| <!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="Source of the Rust file `/root/.cargo/git/checkouts/incubator-teaclave-crates-c8106113f74feefc/ede1f68/rusty-machine/src/learning/gp.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>gp.rs - source</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceSerif4-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../FiraSans-Regular.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../FiraSans-Medium.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceCodePro-Regular.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceSerif4-Bold.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../SourceCodePro-Semibold.ttf.woff2"><link rel="stylesheet" href="../../../normalize.css"><link rel="stylesheet" href="../../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" href="../../../ayu.css" disabled><link rel="stylesheet" href="../../../dark.css" disabled><link rel="stylesheet" href="../../../light.css" id="themeStyle"><script id="default-settings" ></script><script src="../../../storage.js"></script><script defer src="../../../source-script.js"></script><script defer src="../../../source-files.js"></script><script defer src="../../../main.js"></script><noscript><link rel="stylesheet" href="../../../noscript.css"></noscript><link rel="alternate icon" type="image/png" href="../../../favicon-16x16.png"><link rel="alternate icon" type="image/png" href="../../../favicon-32x32.png"><link rel="icon" type="image/svg+xml" href="../../../favicon.svg"></head><body class="rustdoc source"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><a class="sidebar-logo" href="../../../rusty_machine/index.html"><div class="logo-container"><img class="rust-logo" src="../../../rust-logo.svg" alt="logo"></div></a></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../../rusty_machine/index.html"><img class="rust-logo" src="../../../rust-logo.svg" alt="logo"></a><form class="search-form"><div class="search-container"><span></span><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../../../help.html">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../../wheel.svg"></a></div></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><span id="1">1</span> |
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| </pre><pre class="rust"><code><span class="doccomment">//! Gaussian Processes |
| //! |
| //! Provides implementation of gaussian process regression. |
| //! |
| //! # Usage |
| //! |
| //! ``` |
| //! use rusty_machine::learning::gp; |
| //! use rusty_machine::learning::SupModel; |
| //! use rusty_machine::linalg::Matrix; |
| //! use rusty_machine::linalg::Vector; |
| //! |
| //! let mut gaussp = gp::GaussianProcess::default(); |
| //! gaussp.noise = 10f64; |
| //! |
| //! let train_data = Matrix::new(10,1,vec![0.,1.,2.,3.,4.,5.,6.,7.,8.,9.]); |
| //! let target = Vector::new(vec![0.,1.,2.,3.,4.,4.,3.,2.,1.,0.]); |
| //! |
| //! gaussp.train(&train_data, &target).unwrap(); |
| //! |
| //! let test_data = Matrix::new(5,1,vec![2.3,4.4,5.1,6.2,7.1]); |
| //! |
| //! let outputs = gaussp.predict(&test_data).unwrap(); |
| //! ``` |
| //! Alternatively one could use `gaussp.get_posterior()` which would return both |
| //! the predictive mean and covariance. However, this is likely to change in |
| //! a future release. |
| |
| </span><span class="kw">use </span>learning::toolkit::kernel::{Kernel, SquaredExp}; |
| <span class="kw">use </span>linalg::{Matrix, BaseMatrix, Decomposition, Cholesky}; |
| <span class="kw">use </span>linalg::Vector; |
| <span class="kw">use </span>learning::{LearningResult, SupModel}; |
| <span class="kw">use </span>learning::error::{Error, ErrorKind}; |
| |
| <span class="doccomment">/// Trait for GP mean functions. |
| </span><span class="kw">pub trait </span>MeanFunc { |
| <span class="doccomment">/// Compute the mean function applied elementwise to a matrix. |
| </span><span class="kw">fn </span>func(<span class="kw-2">&</span><span class="self">self</span>, x: Matrix<f64>) -> Vector<f64>; |
| } |
| |
| <span class="doccomment">/// Constant mean function |
| </span><span class="attribute">#[derive(Clone, Copy, Debug)] |
| </span><span class="kw">pub struct </span>ConstMean { |
| a: f64, |
| } |
| |
| <span class="doccomment">/// Constructs the zero function. |
| </span><span class="kw">impl </span>Default <span class="kw">for </span>ConstMean { |
| <span class="kw">fn </span>default() -> ConstMean { |
| ConstMean { a: <span class="number">0f64 </span>} |
| } |
| } |
| |
