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| author | Andrew Or <andrewor14@apache.org> | 2014-11-24 23:38:52 +0000 |
|---|---|---|
| committer | Andrew Or <andrewor14@apache.org> | 2014-11-24 23:38:52 +0000 |
| commit | 439eeb021dcb8891bcf0129fdc2e973ea2633833 (patch) | |
| tree | bb62dbced8a22b544628fe435232238c3f664175 /site/docs/1.1.1/mllib-linear-methods.html | |
| parent | ad7c51b025452f669eeec864ddc6737da486889b (diff) | |
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Add docs for Spark 1.1.1
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diff --git a/site/docs/1.1.1/mllib-linear-methods.html b/site/docs/1.1.1/mllib-linear-methods.html new file mode 100644 index 000000000..0117ef7f8 --- /dev/null +++ b/site/docs/1.1.1/mllib-linear-methods.html @@ -0,0 +1,771 @@ +<!DOCTYPE html> +<!--[if lt IE 7]> <html class="no-js lt-ie9 lt-ie8 lt-ie7"> <![endif]--> +<!--[if IE 7]> <html class="no-js lt-ie9 lt-ie8"> <![endif]--> +<!--[if IE 8]> <html class="no-js lt-ie9"> <![endif]--> +<!--[if gt IE 8]><!--> <html class="no-js"> <!--<![endif]--> + <head> + <meta charset="utf-8"> + <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> + <title>Linear Methods - MLlib - Spark 1.1.1 Documentation</title> + <meta name="description" content=""> + + + + <link rel="stylesheet" href="css/bootstrap.min.css"> + <style> + body { + padding-top: 60px; + padding-bottom: 40px; + } + </style> + <meta name="viewport" content="width=device-width"> + <link rel="stylesheet" href="css/bootstrap-responsive.min.css"> + <link rel="stylesheet" href="css/main.css"> + + <script src="js/vendor/modernizr-2.6.1-respond-1.1.0.min.js"></script> + + <link rel="stylesheet" href="css/pygments-default.css"> + + + <!-- Google analytics script --> + <script type="text/javascript"> + var _gaq = _gaq || []; + _gaq.push(['_setAccount', 'UA-32518208-1']); + _gaq.push(['_trackPageview']); + + (function() { + var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; + ga.src = ('https:' == document.location.protocol ? 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Linear Methods</h1> + + + <ul id="markdown-toc"> + <li><a href="#mathematical-formulation">Mathematical formulation</a> <ul> + <li><a href="#loss-functions">Loss functions</a></li> + <li><a href="#regularizers">Regularizers</a></li> + </ul> + </li> + <li><a href="#binary-classification">Binary classification</a> <ul> + <li><a href="#linear-support-vector-machines-svms">Linear support vector machines (SVMs)</a></li> + <li><a href="#logistic-regression">Logistic regression</a></li> + <li><a href="#evaluation-metrics">Evaluation metrics</a></li> + <li><a href="#examples">Examples</a></li> + </ul> + </li> + <li><a href="#linear-least-squares-lasso-and-ridge-regression">Linear least squares, Lasso, and ridge regression</a> <ul> + <li><a href="#examples-1">Examples</a></li> + </ul> + </li> + <li><a href="#streaming-linear-regression">Streaming linear regression</a> <ul> + <li><a href="#examples-2">Examples</a></li> + </ul> + </li> + <li><a href="#implementation-developer">Implementation (developer)</a></li> +</ul> + +<p><code>\[ +\newcommand{\R}{\mathbb{R}} +\newcommand{\E}{\mathbb{E}} +\newcommand{\x}{\mathbf{x}} +\newcommand{\y}{\mathbf{y}} +\newcommand{\wv}{\mathbf{w}} +\newcommand{\av}{\mathbf{\alpha}} +\newcommand{\bv}{\mathbf{b}} +\newcommand{\N}{\mathbb{N}} +\newcommand{\id}{\mathbf{I}} +\newcommand{\ind}{\mathbf{1}} +\newcommand{\0}{\mathbf{0}} +\newcommand{\unit}{\mathbf{e}} +\newcommand{\one}{\mathbf{1}} +\newcommand{\zero}{\mathbf{0}} +\]</code></p> + +<h2 id="mathematical-formulation">Mathematical formulation</h2> + +<p>Many standard <em>machine learning</em> methods can be formulated as a convex optimization problem, i.e. +the task of finding a minimizer of a convex function <code>$f$</code> that depends on a variable vector +<code>$\wv$</code> (called <code>weights</code> in the code), which has <code>$d$</code> entries. +Formally, we can write this as the optimization problem <code>$\min_{\wv \in\R^d} \; f(\wv)$</code>, where +the objective function is of the form +<code>\begin{equation} + f(\wv) := \lambda\, R(\wv) + + \frac1n \sum_{i=1}^n L(\wv;\x_i,y_i) + \label{eq:regPrimal} + \ . +\end{equation}</code> +Here the vectors <code>$\x_i\in\R^d$</code> are the training data examples, for <code>$1\le i\le n$</code>, and +<code>$y_i\in\R$</code> are their corresponding labels, which we want to predict. +We call the method <em>linear</em> if $L(\wv; \x, y)$ can be expressed as a function of $\wv^T x$ and $y$. +Several of MLlib’s classification and regression algorithms fall into this category, +and are discussed here.