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| <html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Home · DynamicPPL</title><meta name="title" content="Home · DynamicPPL"/><meta property="og:title" content="Home · DynamicPPL"/><meta property="twitter:title" content="Home · DynamicPPL"/><meta name="description" content="Documentation for DynamicPPL."/><meta property="og:description" content="Documentation for DynamicPPL."/><meta property="twitter:description" content="Documentation for DynamicPPL."/><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link 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id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/TuringLang/DynamicPPL.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/TuringLang/DynamicPPL.jl/blob/master/docs/src/index.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a 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Using Julia version 1.10.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> |
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| <html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>The Probability Interface · DynamicPPL</title><meta name="title" content="The Probability Interface · DynamicPPL"/><meta property="og:title" content="The Probability Interface · DynamicPPL"/><meta property="twitter:title" content="The Probability Interface · DynamicPPL"/><meta name="description" content="Documentation for DynamicPPL."/><meta property="og:description" content="Documentation for DynamicPPL."/><meta property="twitter:description" content="Documentation for DynamicPPL."/><script data-outdated-warner src="../../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script src="../../search_index.js"></script><script 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></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.svg" alt="DynamicPPL logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../../">DynamicPPL</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li><a class="tocitem" href="../../api/">API</a></li><li><span class="tocitem">Tutorials</span><ul><li class="is-active"><a class="tocitem" href>The Probability Interface</a><ul class="internal"><li><a class="tocitem" href="#Conditioning-and-Deconditioning"><span>Conditioning and Deconditioning</span></a></li><li><a class="tocitem" href="#Probabilities-and-Densities"><span>Probabilities and Densities</span></a></li><li><a class="tocitem" href="#Example:-Cross-validation"><span>Example: Cross-validation</span></a></li></ul></li></ul></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"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Tutorials</a></li><li class="is-active"><a href>The Probability Interface</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>The Probability Interface</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/TuringLang/DynamicPPL.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/TuringLang/DynamicPPL.jl/blob/master/docs/src/tutorials/prob-interface.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="The-Probability-Interface"><a class="docs-heading-anchor" href="#The-Probability-Interface">The Probability Interface</a><a id="The-Probability-Interface-1"></a><a class="docs-heading-anchor-permalink" href="#The-Probability-Interface" title="Permalink"></a></h1><p>The easiest way to manipulate and query DynamicPPL models is via the DynamicPPL probability interface.</p><p>Let's use a simple model of normally-distributed data as an example.</p><pre><code class="language-julia hljs">using DynamicPPL | ||
| using Distributions | ||
| using FillArrays | ||
|
|
||
| using LinearAlgebra | ||
| using Random | ||
|
|
||
| @model function gdemo(n) | ||
| μ ~ Normal(0, 1) | ||
| x ~ MvNormal(Fill(μ, n), I) | ||
| return nothing | ||
| end</code></pre><p>We generate some data using <code>μ = 0</code>:</p><pre><code class="language-julia hljs">Random.seed!(1776) | ||
| dataset = randn(100)</code></pre><h2 id="Conditioning-and-Deconditioning"><a class="docs-heading-anchor" href="#Conditioning-and-Deconditioning">Conditioning and Deconditioning</a><a id="Conditioning-and-Deconditioning-1"></a><a class="docs-heading-anchor-permalink" href="#Conditioning-and-Deconditioning" title="Permalink"></a></h2><p>Bayesian models can be transformed with two main operations, conditioning and deconditioning (also known as marginalization). Conditioning takes a variable and fixes its value as known. We do this by passing a model and a collection of conditioned variables to <a href="../../api/#Base.:|-Tuple{Model, Any}"><code>|</code></a> or its alias <a href="../../api/#AbstractPPL.condition"><code>condition</code></a>:</p><pre><code class="language-julia hljs">model = gdemo(length(dataset)) | (x=dataset, μ=0)</code></pre><p>This operation can be reversed by applying <a href="../../api/#AbstractPPL.decondition"><code>decondition</code></a>:</p><pre><code class="language-julia hljs">decondition(model)</code></pre><p>We can also decondition only some of the variables:</p><pre><code class="language-julia hljs">decondition(model, :μ)</code></pre><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>Sometimes it is helpful to define convenience functions for conditioning on some variable(s). For instance, in this example we might want to define a version of <code>gdemo</code> that conditions on some observations of <code>x</code>:</p><pre><code class="language-julia hljs">gdemo(x::AbstractVector{<:Real}) = gdemo(length(x)) | (; x)</code></pre><p>For illustrative purposes, however, we do not use this function in the examples below.