A lot of modern machine learning is related to this idea of "compression", or maybe to use a fancier term "representations". Taking a huge dimensional space (e.g. images of 256 x 256 x 3 pixels = 196608 dimensions) and somehow compressing it into a 1000 or so dimensional representation seems like pretty good compression to me! Unfortunately, it's not a lossless compression (or representation). Somehow though, it seems intuitive that there must be a way to use what is learned in these powerful lossy representations to help us better perform lossless compression, right? Of course there is! (It would be too anti-climatic of a setup otherwise.)
This post is going to introduce a method to perform lossless compression that leverages the learned "compression" of a machine learning latent variable model using the Bits-Back coding algorithm. Depending on how you first think about it, this seems like it should either be (a) really easy or (b) not possible at all. The reality is kind of in between with an elegant theoretical algorithm that is brought down by the realities of discretization and imperfect learning by the model. In today's post, I'll skim over some preliminaries (mostly referring you to previous posts), go over the main Bits-Back coding algorithm in detail, and discuss some of the implementation details and experiments that I did while trying to write a toy version of the algorithm.