</p> + +<p>The objective function <code>$f$</code> has two parts: +the regularizer that controls the complexity of the model, +and the loss that measures the error of the model on the training data. +The loss function <code>$L(\wv;.)$</code> is typically a convex function in <code>$\wv$</code>. The +fixed regularization parameter <code>$\lambda \ge 0$</code> (<code>regParam</code> in the code) +defines the trade-off between the two goals of minimizing the loss (i.e., +training error) and minimizing model complexity (i.e., to avoid overfitting).</p> + +<h3 id="loss-functions">Loss functions</h3> + +<p>The following table summarizes the loss functions and their gradients or sub-gradients for the +methods MLlib supports:</p> + +<table class="table"> + <thead> + <tr><th></th><th>loss function $L(\wv; \x, y)$</th><th>gradient or sub-gradient</th></tr> + </thead> + <tbody> + <tr> + <td>hinge loss</td><td>$\max \{0, 1-y \wv^T \x \}, \quad y \in \{-1, +1\}$</td> + <td>$\begin{cases}-y \cdot \x & \text{if $y \wv^T \x <1$}, \\ 0 & +\text{otherwise}.\end{cases}$</td> + </tr> + <tr> + <td>logistic loss</td><td>$\log(1+\exp( -y \wv^T \x)), \quad y \in \{-1, +1\}$</td> + <td>$-y \left(1-\frac1{1+\exp(-y \wv^T \x)} \right) \cdot \x$</td> + </tr> + <tr> + <td>squared loss</td><td>$\frac{1}{2} (\wv^T \x - y)^2, \quad y \in \R$</td> + <td>$(\wv^T \x - y) \cdot \x$</td> + </tr> + </tbody> +</table> + +<h3 id="regularizers">Regularizers</h3> + +<p>The purpose of the +<a href="http://en.wikipedia.org/wiki/Regularization_(mathematics)">regularizer</a> is to +encourage simple models and avoid overfitting. We support the following +regularizers in MLlib:</p> + +<table class="table"> + <thead> + <tr><th></th><th>regularizer $R(\wv)$</th><th>gradient or sub-gradient</th></tr> + </thead> + <tbody> + <tr> + <td>zero (unregularized)</td><td>0</td><td>$\0$</td> + </tr> + <tr> + <td>L2</td><td>$\frac{1}{2}\|\wv\|_2^2$</td><td>$\wv$</td> + </tr> + <tr> + <td>L1</td><td>$\|\wv\|_1$</td><td>$\mathrm{sign}(\wv)$</td> + </tr> + </tbody> +</table> + +<p>Here <code>$\mathrm{sign}(\wv)$</code> is the vector consisting of the signs (<code>$\pm1$</code>) of all the entries +of <code>$\wv$</code>.</p> + +<p>L2-regularized problems are generally easier to solve than L1-regularized due to smoothness. +However, L1 regularization can help promote sparsity in weights leading to smaller and more interpretable models, the latter of which can be useful for feature selection. +It is not recommended to train models without any regularization, +especially when the number of training examples is small.</p> + +<h2 id="binary-classification">Binary classification</h2> + +<p><a href="http://en.wikipedia.org/wiki/Binary_classification">Binary classification</a> +aims to divide items into two categories: positive and negative. MLlib +supports two linear methods for binary classification: linear support vector +machines (SVMs) and logistic regression. For both methods, MLlib supports +L1 and L2 regularized variants. The training data set is represented by an RDD +of <a href="mllib-data-types.html">LabeledPoint</a> in MLlib. Note that, in the +mathematical formulation in this guide, a training label $y$ is denoted as +either $+1$ (positive) or $-1$ (negative), which is convenient for the +formulation. <em>However</em>, the negative label is represented by $0$ in MLlib +instead of $-1$, to be consistent with multiclass labeling.