Fast inference for Gaussian processes in problems involving time
Author willtebbutt
2 Stars
Updated Last
10 Months Ago
Started In
March 2020


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TemporalGPs.jl is a tool to make Gaussian processes (GPs) defined using Stheno.jl fast for time-series. It provides a single-function public API that lets you specify that this package should perform inference, rather than Stheno.jl.

Example Usage

using Stheno, TemporalGPs

# Specify a Stheno.jl GP as usual
f_naive = GP(Matern32(), GPC())

# Wrap it in an object that TemporalGPs knows how to handle.
f = to_sde(f_naive)

# Project onto finite-dimensional distribution as usual.
x = range(-5.0, 5.0; length=10_000_000)
fx = f(x, 0.1)

# Sample from the prior as usual.
y = rand(fx)

# Compute the log marginal likelihood of the data as usual.
logpdf(fx, y)

Performance Optimisations

There are a couple of ways that TemporalGPs.jl can represent things internally. In particular, it can use regular Julia Vector and Matrix objects, or the StaticArrays.jl package to optimise in certain cases. The default is the former. To employ the latter, just add an extra argument to the to_sde function:

f = to_sde(f_naive, SArrayStorage(Float64))

This tells TemporalGPs that you want all parameters of f and anything derived from it to be a subtype of a SArray with element-type Float64, rather than (for example) a Matrix{Float64}s and Vector{Float64}. The decision made here can have quite a dramatic effect on performance, as shown in the graph below.

Preliminary Benchmarking Results

"naive" timings are with the usual Stheno.jl inference routines, and is the default implementation for GPs. "lgssm" timings are conducted using ssm with no additional arguments. "static-lgssm" uses the SArray{Float64} option discussed above.

Gradient computations use Zygote. Custom adjoints have been implemented to achieve this level of performance.

On-going Work

  • Optimisation -- in particular work needs to be done to reduce the allocations made when the default storage is employed.
  • Feature coverage -- only a subset of Stheno.jl's functionality is currently available, but it's possible to cover much more.

If you're interested in helping out with this stuff, please get in touch.

Relevant literature

See chapter 12 of [1] for the basics.

[1] - Särkkä, Simo, and Arno Solin. Applied stochastic differential equations. Vol. 10. Cambridge University Press, 2019.


  • And time-rescaling is assumed to be a strictly increasing function of time. If this is not the case, then your code will fail silently. This could be addressed via careful engineering.

Used By Packages

No packages found.