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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Gaussian Process for Event likelihoods · AugmentedGaussianProcesses</title><script async src="https://www.googletagmanager.com/gtag/js?id=UA-129106538-2"></script><script> window.dataLayer = window.dataLayer || [];
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src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../../assets/themeswap.js"></script><link href="../../assets/icon.ico" rel="icon" type="image/x-icon"/></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.png" alt="AugmentedGaussianProcesses logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../../">AugmentedGaussianProcesses</a></span></div><form class="docs-search" action="../../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li><a class="tocitem" href="../../background/">Background</a></li><li><a class="tocitem" href="../../userguide/">User Guide</a></li><li><a class="tocitem" href="../../kernel/">Kernels</a></li><li><span class="tocitem">Examples</span><ul><li><a class="tocitem" href="../gpclassification/">Gaussian Process Classification</a></li><li class="is-active"><a class="tocitem" href>Gaussian Process for Event likelihoods</a><ul class="internal"><li><a class="tocitem" href="#Preliminary-steps"><span>Preliminary steps</span></a></li><li><a class="tocitem" href="#Creating-some-random-data"><span>Creating some random data</span></a></li><li><a class="tocitem" href="#Run-GP-model-with-negative-binomial-likelihood-to-learn-p"><span>Run GP model with negative binomial likelihood to learn p</span></a></li><li><a class="tocitem" href="#Running-the-same-model-but-with-a-Poisson-likelihood"><span>Running the same model but with a Poisson likelihood</span></a></li><li><a class="tocitem" href="#Comparison-between-the-two-likelihoods"><span>Comparison between the two likelihoods</span></a></li></ul></li><li><a class="tocitem" href="../gpregression/">Gaussian Process Regression (for large data)</a></li><li><a class="tocitem" href="../multiclassgp/">Gaussian Process Multi-Class Classification</a></li><li><a class="tocitem" href="../onlinegp/">Online Gaussian Process</a></li><li><a class="tocitem" href="../sampling/">Sampling from a GP</a></li></ul></li><li><a class="tocitem" href="../../comparison/">Julia GP Packages</a></li><li><a class="tocitem" href="../../api/">API</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Examples</a></li><li class="is-active"><a href>Gaussian Process for Event likelihoods</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Gaussian Process for Event likelihoods</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/theogf/AugmentedGaussianProcesses.jl/blob/master/docs/examples/gpevents.jl" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Gaussian-Process-for-Event-likelihoods"><a class="docs-heading-anchor" href="#Gaussian-Process-for-Event-likelihoods">Gaussian Process for Event likelihoods</a><a id="Gaussian-Process-for-Event-likelihoods-1"></a><a class="docs-heading-anchor-permalink" href="#Gaussian-Process-for-Event-likelihoods" title="Permalink"></a></h1><p><a href="https://nbviewer.jupyter.org/github/theogf/AugmentedGaussianProcesses.jl/blob/gh-pages/v0.10.5/examples/notebooks/gpevents.ipynb"><img src="https://img.shields.io/badge/show-nbviewer-579ACA.svg" alt/></a></p><h2 id="Preliminary-steps"><a class="docs-heading-anchor" href="#Preliminary-steps">Preliminary steps</a><a id="Preliminary-steps-1"></a><a class="docs-heading-anchor-permalink" href="#Preliminary-steps" title="Permalink"></a></h2><h3 id="Loading-necessary-packages"><a class="docs-heading-anchor" href="#Loading-necessary-packages">Loading necessary packages</a><a id="Loading-necessary-packages-1"></a><a class="docs-heading-anchor-permalink" href="#Loading-necessary-packages" title="Permalink"></a></h3><pre><code class="language-julia hljs">using Plots
using AugmentedGaussianProcesses
const AGP = AugmentedGaussianProcesses
using Distributions</code></pre><h2 id="Creating-some-random-data"><a class="docs-heading-anchor" href="#Creating-some-random-data">Creating some random data</a><a id="Creating-some-random-data-1"></a><a class="docs-heading-anchor-permalink" href="#Creating-some-random-data" title="Permalink"></a></h2><pre><code class="language-julia hljs">n_data = 200