</p> + +<h3 id="linear-support-vector-machines-svms">Linear support vector machines (SVMs)</h3> + +<p>The <a href="http://en.wikipedia.org/wiki/Support_vector_machine#Linear_SVM">linear SVM</a> +is a standard method for large-scale classification tasks. It is a linear method as described above in equation <code>$\eqref{eq:regPrimal}$</code>, with the loss function in the formulation given by the hinge loss:</p> + +<p><code>\[ +L(\wv;\x,y) := \max \{0, 1-y \wv^T \x \}. +\]</code> +By default, linear SVMs are trained with an L2 regularization. +We also support alternative L1 regularization. In this case, +the problem becomes a <a href="http://en.wikipedia.org/wiki/Linear_programming">linear program</a>.</p> + +<p>The linear SVMs algorithm outputs an SVM model. Given a new data point, +denoted by $\x$, the model makes predictions based on the value of $\wv^T \x$. +By the default, if $\wv^T \x \geq 0$ then the outcome is positive, and negative +otherwise.</p> + +<h3 id="logistic-regression">Logistic regression</h3> + +<p><a href="http://en.wikipedia.org/wiki/Logistic_regression">Logistic regression</a> is widely used to predict a +binary response. +It is a linear method as described above in equation <code>$\eqref{eq:regPrimal}$</code>, with the loss +function in the formulation given by the logistic loss: +<code>\[ +L(\wv;\x,y) := \log(1+\exp( -y \wv^T \x)). +\]</code></p> + +<p>The logistic regression algorithm outputs a logistic regression model. Given a +new data point, denoted by $\x$, the model makes predictions by +applying the logistic function +<code>\[ +\mathrm{f}(z) = \frac{1}{1 + e^{-z}} +\]</code> +where $z = \wv^T \x$. +By default, if $\mathrm{f}(\wv^T x) > 0.5$, the outcome is positive, or +negative otherwise, though unlike linear SVMs, the raw output of the logistic regression +model, $\mathrm{f}(z)$, has a probabilistic interpretation (i.e., the probability +that $\x$ is positive).</p> + +<h3 id="evaluation-metrics">Evaluation metrics</h3> + +<p>MLlib supports common evaluation metrics for binary classification (not available in PySpark). +This +includes precision, recall, <a href="http://en.wikipedia.org/wiki/F1_score">F-measure</a>, +<a href="http://en.wikipedia.org/wiki/Receiver_operating_characteristic">receiver operating characteristic (ROC)</a>, +precision-recall curve, and +<a href="http://en.wikipedia.org/wiki/Receiver_operating_characteristic#Area_under_the_curve">area under the curves (AUC)</a>. +AUC is commonly used to compare the performance of various models while +precision/recall/F-measure can help determine the appropriate threshold to use +for prediction purposes. </p> + +<h3 id="examples">Examples</h3> + +<div class="codetabs"> + +<div data-lang="scala"> + <p>The following code snippet illustrates how to load a sample dataset, execute a +training algorithm on this training data using a static method in the algorithm +object, and make predictions with the resulting model to compute the training +error.</p> + + <div class="highlight"><pre><code class="scala"><span class="k">import</span> <span class="nn">org.apache.spark.SparkContext</span> +<span class="k">import</span> <span class="nn">org.apache.spark.mllib.classification.SVMWithSGD</span> +<span class="k">import</span> <span class="nn">org.apache.spark.mllib.evaluation.BinaryClassificationMetrics</span> +<span class="k">import</span> <span class="nn">org.apache.spark.mllib.regression.LabeledPoint</span> +<span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vectors</span> +<span class="k">import</span> <span class="nn">org.apache.spark.mllib.util.MLUtils</span> + +<span class="c1">// Load training data in LIBSVM format.</span> +<span class="k">val</span> <span class="n">data</span> <span class="k">=</span> <span class="nc">MLUtils</span><span class="o">.</span><span class="n">loadLibSVMFile</span><span class="o">(</span><span class="n">sc</span><span class="o">,</span> <span class="s">"data/mllib/sample_libsvm_data.txt"</span><span class="o">)</span> + +<span class="c1">// Split data into training (60%) and test (40%).</span> +<span class="k">val</span> <span class="n">splits</span> <span class="k">=</span> <span class="n">data</span><span class="o">.</span><span class="n">randomSplit</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="mf">0.6</span><span class="o">,</span> <span class="mf">0.4</span><span class="o">),</span> <span class="n">seed</span> <span class="k">=</span> <span class="mi">11L</span><span class="o">)</span> +<span class="k">val</span> <span class="n">training</span> <span class="k">=</span> <span class="n">splits</span><span class="o">(</span><span class="mi">0</span><span class="o">).