AbstractGPsMakie

Plots of Gaussian processes with AbstractGPs and Makie

Quick start

This guide shows the basic functionality of AbstractGPsMakie.

First, we load a Makie plotting backend. Here we import CairoMakie, other available backends are WGLMakie and GLMakie.

using CairoMakie

We load a custom set of colors and globally set the x-axis limits.

using CairoMakie.Makie.ColorSchemes: Set1_4

set_theme!(
    palette=(color=Set1_4, patchcolor=tuple.(Set1_4, 0.2)),
    Axis=(limits=((0, 10), nothing),),
)

We perform a simple Gaussian process (GP) regression with AbstractGPs. We use a squared exponential kernel for our GP.

using AbstractGPs

gp = GP(SqExponentialKernel())

We assume that data are observed under i.i.d. Gaussian noise with zero mean and variance 0.01. We generate some random observations.

using Random

Random.seed!(1234)

x = 10 .* rand(10)
gpx = gp(x, 0.01)
y = rand(gpx)

scatter(x, y)

We compute the posterior.

posterior_gp = posterior(gpx, y)

We plot the posterior with AbstractGPsMakie. The bandscale parameter (default: 1) determines the amount of standard deviations from the mean that are highlighted in the plot.

using AbstractGPsMakie

plot(0:0.01:10, posterior_gp; bandscale=3, color=Cycled(2))
scatter!(x, y)

We add 10 samples from the posterior on top.

plot(0:0.01:10, posterior_gp; bandscale=3, color=Cycled(2))
gpsample!(0:0.01:10, posterior_gp; samples=10, color=Cycled(3))
scatter!(x, y)

We can visualize a manifold of similar samples by animating the generated samples.^[PH2013]

scene = plot(0:0.01:10, posterior_gp; bandscale=3, color=Cycled(2))
samples = gpsample!(0:0.01:10, posterior_gp; samples=10, color=Cycled(3))
scatter!(x, y)

record(scene, "posterior_animation.mp4", 0:0.01:4) do x
    samples.orbit[] = x
end