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GPARs.jl is a rudimentary implementation of the Gaussian Process Autoregressive Regressor (GPAR), introduced in our AISTATS paper. See CITATION.bib for an appropriate bibtex citation.

We also maintain a Python version of this package -- this is much more fully featured, and we recommend that you use this implementation if you require the full collection of techniques introduced in that paper.

Basic Usage

using AbstractGPs
using GPARs
using Random

# Build a GPAR from a collection of GPs. For more info on how to specify particular
# kernels and their parameters, please see [AbstractGPs.jl]( or
# [Stheno.jl](
# You should think of this as a vector-valued regressor.
f = GPAR([GP(SEKernel()) for _ in 1:3])

# Specify inputs. `ColVecs` says "interpret this matrix as a vector of column-vecrors".
# Inputs are 2 dimensional, and there are 10 of them. This means that the pth GP in f
# will receive (2 + (p-1))-dimensional inputs, of which the first 2 dimensions comprise
# x, and the remaining the outputs of the first p-1 GPs in f.
x = ColVecs(randn(2, 10))

# Specify noise variance for each output.
Σs = rand(3) .+ 0.1

# Generate samples from the regressor at inputs `x` under observation noise `Σs`.
# You'll see that these are `ColVecs` of length `N`, each element of which is a length 3
# vector.
y = rand(MersenneTwister(123456), f(x, Σs))
y.X # this produces the matrix underlying the observations.

# Compute the log marginal likelihood of the observations under the model.
logpdf(f(x, Σs), y)

# Generate a new GPAR that is conditioned on these observations. This is just another
# GPAR object (in the simplest case, GPARs are closed under conditioning).
f_post = posterior(f(x, Σs), y)

# Since `f_post` is just another GPAR, we can use it to generate posterior samples
# and to compute log posterior predictive probabilities in the same way as the prior.
x_post = ColVecs(randn(2, 15))
rng = MersenneTwister(123456)
y_post = rand(rng, f_post(x, Σs))
logpdf(f_post(x, Σs), y_post)

Using this functionality, you have everything you need to do learning using standard off-the-shelf functionality (Zygote.jl to get gradients, Optim.jl to get optimisers such as (L-)BFGS, and ParameterHandling.jl to make dealing with large numbers of model parameters more straightforward. See the examples in Stheno.jl's docs for inspiration.