</span><span class="n">cache</span><span class="o">()</span> +<span class="k">val</span> <span class="n">test</span> <span class="k">=</span> <span class="n">splits</span><span class="o">(</span><span class="mi">1</span><span class="o">)</span> + +<span class="c1">// Run training algorithm to build the model</span> +<span class="k">val</span> <span class="n">numIterations</span> <span class="k">=</span> <span class="mi">100</span> +<span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="nc">SVMWithSGD</span><span class="o">.</span><span class="n">train</span><span class="o">(</span><span class="n">training</span><span class="o">,</span> <span class="n">numIterations</span><span class="o">)</span> + +<span class="c1">// Clear the default threshold.</span> +<span class="n">model</span><span class="o">.</span><span class="n">clearThreshold</span><span class="o">()</span> + +<span class="c1">// Compute raw scores on the test set. </span> +<span class="k">val</span> <span class="n">scoreAndLabels</span> <span class="k">=</span> <span class="n">test</span><span class="o">.</span><span class="n">map</span> <span class="o">{</span> <span class="n">point</span> <span class="k">=></span> + <span class="k">val</span> <span class="n">score</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="o">(</span><span class="n">point</span><span class="o">.</span><span class="n">features</span><span class="o">)</span> + <span class="o">(</span><span class="n">score</span><span class="o">,</span> <span class="n">point</span><span class="o">.</span><span class="n">label</span><span class="o">)</span> +<span class="o">}</span> + +<span class="c1">// Get evaluation metrics.</span> +<span class="k">val</span> <span class="n">metrics</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">BinaryClassificationMetrics</span><span class="o">(</span><span class="n">scoreAndLabels</span><span class="o">)</span> +<span class="k">val</span> <span class="n">auROC</span> <span class="k">=</span> <span class="n">metrics</span><span class="o">.</span><span class="n">areaUnderROC</span><span class="o">()</span> + +<span class="n">println</span><span class="o">(</span><span class="s">"Area under ROC = "</span> <span class="o">+</span> <span class="n">auROC</span><span class="o">)</span> +</code></pre></div> + + <p>The <code>SVMWithSGD.train()</code> method by default performs L2 regularization with the +regularization parameter set to 1.0. If we want to configure this algorithm, we +can customize <code>SVMWithSGD</code> further by creating a new object directly and +calling setter methods. All other MLlib algorithms support customization in +this way as well. For example, the following code produces an L1 regularized +variant of SVMs with regularization parameter set to 0.1, and runs the training +algorithm for 200 iterations.</p> + + <div class="highlight"><pre><code class="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.optimization.L1Updater</span> + +<span class="k">val</span> <span class="n">svmAlg</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">SVMWithSGD</span><span class="o">()</span> +<span class="n">svmAlg</span><span class="o">.</span><span class="n">optimizer</span><span class="o">.</span> + <span class="n">setNumIterations</span><span class="o">(</span><span class="mi">200</span><span class="o">).</span> + <span class="n">setRegParam</span><span class="o">(</span><span class="mf">0.1</span><span class="o">).</span> + <span class="n">setUpdater</span><span class="o">(</span><span class="k">new</span> <span class="n">L1Updater</span><span class="o">)</span> +<span class="k">val</span> <span class="n">modelL1</span> <span class="k">=</span> <span class="n">svmAlg</span><span class="o">.</span><span class="n">run</span><span class="o">(</span><span class="n">training</span><span class="o">)</span> +</code></pre></div> + + <p><a href="api/scala/index.html#org.apache.spark.mllib.classification.LogisticRegressionWithSGD"><code>LogisticRegressionWithSGD</code></a> can be used in a similar fashion as <code>SVMWithSGD</code>.