements

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.

page1page2page3

 

The full pdf of this post can be found here.

 

 

Useful Control Variates for Variance Reduction

Motivation

For many problems in machine learning (ranging from Generative Models to Reinforcement Learning), we rely on Monte Carlo estimators of gradients for optimization. Often, the noise in our gradient estimators is a major nuisance factor affecting how close we can get to local optima.

There are many tricks around the corner to improve on this issue. A popular one is the “bias removal trick” widely known in the Reinforcement Learning literature.

Many – if not all – of these tricks are particular cases of what is known as a control variate ( link1, link2, link3 ) a very generic method for variance reduction.

In this post I will try to characterize a few interesting and potentially useful applications of control variates and discuss their limitations.

 

img1

img2

img3

 

If you happen to know more interesting facts, theorems or use cases of control variates please let me know.

The pdf source of this post can be found here.