# Posts by Alexandre Andorra

## 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.