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| <div class="left-nav__overlay"></div> |
| |
| |
| <article data-swiftype-index='true'> |
| <a class='edit-link' href="https://github.com/apache/ignite/tree/IGNITE-7595/docs/_docs/machine-learning/regression/linear-regression.adoc" target="_blank">Edit</a> |
| |
| <h1>Linear Regression</h1> |
| |
| <div class="sect1"> |
| <h2 id="overview">Overview</h2> |
| <div class="sectionbody"> |
| <div class="paragraph"> |
| <p>Apache Ignite supports the ordinary least squares Linear Regression algorithm - one of the most basic and powerful machine learning algorithms. This documentation describes how the algorithm works, and is implemented in Apache Ignite.</p> |
| </div> |
| <div class="paragraph"> |
| <p>The basic idea behind the Linear Regression algorithm is an assumption that a dependent variable <code>y</code> and an explanatory variable <code>x</code> are in the following relationship:</p> |
| </div> |
| <div class="imageblock"> |
| <div class="content"> |
| <img src="/docs/2.10.0/images/111.gif" alt="111"> |
| </div> |
| </div> |
| <div class="paragraph"> |
| <p>WARNING:Be aware that further documentation uses a dot product of vectors <code>x</code> and <code>b</code>, and explicitly avoids using a constant term. It is mathematically correct in the case where vector <code>x</code> is supplemented by one value equal to 1.</p> |
| </div> |
| <div class="paragraph"> |
| <p>The above assumption allows us to make a prediction based on a feature vector <code>x</code> if a vector <code>b</code> is known. This fact is reflected in Apache Ignite in the <code>LinearRegressionModel</code> class responsible for making predictions.</p> |
| </div> |
| </div> |
| </div> |
| <div class="sect1"> |
| <h2 id="model">Model</h2> |
| <div class="sectionbody"> |
| <div class="paragraph"> |
| <p>A Model in the case of linear regression is represented by the class <code>LinearRegressionModel</code>. It enables a prediction to be made for a given vector of features, in the following way:</p> |
| </div> |
| <div class="listingblock"> |
| <div class="content"> |
| <pre class="rouge highlight"><code data-lang="java"><span class="nc">LinearRegressionModel</span> <span class="n">model</span> <span class="o">=</span> <span class="o">...;</span> |
| |
| <span class="kt">double</span> <span class="n">prediction</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="na">predict</span><span class="o">(</span><span class="n">observation</span><span class="o">);</span></code></pre> |
| </div> |
| </div> |
| <div class="paragraph"> |
| <p>Model is fully independent object and after the training it can be saved, serialized and restored.</p> |
| </div> |
| </div> |
| </div> |
| <div class="sect1"> |
| <h2 id="trainers">Trainers</h2> |
| <div class="sectionbody"> |
| <div class="paragraph"> |
| <p>Linear Regression is a supervised learning algorithm. This means that to find parameters (vector <code>b</code>), we need to train on a training dataset and minimize the loss function:</p> |
| </div> |
| <div class="imageblock"> |
| <div class="content"> |
| <img src="/docs/2.10.0/images/222.gif" alt="222"> |
| </div> |
| </div> |
| <div class="paragraph"> |
| <p>Apache Ignite provides two linear regression trainers: trainer based on the LSQR algorithm and another trainer based on the Stochastic Gradient Descent method.</p> |
| </div> |
| <div class="sect2"> |
| <h3 id="lsqr-trainer">LSQR Trainer</h3> |
| <div class="paragraph"> |
| <p>The LSQR algorithm finds the least-squares solution to a large, sparse, linear system of equations. The Apache Ignite implementation is a distributed version of this algorithm.</p> |
| </div> |
| <div class="listingblock"> |
| <div class="content"> |
| <pre class="rouge highlight"><code data-lang="java"><span class="c1">// Create linear regression trainer.</span> |
| <span class="nc">LinearRegressionLSQRTrainer</span> <span class="n">trainer</span> <span class="o">=</span> <span class="k">new</span> <span class="nc">LinearRegressionLSQRTrainer</span><span class="o">();</span> |
| |
| <span class="c1">// Train model.</span> |
| <span class="nc">LinearRegressionModel</span> <span class="n">mdl</span> <span class="o">=</span> <span class="n">trainer</span><span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">ignite</span><span class="o">,</span> <span class="n">dataCache</span><span class="o">,</span> <span class="n">vectorizer</span><span class="o">);</span> |
