Online Gaussian Process

Loading necessary packages

Preliminary steps

Load the necessary packages

using Plots
using AugmentedGaussianProcesses
using MLDataUtils, Distributions

We create a toy dataset with a noisy sinus

N = 2000
σ = 0.1
X, y = noisy_sin(N, 0, 20; noise=σ)
X = reshape(X, :, 1) # Put X as a Matrix
X_train = X[1:2:end, :];
y_train = y[1:2:end]; # We split the data equally
X_test = X[2:2:end, :];
y_test = y[2:2:end];
scatter(X_train, y_train)

Plot model at each step

function plot_model(model, X, X_test, X_train, y_train)
    y_pred, sig_pred = proba_y(model, X_test)
    plot(X, sin; lab="f", color=:black, lw=3.0, ylims=(-2, 2))
    plot!(X_test, y_pred; ribbon=sqrt.(sig_pred), lab="Prediction", lw=3.0)
    scatter!(X_train, y_train; msw=0.0, alpha=0.5, lab="Data")
    return scatter!(first.(model[1].Z), mean(model[1]); lab="IP")
plot_model (generic function with 1 method)

Model training

Create a kernel

k = SqExponentialKernel();

Create an inducing point selection method

IP_alg = OIPS(0.8);

Create the model and stream the data

model = OnlineSVGP(k, GaussianLikelihood(σ), AnalyticVI(), IP_alg)
anim = Animation()
size_batch = 100
for (i, (X_batch, y_batch)) in enumerate(eachbatch((X_train, y_train); obsdim=1, size=size_batch))
    train!(model, X_batch, y_batch; iterations=3)
    plot_model(model, X, X_test, X_train[1:(i * size_batch)], y_train[1:(i * size_batch)])
gif(anim; fps=4)

This works just as well with any likelihood! Just try it out!

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