A Primer on Gaussian Processes for Regression Analysis
summary
Hands-on notebooks show how to specify, fit and validate Gaussian process regressions in Python using PyMC3 with gradient MCMC (NUTS/HMC) and occasional MAP optimization; examples include a salmon recruitment regression, count models via a latent GP with Poisson likelihood (slower, possible divergences), a 26,000-runner Boston marathon surface handled by sparse inducing points, and a 2D geostatistics example. Code runs from the GitHub repo, produces posterior draws and predictive bands, and exposes the O(n^3) scaling limits.
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chapters (20)
- 0:00Introduction
- 1:48Audience experience
- 3:15Why use Gaussian processes
- 8:18Limitations of linear regression
- 9:21Bayesian methods
- 13:37Bayesian inference basics
- 15:28PyMC3 for Bayesian modeling
- 24:25Bayesian regression hands-on
- 25:38From regression to Gaussian processes
- 30:59Gaussian processes as infinite Gaussians
- 37:18Building GP priors
- 41:08GP regression for salmon data
- 48:52GP modeling hands-on
- 56:24Non-normal likelihoods
- 1:01:37Poisson regression with GPs
- 1:06:43Challenges with non-conjugate GPs
- 1:14:37Scaling GPs to large data
- 1:18:54Multi-dimensional GPs
- 1:24:18Advanced GP applications
- 1:27:12Summary
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