| |
| <span class="c1">// Make a prediction.</span> |
| <span class="kt">double</span> <span class="n">prediction</span> <span class="o">=</span> <span class="n">mdl</span><span class="o">.</span><span class="na">apply</span><span class="o">(</span><span class="n">coordinates</span><span class="o">);</span></code></pre> |
| </div> |
| </div> |
| </div> |
| <div class="sect2"> |
| <h3 id="sgd-trainer">SGD Trainer</h3> |
| <div class="paragraph"> |
| <p>Another Linear Regression Trainer uses the stochastic gradient descent method to find a minimum of the loss function. The configuration of this trainer is similar to <a href="/docs/2.10.0/machine-learning/binary-classification/multilayer-perceptron">multilayer perceptron trainer</a> configuration and we can specify the type of updater (<code>SGD</code>, <code>RProp</code> of <code>Nesterov</code>), max number of iterations, batch size, number of local iterations and seed.</p> |
| </div> |
| <div class="listingblock"> |
| <div class="content"> |
| <pre class="rouge highlight"><code data-lang="java"><span class="c1">// Create linear regression trainer.</span> |
| <span class="nc">LinearRegressionSGDTrainer</span><span class="o"><?></span> <span class="n">trainer</span> <span class="o">=</span> <span class="k">new</span> <span class="nc">LinearRegressionSGDTrainer</span><span class="o"><>(</span> |
| <span class="k">new</span> <span class="nc">UpdatesStrategy</span><span class="o"><>(</span> |
| <span class="k">new</span> <span class="nf">RPropUpdateCalculator</span><span class="o">(),</span> |
| <span class="nl">RPropParameterUpdate:</span><span class="o">:</span><span class="n">sumLocal</span><span class="o">,</span> |
| <span class="nl">RPropParameterUpdate:</span><span class="o">:</span><span class="n">avg</span> |
| <span class="o">),</span> |
| <span class="mi">100000</span><span class="o">,</span> <span class="c1">// Max iterations.</span> |
| <span class="mi">10</span><span class="o">,</span> <span class="c1">// Batch size.</span> |
| <span class="mi">100</span><span class="o">,</span> <span class="c1">// Local iterations.</span> |
| <span class="mi">123L</span> <span class="c1">// Random seed.</span> |
| <span class="o">);</span> |
| |
| <span class="c1">// Train model.</span> |
| <span class="nc">LinearRegressionModel</span> <span class="n">mdl</span> <span class="o">=</span> <span class="n">trainer</span><span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">ignite</span><span class="o">,</span> <span class="n">dataCache</span><span class="o">,</span> <span class="n">vectorizer</span><span class="o">);</span> |
| |
| <span class="c1">// Make a prediction.</span> |
| <span class="kt">double</span> <span class="n">prediction</span> <span class="o">=</span> <span class="n">mdl</span><span class="o">.</span><span class="na">apply</span><span class="o">(</span><span class="n">coordinates</span><span class="o">);</span></code></pre> |
| </div> |
| </div> |
| </div> |
| </div> |
| </div> |
| <div class="sect1"> |
| <h2 id="examples">Examples</h2> |
| <div class="sectionbody"> |
| <div class="paragraph"> |
| <p>To see how the Linear Regression can be used in practice, try these <a href="https://github.com/apache/ignite/tree/master/examples/src/main/java/org/apache/ignite/examples/ml/regression/linear">examples</a> that are available on GitHub and delivered with every Apache Ignite distribution.</p> |
| </div> |
| </div> |
| </div> |
| <div class="copyright"> |
| © 2021 The Apache Software Foundation.<br/> |
| Apache, Apache Ignite, the Apache feather and the Apache Ignite logo are either registered trademarks or trademarks of The Apache Software Foundation. |
| |
| </div> |
| |
| </article> |
| <nav class="right-nav" data-swiftype-index='false'> |
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| <ul class="sectlevel1"> |
| <li><a href="#overview">Overview</a></li> |
| <li><a href="#model">Model</a></li> |
| <li><a href="#trainers">Trainers</a> |
| <ul class="sectlevel2"> |
| <li><a href="#lsqr-trainer">LSQR Trainer</a></li> |
| <li><a href="#sgd-trainer">SGD Trainer</a></li> |
| </ul> |
| </li> |
| <li><a href="#examples">Examples</a></li> |
| </ul> |
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