</p> + + </div> + +<div data-lang="java"> + <p>All of MLlib’s methods use Java-friendly types, so you can import and call them there the same +way you do in Scala. The only caveat is that the methods take Scala RDD objects, while the +Spark Java API uses a separate <code>JavaRDD</code> class. You can convert a Java RDD to a Scala one by +calling <code>.rdd()</code> on your <code>JavaRDD</code> object. A standalone application example +that is equivalent to the provided example in Scala is given bellow:</p> + + <div class="highlight"><pre><code class="java"><span class="kn">import</span> <span class="nn">java.util.Random</span><span class="o">;</span> + +<span class="kn">import</span> <span class="nn">scala.Tuple2</span><span class="o">;</span> + +<span class="kn">import</span> <span class="nn">org.apache.spark.api.java.*</span><span class="o">;</span> +<span class="kn">import</span> <span class="nn">org.apache.spark.api.java.function.Function</span><span class="o">;</span> +<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.classification.*</span><span class="o">;</span> +<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.evaluation.BinaryClassificationMetrics</span><span class="o">;</span> +<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vector</span><span class="o">;</span> +<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.regression.LabeledPoint</span><span class="o">;</span> +<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.util.MLUtils</span><span class="o">;</span> +<span class="kn">import</span> <span class="nn">org.apache.spark.SparkConf</span><span class="o">;</span> +<span class="kn">import</span> <span class="nn">org.apache.spark.SparkContext</span><span class="o">;</span> + +<span class="kd">public</span> <span class="kd">class</span> <span class="nc">SVMClassifier</span> <span class="o">{</span> + <span class="kd">public</span> <span class="kd">static</span> <span class="kt">void</span> <span class="nf">main</span><span class="o">(</span><span class="n">String</span><span class="o">[]</span> <span class="n">args</span><span class="o">)</span> <span class="o">{</span> + <span class="n">SparkConf</span> <span class="n">conf</span> <span class="o">=</span> <span class="k">new</span> <span class="n">SparkConf</span><span class="o">().</span><span class="na">setAppName</span><span class="o">(</span><span class="s">"SVM Classifier Example"</span><span class="o">);</span> + <span class="n">SparkContext</span> <span class="n">sc</span> <span class="o">=</span> <span class="k">new</span> <span class="n">SparkContext</span><span class="o">(</span><span class="n">conf</span><span class="o">);</span> + <span class="n">String</span> <span class="n">path</span> <span class="o">=</span> <span class="s">"data/mllib/sample_libsvm_data.txt"</span><span class="o">;</span> + <span class="n">JavaRDD</span><span class="o"><</span><span class="n">LabeledPoint</span><span class="o">></span> <span class="n">data</span> <span class="o">=</span> <span class="n">MLUtils</span><span class="o">.</span><span class="na">loadLibSVMFile</span><span class="o">(</span><span class="n">sc</span><span class="o">,</span> <span class="n">path</span><span class="o">).</span><span class="na">toJavaRDD</span><span class="o">();</span> + + <span class="c1">// Split initial RDD into two... [60% training data, 40% testing data].</span> + <span class="n">JavaRDD</span><span class="o"><</span><span class="n">LabeledPoint</span><span class="o">></span> <span class="n">training</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="na">sample</span><span class="o">(</span><span class="kc">false</span><span class="o">,</span> <span class="mf">0.6</span><span class="o">,</span> <span class="mi">11L</span><span class="o">);</span> + <span class="n">training</span><span class="o">.</span><span class="na">cache</span><span class="o">();</span> + <span class="n">JavaRDD</span><span class="o"><</span><span class="n">LabeledPoint</span><span class="o">></span> <span class="n">test</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="na">subtract</span><span class="o">(</span><span class="n">training</span><span class="o">);</span> + + <span class="c1">// Run training algorithm to build the model.