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RxGP.jl

Julia package for sparse Gaussian process inference via reactive message passing on factor graphs.

RxGP provides custom factor nodes and message passing update rules for Sparse Variational Gaussian Process (SVGP) models within the RxInfer.jl ecosystem. It enables efficient, scalable GP regression and GP state-space modelling by embedding sparse GP computations directly into a factor graph, where inference is performed automatically through message passing.

Why RxGP?

Gaussian processes are powerful non-parametric models, but standard GP inference scales cubically in the number of observations. Sparse variational approximations reduce this cost by introducing a small set of inducing points, but integrating sparse GPs into larger probabilistic models (e.g. state-space models) typically requires custom, hand-derived inference algorithms.

RxGP solves this by packaging the sparse GP computation into dedicated factor nodes — UniSGP, UniSGP_dID, and MultiSGP — that plug directly into the ReactiveMP.jl message passing engine. This means you can:

  • Compose GP components with arbitrary probabilistic model elements (state-space dynamics, switching models, etc.) using standard GraphPPL.jl syntax.
  • Infer all latent variables (function values, inducing variables, noise precisions, hyperparameters, and uncertain inputs) jointly via variational message passing — no manual derivations required.
  • Observe function values, gradients, or both simultaneously with the :fn, :grad, and :joint_fn_grad operator modes.

Package Features

  • Three sparse GP factor nodes with full message passing rules on every edge:
    • UniSGP — Univariate (scalar output) sparse GP observations.
    • UniSGP_dID — Univariate sparse GP with derivative/gradient observations.
    • MultiSGP — Multivariate (vector output) sparse GP observations.
  • Flexible kernel specification via get_simple_kernel_and_params, supporting squared-exponential (:SE), multi-SE (:SEn), spectral-mixture (:SMn), and combined (:SEn_SMn) kernels.
  • Automatic and analytic differentiation of kernels for gradient observation models (:AD and :AN modes).
  • Generalized Unscented Transform (GenUnscented) for approximate kernel expectations under uncertain inputs.
  • Posterior prediction via predict_GP for test-time inference with trained models.
  • High-performance caching (GPCache) with in-place matrix operations to minimise allocations during inference.
  • Hyperparameter optimisation utilities (neg_log_backwardmess_fast, grad_llh_default!) for gradient-based tuning of kernel parameters.

How to get started?

Head to the Getting started section.

Table of Contents

Index