| <span class="kw">impl </span>MeanFunc <span class="kw">for </span>ConstMean { |
| <span class="kw">fn </span>func(<span class="kw-2">&</span><span class="self">self</span>, x: Matrix<f64>) -> Vector<f64> { |
| Vector::zeros(x.rows()) + <span class="self">self</span>.a |
| } |
| } |
| |
| <span class="doccomment">/// Gaussian Process struct |
| /// |
| /// Gaussian process with generic kernel and deterministic mean function. |
| /// Can be used for gaussian process regression with noise. |
| /// Currently does not support classification. |
| </span><span class="attribute">#[derive(Debug)] |
| </span><span class="kw">pub struct </span>GaussianProcess<T: Kernel, U: MeanFunc> { |
| ker: T, |
| mean: U, |
| <span class="doccomment">/// The observation noise of the GP. |
| </span><span class="kw">pub </span>noise: f64, |
| alpha: <span class="prelude-ty">Option</span><Vector<f64>>, |
| train_mat: <span class="prelude-ty">Option</span><Matrix<f64>>, |
| train_data: <span class="prelude-ty">Option</span><Matrix<f64>>, |
| } |
| |
| <span class="doccomment">/// Construct a default Gaussian Process |
| /// |
| /// The defaults are: |
| /// |
| /// - Squared Exponential kernel. |
| /// - Zero-mean function. |
| /// - Zero noise. |
| /// |
| /// Note that zero noise can often lead to numerical instability. |
| /// A small value for the noise may be a better alternative. |
| </span><span class="kw">impl </span>Default <span class="kw">for </span>GaussianProcess<SquaredExp, ConstMean> { |
| <span class="kw">fn </span>default() -> GaussianProcess<SquaredExp, ConstMean> { |
| GaussianProcess { |
| ker: SquaredExp::default(), |
| mean: ConstMean::default(), |
| noise: <span class="number">0f64</span>, |
| train_mat: <span class="prelude-val">None</span>, |
| train_data: <span class="prelude-val">None</span>, |
| alpha: <span class="prelude-val">None</span>, |
| } |
| } |
| } |
| |
| <span class="kw">impl</span><T: Kernel, U: MeanFunc> GaussianProcess<T, U> { |
| <span class="doccomment">/// Construct a new Gaussian Process. |
| /// |
| /// # Examples |
| /// |
| /// ``` |
| /// use rusty_machine::learning::gp; |
| /// use rusty_machine::learning::toolkit::kernel; |
| /// |
| /// let ker = kernel::SquaredExp::default(); |
| /// let mean = gp::ConstMean::default(); |
| /// let gaussp = gp::GaussianProcess::new(ker, mean, 1e-3f64); |
| /// ``` |
| </span><span class="kw">pub fn </span>new(ker: T, mean: U, noise: f64) -> GaussianProcess<T, U> { |
| GaussianProcess { |
| ker: ker, |
| mean: mean, |
| noise: noise, |
| train_mat: <span class="prelude-val">None</span>, |
| train_data: <span class="prelude-val">None</span>, |
| alpha: <span class="prelude-val">None</span>, |
| } |
| } |
| |
| <span class="doccomment">/// Construct a kernel matrix |
| </span><span class="kw">fn </span>ker_mat(<span class="kw-2">&</span><span class="self">self</span>, m1: <span class="kw-2">&</span>Matrix<f64>, m2: <span class="kw-2">&</span>Matrix<f64>) -> LearningResult<Matrix<f64>> { |
| <span class="kw">if </span>m1.cols() != m2.cols() { |
| <span class="prelude-val">Err</span>(Error::new(ErrorKind::InvalidState, |
| <span class="string">"Inputs to kernel matrices have different column counts."</span>)) |
| } <span class="kw">else </span>{ |
| <span class="kw">let </span>dim1 = m1.rows(); |
| <span class="kw">let </span>dim2 = m2.rows(); |
| |
| <span class="kw">let </span><span class="kw-2">mut </span>ker_data = Vec::with_capacity(dim1 * dim2); |
| ker_data.extend(m1.row_iter().flat_map(|row1| { |
| m2.row_iter() |
| .map(<span class="kw">move </span>|row2| <span class="self">self</span>.ker.kernel(row1.raw_slice(), row2.raw_slice())) |
| })); |
| |
| <span class="prelude-val">Ok</span>(Matrix::new(dim1, dim2, ker_data)) |
| } |
| } |
| } |
| |
| <span class="kw">impl</span><T: Kernel, U: MeanFunc> SupModel<Matrix<f64>, Vector<f64>> <span class="kw">for </span>GaussianProcess<T, U> { |
| <span class="doccomment">/// Predict output from inputs. |
| </span><span class="kw">fn </span>predict(<span class="kw-2">&</span><span class="self">self</span>, inputs: <span class="kw-2">&</span>Matrix<f64>) -> LearningResult<Vector<f64>> { |
| |
| <span class="comment">// Messy referencing for succint syntax |
| </span><span class="kw">if let </span>(<span class="kw-2">&</span><span class="prelude-val">Some</span>(<span class="kw-2">ref </span>alpha), <span class="kw-2">&</span><span class="prelude-val">Some</span>(<span class="kw-2">ref </span>t_data)) = (<span class="kw-2">&</span><span class="self">self</span>.alpha, <span class="kw-2">&</span><span class="self">self</span>.train_data) { |