</p></div></div><h2 id="Probabilities-and-Densities"><a class="docs-heading-anchor" href="#Probabilities-and-Densities">Probabilities and Densities</a><a id="Probabilities-and-Densities-1"></a><a class="docs-heading-anchor-permalink" href="#Probabilities-and-Densities" title="Permalink"></a></h2><p>We often want to calculate the (unnormalized) probability density for an event. This probability might be a prior, a likelihood, or a posterior (joint) density. DynamicPPL provides convenient functions for this. For example, we can calculate the joint probability of a set of samples (here drawn from the prior) with <a href="../../api/#DynamicPPL.logjoint"><code>logjoint</code></a>:</p><pre><code class="language-julia hljs">model = gdemo(length(dataset)) | (x=dataset,) | ||
|
|
||
| Random.seed!(124) | ||
| sample = rand(model) | ||
| logjoint(model, sample)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">-181.7247437162069</code></pre><p>For models with many variables <code>rand(model)</code> can be prohibitively slow since it returns a <code>NamedTuple</code> of samples from the prior distribution of the unconditioned variables. We recommend working with samples of type <code>DataStructures.OrderedDict</code> in this case:</p><pre><code class="language-julia hljs">using DataStructures | ||
|
|
||
| Random.seed!(124) | ||
| sample_dict = rand(OrderedDict, model) | ||
| logjoint(model, sample_dict)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">-181.7247437162069</code></pre><p>The prior probability and the likelihood of a set of samples can be calculated with the functions <a href="../../api/#StatsAPI.loglikelihood"><code>loglikelihood</code></a> and <a href="../../api/#DynamicPPL.logjoint"><code>logjoint</code></a>, respectively:</p><pre><code class="language-julia hljs">logjoint(model, sample) ≈ loglikelihood(model, sample) + logprior(model, sample)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">true</code></pre><pre><code class="language-julia hljs">logjoint(model, sample_dict) ≈ | ||
| loglikelihood(model, sample_dict) + logprior(model, sample_dict)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">true</code></pre><h2 id="Example:-Cross-validation"><a class="docs-heading-anchor" href="#Example:-Cross-validation">Example: Cross-validation</a><a id="Example:-Cross-validation-1"></a><a class="docs-heading-anchor-permalink" href="#Example:-Cross-validation" title="Permalink"></a></h2><p>To give an example of the probability interface in use, we can use it to estimate the performance of our model using cross-validation. In cross-validation, we split the dataset into several equal parts. Then, we choose one of these sets to serve as the validation set. Here, we measure fit using the cross entropy (Bayes loss).<sup class="footnote-reference"><a id="citeref-1" href="#footnote-1">[1]</a></sup></p><pre><code class="language-julia hljs">using MLUtils | ||
|
|
||
| function cross_val( | ||
| dataset::AbstractVector{<:Real}; | ||
| nfolds::Int=5, | ||
| nsamples::Int=1_000, | ||
| rng::Random.AbstractRNG=Random.default_rng(), | ||
| ) | ||
| # Initialize `loss` in a way such that the loop below does not change its type | ||
| model = gdemo(1) | (x=[first(dataset)],) | ||
| loss = zero(logjoint(model, rand(rng, model))) | ||
|
|
||
| for (train, validation) in kfolds(dataset, nfolds) | ||
| # First, we train the model on the training set, i.e., we obtain samples from the posterior. | ||
| # For normally-distributed data, the posterior can be computed in closed form. | ||
| # For general models, however, typically samples will be generated using MCMC with Turing. | ||
| posterior = Normal(mean(train), 1) | ||
| samples = rand(rng, posterior, nsamples) | ||
|
|
||
| # Evaluation on the validation set. | ||
| validation_model = gdemo(length(validation)) | (x=validation,) | ||
| loss += sum(samples) do sample | ||
| logjoint(validation_model, (μ=sample,)) | ||
| end | ||
| end | ||
|
|
||
| return loss | ||
| end | ||
|
|
||
| cross_val(dataset)</code></pre><pre class="documenter-example-output"><code class="nohighlight hljs ansi">-212760.30282411768</code></pre><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a>See <a href="https://github.com/TuringLang/ParetoSmooth.jl">ParetoSmooth.jl</a> for a faster and more accurate implementation of cross-validation than the one provided here.</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../api/">« API</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Wednesday 14 February 2024 16:34">Wednesday 14 February 2024</span>. Using Julia version 1.10.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html> |
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