Gaussian processes

Worked examples for Gaussian-process models — sparse variational GPs, inter-domain inducing features, deep-kernel constructions, Kronecker-structured priors with non-Gaussian likelihoods. Each sub-section pairs a short motivation with runnable notebooks.

Sub-sections¶

• SVGP with pyrox — stochastic variational GP regression using pyrox.gp: the standard inducing-point variant, a mini-batched variant, an inter-domain variant with spherical-harmonic inducing features (VISH), and a deep-kernel variant with random Fourier features chained behind a small MLP.
• Kronecker GPs + non-Gaussian likelihoods — four notebooks building from an additive space + time GP (gaussx.KroneckerSum) → a multiplicative variant with a spatially varying warming rate (gaussx.SumKronecker) → a spatially non-stationary GEV (per-location $\sigma(s)$, $\xi(s)$) handled by 3-D Gauss–Hermite ELL → a Gaussian copula on the per-year cross-station residuals to model spatial dependence. Produces 25/100-year return-level maps, the 2024 $\to$ 2050 warming-shift pattern, the spatial map of tail-thickness contrast, and joint exceedance probabilities that respect station correlations.

Running¶

These notebooks share the pyrox pixi environment declared in the repo-root pixi.toml. That env bundles pyrox (from git main), jax/jaxlib clamped to the numpyro-compatible line, cartopy for the Kronecker-GEV maps, and a full Jupyter stack.

# Install the env (first time only)
pixi install -e pyrox

# Open Jupyter Lab and browse to a notebook
pixi run -e pyrox jupyter lab

# Or re-execute every notebook in this project in one go
pixi run -e pyrox execute-gaussian-processes

Run all commands from the repo root — the projects/gaussian_processes/ directory itself is not a standalone uv/pixi project, so cd-ing into it and invoking a task there will not resolve.