| <span class="kw">let </span>mean = <span class="self">self</span>.mean.func(inputs.clone()); |
| <span class="kw">let </span>post_mean = <span class="self">self</span>.ker_mat(inputs, t_data)<span class="question-mark">? </span>* alpha; |
| <span class="prelude-val">Ok</span>(mean + post_mean) |
| } <span class="kw">else </span>{ |
| <span class="prelude-val">Err</span>(Error::new(ErrorKind::UntrainedModel, <span class="string">"The model has not been trained."</span>)) |
| } |
| } |
| |
| <span class="doccomment">/// Train the model using data and outputs. |
| </span><span class="kw">fn </span>train(<span class="kw-2">&mut </span><span class="self">self</span>, inputs: <span class="kw-2">&</span>Matrix<f64>, targets: <span class="kw-2">&</span>Vector<f64>) -> LearningResult<()> { |
| <span class="kw">let </span>noise_mat = Matrix::identity(inputs.rows()) * <span class="self">self</span>.noise; |
| |
| <span class="kw">let </span>ker_mat = <span class="self">self</span>.ker_mat(inputs, inputs).unwrap(); |
| |
| <span class="kw">let </span>train_mat = Cholesky::decompose(ker_mat + noise_mat).map_err(|<span class="kw">_</span>| { |
| Error::new(ErrorKind::InvalidState, |
| <span class="string">"Could not compute Cholesky decomposition."</span>) |
| })<span class="question-mark">?</span>.unpack(); |
| |
| <span class="kw">let </span>x = train_mat.solve_l_triangular(targets - <span class="self">self</span>.mean.func(inputs.clone())).unwrap(); |
| <span class="kw">let </span>alpha = train_mat.transpose().solve_u_triangular(x).unwrap(); |
| |
| <span class="self">self</span>.train_mat = <span class="prelude-val">Some</span>(train_mat); |
| <span class="self">self</span>.train_data = <span class="prelude-val">Some</span>(inputs.clone()); |
| <span class="self">self</span>.alpha = <span class="prelude-val">Some</span>(alpha); |
| |
| <span class="prelude-val">Ok</span>(()) |
| } |
| } |
| |
| <span class="kw">impl</span><T: Kernel, U: MeanFunc> GaussianProcess<T, U> { |
| <span class="doccomment">/// Compute the posterior distribution [UNSTABLE] |
| /// |
| /// Requires the model to be trained first. |
| /// |
| /// Outputs the posterior mean and covariance matrix. |
| </span><span class="kw">pub fn </span>get_posterior(<span class="kw-2">&</span><span class="self">self</span>, |
| inputs: <span class="kw-2">&</span>Matrix<f64>) |
| -> LearningResult<(Vector<f64>, Matrix<f64>)> { |
| <span class="kw">if let </span>(<span class="kw-2">&</span><span class="prelude-val">Some</span>(<span class="kw-2">ref </span>t_mat), <span class="kw-2">&</span><span class="prelude-val">Some</span>(<span class="kw-2">ref </span>alpha), <span class="kw-2">&</span><span class="prelude-val">Some</span>(<span class="kw-2">ref </span>t_data)) = (<span class="kw-2">&</span><span class="self">self</span>.train_mat, |
| <span class="kw-2">&</span><span class="self">self</span>.alpha, |
| <span class="kw-2">&</span><span class="self">self</span>.train_data) { |
| <span class="kw">let </span>mean = <span class="self">self</span>.mean.func(inputs.clone()); |
| |
| <span class="kw">let </span>post_mean = mean + <span class="self">self</span>.ker_mat(inputs, t_data)<span class="question-mark">? </span>* alpha; |
| |
| <span class="kw">let </span>test_mat = <span class="self">self</span>.ker_mat(inputs, t_data)<span class="question-mark">?</span>; |
| <span class="kw">let </span><span class="kw-2">mut </span>var_data = Vec::with_capacity(inputs.rows() * inputs.cols()); |
| <span class="kw">for </span>row <span class="kw">in </span>test_mat.row_iter() { |
| <span class="kw">let </span>test_point = Vector::new(row.raw_slice()); |
| var_data.append(<span class="kw-2">&mut </span>t_mat.solve_l_triangular(test_point).unwrap().into_vec()); |
| } |
| |
| <span class="kw">let </span>v_mat = Matrix::new(test_mat.rows(), test_mat.cols(), var_data); |
| |
| <span class="kw">let </span>post_var = <span class="self">self</span>.ker_mat(inputs, inputs)<span class="question-mark">? </span>- <span class="kw-2">&</span>v_mat * v_mat.transpose(); |
| |
| <span class="prelude-val">Ok</span>((post_mean, post_var)) |
| } <span class="kw">else </span>{ |
| <span class="prelude-val">Err</span>(Error::new_untrained()) |
| } |
| } |
| } |
| </code></pre></div> |
| </section></div></main><div id="rustdoc-vars" data-root-path="../../../" data-current-crate="rusty_machine" data-themes="ayu,dark,light" data-resource-suffix="" data-rustdoc-version="1.66.0-nightly (5c8bff74b 2022-10-21)" ></div></body></html> |
