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Quarto GHA Workflow Runner committed Nov 16, 2023
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Expand Down Expand Up @@ -420,6 +417,7 @@ <h1>Gaussian Processes</h1>
<p>This article demonstrates the how to use Bambi with Gaussian Processes with 1 dimensional predictors. Bambi supports Gaussian Processes through the approximation known as Hilbert Space Gaussian Processes (HSGP).</p>
<p>HSGP is a framework that falls under the class of low-rank approximations that are based on forming a basis function approximation with <span class="math inline">\(m\)</span> basis functions, where <span class="math inline">\(m\)</span> is usually much less smaller than <span class="math inline">\(n\)</span>, the number of observations.</p>
<p>For references see <a href="https://arxiv.org/abs/1401.5508">Hilbert Space Methods for Reduced-Rank Gaussian Process Regression</a> and <a href="https://arxiv.org/abs/2004.11408">Practical Hilbert Space Approximate Bayesian Gaussian Processes for Probabilistic Programming</a>.</p>
<p>If you prefer a video format, have a look at <a href="https://www.youtube.com/watch?v=ri5sJAdcYHk&amp;ab_channel=PyMCDevelopers">Introduction to Hilbert Space GPs in PyMC</a> given by Bill Engels.</p>
<div class="cell" data-execution_count="1">
<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="im">from</span> formulae <span class="im">import</span> design_matrices</span>
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<section id="gaussian-processes-in-2d" class="level1">
<h1>Gaussian Processes in 2D</h1>
<p>This article demonstrates how to use Bambi with Gaussian Processes with 2 dimensional predictors. Bambi supports Gaussian Processes through the low-rank approximation known as Hilbert Space Gaussian Processes. For references see <a href="https://arxiv.org/abs/1401.5508">Hilbert Space Methods for Reduced-Rank Gaussian Process Regression</a> and <a href="https://arxiv.org/abs/2004.11408">Practical Hilbert Space Approximate Bayesian Gaussian Processes for Probabilistic Programming</a>.</p>
<p>For a demonstration of Gaussian Processes in 1D together with a more in depth explanation see <strong>To Do</strong>.</p>
<p>If you prefer a video format, have a look at <a href="https://www.youtube.com/watch?v=ri5sJAdcYHk&amp;ab_channel=PyMCDevelopers">Introduction to Hilbert Space GPs in PyMC</a> given by Bill Engels.</p>
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<div class="sourceCode cell-code" id="cb1"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="im">import</span> arviz <span class="im">as</span> az</span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="im">import</span> bambi <span class="im">as</span> bmb</span>
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