Gaussian Process Notes

written by Eric J. Ma on 2018-12-16 | tags: data science bayesian

I first learned GPs about two years back, and have been fascinated by the idea. I learned it through a video by David MacKay, and managed to grok it enough that I could put it to use in simple settings. That was reflected in my Flu Forecaster project, in which my GPs were trained only on individual latent spaces.

Recently, though, I decided to seriously sit down and try to grok the math behind GPs (and other machine learning models). To do so, I worked through Nando de Freitas' YouTube videos on GPs. (Super thankful that he has opted to put these videos up online!)

The product of this learning is two-fold. Firstly, I have added a GP notebook to my Bayesian analysis recipes repository.

Secondly, I have also put together some hand-written notes on GPs. (For those who are curious, I first hand-wrote them on paper, then copied them into my iPad mini using a Wacom stylus. We don't have the budget at the moment for an iPad Pro!) They can be downloaded here.

Some lessons learned:

  • Algebra is indeed a technology of sorts (to quote Jeremy Kun's book). Being less sloppy than I used to be gives me the opportunity to connect ideas on the page to ideas in my head, and express them more succinctly.
  • Grokking the math behind GPs at the minimum requires one thing: remembering, or else knowing how to derive, the formula for how to get the distribution parameters of a multivariate Gaussian conditioned on some of of its variables.
  • Once I grokked the math, implementing a GP using only NumPy was trivial; also, extending it to higher dimensions was similarly trivial!