Posts by Alexandre Andorra
Boundary Conditions in the Hilbert Space GP Approximation
- 30 September 2026
The Hilbert space Gaussian process approximation (HSGP, Solin and Särkkä [2020],
Riutort-Mayol et al. [2022]) represents a stationary GP on a box \([-L, L]\) using the
eigenfunctions of the Laplacian. Those eigenfunctions depend on what we ask the GP to do at the
ends of the box. This notebook explains the four boundary conditions available in
pymc.gp.HSGP, shows where the choice makes no difference at all, where it is the only
way to express what you know about the function, and where it helps with caveats.
Gaussian Processes: HSGP Advanced Usage
- 28 June 2024
The Hilbert Space Gaussian processes approximation is a low-rank GP approximation that is particularly well-suited to usage in probabilistic programming languages like PyMC. It approximates the GP using a pre-computed and fixed set of basis functions that don’t depend on the form of the covariance kernel or its hyperparameters. It’s a parametric approximation, so prediction in PyMC can be done as one would with a linear model via pm.Data or pm.set_data. You don’t need to define the .conditional distribution that non-parameteric GPs rely on. This makes it much easier to integrate an HSGP, instead of a GP, into your existing PyMC model. Additionally, unlike many other GP approximations, HSGPs can be used anywhere within a model and with any likelihood function.
Gaussian Processes: HSGP Reference & First Steps
- 10 June 2024
The Hilbert Space Gaussian processes approximation is a low-rank GP approximation that is particularly well-suited to usage in probabilistic programming languages like PyMC. It approximates the GP using a pre-computed and fixed set of basis functions that don’t depend on the form of the covariance kernel or its hyperparameters. It’s a parametric approximation, so prediction in PyMC can be done as one would with a linear model via pm.Data or pm.set_data. You don’t need to define the .conditional distribution that non-parameteric GPs rely on. This makes it much easier to integrate an HSGP, instead of a GP, into your existing PyMC model. Additionally, unlike many other GP approximations, HSGPs can be used anywhere within a model and with any likelihood function.