X = (rand(n_data) .- 0.5) * 40
r = 5.0
Y = rand.(NegativeBinomial.(r, AGP.logistic.(sin.(X))))
scatter(X, Y)</code></pre><?xml version="1.0" encoding="utf-8"?>
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<h2 id="Run-GP-model-with-negative-binomial-likelihood-to-learn-p"><a class="docs-heading-anchor" href="#Run-GP-model-with-negative-binomial-likelihood-to-learn-p">Run GP model with negative binomial likelihood to learn p</a><a id="Run-GP-model-with-negative-binomial-likelihood-to-learn-p-1"></a><a class="docs-heading-anchor-permalink" href="#Run-GP-model-with-negative-binomial-likelihood-to-learn-p" title="Permalink"></a></h2><pre><code class="language-julia hljs">kernel = SqExponentialKernel() ∘ ScaleTransform(1.0)
m_negbinomial = VGP(
X, Y, kernel, NegBinomialLikelihood(r), AnalyticVI(); optimiser=false, verbose=2
)
@time train!(m_negbinomial, 20)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">[ Info: Starting training Variational Gaussian Process with a Negative Binomial Likelihood (r = 5.0) infered by Analytic Variational Inference with 200 samples, 200 features and 1 latent GP
[ Info: Training ended after 20 iterations. Total number of iterations 20
0.059920 seconds (1.12 k allocations: 43.446 MiB, 26.47% gc time)</code></pre><h2 id="Running-the-same-model-but-with-a-Poisson-likelihood"><a class="docs-heading-anchor" href="#Running-the-same-model-but-with-a-Poisson-likelihood">Running the same model but with a Poisson likelihood</a><a id="Running-the-same-model-but-with-a-Poisson-likelihood-1"></a><a class="docs-heading-anchor-permalink" href="#Running-the-same-model-but-with-a-Poisson-likelihood" title="Permalink"></a></h2><pre><code class="language-julia hljs">kernel = SqExponentialKernel() ∘ ScaleTransform(1.0)
m_poisson = VGP(
X, Y, kernel, PoissonLikelihood(r), AnalyticVI(); optimiser=false, verbose=2
)
@time train!(m_poisson, 20)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">[ Info: Starting training Variational Gaussian Process with a Poisson Likelihood (λ = 5.0) infered by Analytic Variational Inference with 200 samples, 200 features and 1 latent GP
[ Info: Training ended after 20 iterations. Total number of iterations 20
0.076833 seconds (33.28 k allocations: 54.035 MiB, 30.35% gc time)</code></pre><p>Prediction and plot function on a grid Create a grid and compute prediction on it</p><pre><code class="language-julia hljs">function compute_grid(model, n_grid=50)
mins = -20
maxs = 20
x_grid = range(mins, maxs; length=n_grid) # Create a grid
y_grid, sig_y_grid = proba_y(model, reshape(x_grid, :, 1)) # Predict the mean and variance on the grid
return y_grid, sig_y_grid, x_grid
end</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">compute_grid (generic function with 2 methods)</code></pre><p>Plot the data as a scatter plot</p><pre><code class="language-julia hljs">function plot_data(X, Y)
return Plots.scatter(X, Y; alpha=0.33, msw=0.0, lab="", size=(800, 500))
end
function plot_model(model, X, Y, title=nothing)
n_grid = 100
y_grid, sig_y_grid, x_grid = compute_grid(model, n_grid)
p = plot_data(X, Y)
Plots.plot!(
p,
x_grid,
y_grid;
ribbon=2 * sqrt.(sig_y_grid), # Plot 2 std deviations
title=title,
color="red",
lab="",
linewidth=3.0,
)
if model isa SVGP # Plot the inducing points as well
Plots.plot!(
p,
vec(model.f[1].Z),
zeros(dim(model.f[1]));
msize=2.0,
color="black",
t=:scatter,
lab="",
)
end
return p
end;</code></pre><h2 id="Comparison-between-the-two-likelihoods"><a class="docs-heading-anchor" href="#Comparison-between-the-two-likelihoods">Comparison between the two likelihoods</a><a id="Comparison-between-the-two-likelihoods-1"></a><a class="docs-heading-anchor-permalink" href="#Comparison-between-the-two-likelihoods" title="Permalink"></a></h2><pre><code class="language-julia hljs">Plots.plot(
plot_model.(
[m_negbinomial, m_poisson], Ref(X), Ref(Y), ["Neg. Binomial", "Poisson"]
)...;
layout=(1, 2),
)</code></pre><?xml version="1.0" encoding="utf-8"?>
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