</span> + <span class="kt">int</span> <span class="n">numIterations</span> <span class="o">=</span> <span class="mi">100</span><span class="o">;</span> + <span class="kd">final</span> <span class="n">SVMModel</span> <span class="n">model</span> <span class="o">=</span> <span class="n">SVMWithSGD</span><span class="o">.</span><span class="na">train</span><span class="o">(</span><span class="n">training</span><span class="o">.</span><span class="na">rdd</span><span class="o">(),</span> <span class="n">numIterations</span><span class="o">);</span> + + <span class="c1">// Clear the default threshold.</span> + <span class="n">model</span><span class="o">.</span><span class="na">clearThreshold</span><span class="o">();</span> + + <span class="c1">// Compute raw scores on the test set.</span> + <span class="n">JavaRDD</span><span class="o"><</span><span class="n">Tuple2</span><span class="o"><</span><span class="n">Object</span><span class="o">,</span> <span class="n">Object</span><span class="o">>></span> <span class="n">scoreAndLabels</span> <span class="o">=</span> <span class="n">test</span><span class="o">.</span><span class="na">map</span><span class="o">(</span> + <span class="k">new</span> <span class="n">Function</span><span class="o"><</span><span class="n">LabeledPoint</span><span class="o">,</span> <span class="n">Tuple2</span><span class="o"><</span><span class="n">Object</span><span class="o">,</span> <span class="n">Object</span><span class="o">>>()</span> <span class="o">{</span> + <span class="kd">public</span> <span class="n">Tuple2</span><span class="o"><</span><span class="n">Object</span><span class="o">,</span> <span class="n">Object</span><span class="o">></span> <span class="n">call</span><span class="o">(</span><span class="n">LabeledPoint</span> <span class="n">p</span><span class="o">)</span> <span class="o">{</span> + <span class="n">Double</span> <span class="n">score</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">p</span><span class="o">.</span><span class="na">features</span><span class="o">());</span> + <span class="k">return</span> <span class="k">new</span> <span class="n">Tuple2</span><span class="o"><</span><span class="n">Object</span><span class="o">,</span> <span class="n">Object</span><span class="o">>(</span><span class="n">score</span><span class="o">,</span> <span class="n">p</span><span class="o">.</span><span class="na">label</span><span class="o">());</span> + <span class="o">}</span> + <span class="o">}</span> + <span class="o">);</span> + + <span class="c1">// Get evaluation metrics.</span> + <span class="n">BinaryClassificationMetrics</span> <span class="n">metrics</span> <span class="o">=</span> + <span class="k">new</span> <span class="nf">BinaryClassificationMetrics</span><span class="o">(</span><span class="n">JavaRDD</span><span class="o">.</span><span class="na">toRDD</span><span class="o">(</span><span class="n">scoreAndLabels</span><span class="o">));</span> + <span class="kt">double</span> <span class="n">auROC</span> <span class="o">=</span> <span class="n">metrics</span><span class="o">.</span><span class="na">areaUnderROC</span><span class="o">();</span> + + <span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">"Area under ROC = "</span> <span class="o">+</span> <span class="n">auROC</span><span class="o">);</span> + <span class="o">}</span> +<span class="o">}</span> +</code></pre></div> + + <p>The <code>SVMWithSGD.train()</code> method by default performs L2 regularization with the +regularization parameter set to 1.0. If we want to configure this algorithm, we +can customize <code>SVMWithSGD</code> further by creating a new object directly and +calling setter methods. All other MLlib algorithms support customization in +this way as well. For example, the following code produces an L1 regularized +variant of SVMs with regularization parameter set to 0.1, and runs the training +algorithm for 200 iterations.</p> + + <div class="highlight"><pre><code class="java"><span class="kn">import</span> <span class="nn">org.apache.spark.mllib.optimization.L1Updater</span><span class="o">;</span> + +<span class="n">SVMWithSGD</span> <span class="n">svmAlg</span> <span class="o">=</span> <span class="k">new</span> <span class="n">SVMWithSGD</span><span class="o">();</span> +<span class="n">svmAlg</span><span class="o">.</span><span class="na">optimizer</span><span class="o">()</span> + <span class="o">.</span><span class="na">setNumIterations</span><span class="o">(</span><span class="mi">200</span><span class="o">)</span> + <span class="o">.</span><span class="na">setRegParam</span><span class="o">(</span><span class="mf">0.1</span><span class="o">)</span> + <span class="o">.</span><span class="na">setUpdater</span><span class="o">(</span><span class="k">new</span> <span class="n">L1Updater</span><span class="o">());</span> +<span class="kd">final</span> <span class="n">SVMModel</span> <span class="n">modelL1</span> <span class="o">=</span> <span class="n">svmAlg</span><span class="o">.</span><span class="na">run</span><span class="o">(</span><span class="n">training</span><span class="o">.</span><span class="na">rdd</span><span class="o">());</span> +</code></pre></div> + + <p>In order to run the above standalone application, follow the instructions +provided in the <a href="quick-start.html#standalone-applications">Standalone +Applications</a> section of the Spark +quick-start guide. Be sure to also include <em>spark-mllib</em> to your build file as +a dependency.</p> + </div> + +<div data-lang="python"> + <p>The following example shows how to load a sample dataset, build Logistic Regression model, +and make predictions with the resulting model to compute the training error.</p> + + <div class="highlight"><pre><code class="python"><span class="kn">from</span> <span class="nn">pyspark.mllib.classification</span> <span class="kn">import</span> <span class="n">LogisticRegressionWithSGD</span> +<span class="kn">from</span> <span class="nn">pyspark.mllib.regression</span> <span class="kn">import</span> <span class="n">LabeledPoint</span> +<span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">array</span> + +<span class="c"># Load and parse the data</span> +<span class="k">def</span> <span class="nf">parsePoint</span><span class="p">(</span><span class="n">line</span><span class="p">):</span> + <span class="n">values</span> <span class="o">=</span> <span class="p">[</span><span class="nb">float</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">line</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="s">' '</span><span class="p">)]</span> + <span class="k">return</span> <span class="n">LabeledPoint</span><span class="p">(</span><span class="n">values</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">values</span><span class="p">[</span><span class="mi">1</span><span class="p">:])</span> + +<span class="n">data</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">textFile</span><span class="p">(</span><span class="s">"data/mllib/sample_svm_data.txt"</span><span class="p">)</span> +<span class="n">parsedData</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="n">parsePoint</span><span class="p">)</span> + +<span class="c"># Build the model</span> +<span class="n">model</span> <span class="o">=</span> <span class="n">LogisticRegressionWithSGD</span><span class="o">.</span><span class="n">train</span><span class="p">(</span><span class="n">parsedData</span><span class="p">)</span> + +<span class="c"># Evaluating the model on training data</span> +<span class="n">labelsAndPreds</span> <span class="o">=</span> <span class="n">parsedData</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">p</span><span class="p">:</span> <span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">label</span><span class="p">,</span> <span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">features</span><span class="p">)))</span> +<span class="n">trainErr</span> <span class="o">=</span> <span class="n">labelsAndPreds</span><span class="o">.</span><span class="n">filter</span><span class="p">(</span><span class="k">lambda</span> <span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">p</span><span class="p">):</span> <span class="n">v</span> <span class="o">!=</span> <span class="n">p</span><span class="p">)</span><span class="o">.</span><span class="n">count</span><span class="p">()</span> <span class="o">/</span> <span class="nb">float</span><span class="p">(</span><span class="n">parsedData</span><span class="o">.</span><span class="n">count</span><span class="p">())</span> +<span class="k">print</span><span class="p">(</span><span class="s">"Training Error = "</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">trainErr</span><span class="p">))</span> +</code></pre></div> + + </div> +</div> + +<h2 id="linear-least-squares-lasso-and-ridge-regression">Linear least squares, Lasso, and ridge regression</h2> + +<p>Linear least squares is the most common formulation for regression problems. +It is a linear method as described above in equation <code>$\eqref{eq:regPrimal}$</code>, with the loss +function in the formulation given by the squared loss: +<code>\[ +L(\wv;\x,y) := \frac{1}{2} (\wv^T \x - y)^2. +\]</code></p> + +<p>Various related regression methods are derived by using different types of regularization: +<a href="http://en.wikipedia.org/wiki/Ordinary_least_squares"><em>ordinary least squares</em></a> or +<a href="http://en.wikipedia.org/wiki/Linear_least_squares_(mathematics)"><em>linear least squares</em></a> uses + no regularization; <a href="http://en.wikipedia.org/wiki/Ridge_regression"><em>ridge regression</em></a> uses L2 +regularization; and <a href="http://en.wikipedia.org/wiki/Lasso_(statistics)"><em>Lasso</em></a> uses L1 +regularization. For all of these models, the average loss or training error, $\frac{1}{n} \sum_{i=1}^n (\wv^T x_i - y_i)^2$, is +known as the <a href="http://en.wikipedia.org/wiki/Mean_squared_error">mean squared error</a>.</p> + +<h3 id="examples-1">Examples</h3> + +<div class="codetabs"> + +<div data-lang="scala"> + <p>The following example demonstrate how to load training data, parse it as an RDD of LabeledPoint. +The example then uses LinearRegressionWithSGD to build a simple linear model to predict label +values. We compute the mean squared error at the end to evaluate +<a href="http://en.wikipedia.org/wiki/Goodness_of_fit">goodness of fit</a>.</p> + + <div class="highlight"><pre><code class="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.regression.LinearRegressionWithSGD</span> +<span class="k">import</span> <span class="nn">org.apache.spark.mllib.regression.LabeledPoint</span> +<span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vectors</span> + +<span class="c1">// Load and parse the data</span> +<span class="k">val</span> <span class="n">data</span> <span class="k">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">textFile</span><span class="o">(</span><span class="s">"data/mllib/ridge-data/lpsa.data"</span><span class="o">)</span> +<span class="k">val</span> <span class="n">parsedData</span> <span class="k">=</span> <span class="n">data</span><span class="o">.</span><span class="n">map</span> <span class="o">{</span> <span class="n">line</span> <span class="k">=></span> + <span class="k">val</span> <span class="n">parts</span> <span class="k">=</span> <span class="n">line</span><span class="o">.</span><span class="n">split</span><span class="o">(</span><span class="sc">','</span><span class="o">)</span> + <span class="nc">LabeledPoint</span><span class="o">(</span><span class="n">parts</span><span class="o">(</span><span class="mi">0</span><span class="o">).</span><span class="n">toDouble</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">.</span><span class="n">dense</span><span class="o">(</span><span class="n">parts</span><span class="o">(</span><span class="mi">1</span><span class="o">).</span><span class="n">split</span><span class="o">(</span><span class="sc">' '</span><span class="o">).</span><span class="n">map</span><span class="o">(</span><span class="k">_</span><span class="o">.</span><span class="n">toDouble</span><span class="o">)))</span> +<span class="o">}</span> + +<span class="c1">// Building the model</span> +<span class="k">val</span> <span class="n">numIterations</span> <span class="k">=</span> <span class="mi">100</span> +<span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="nc">LinearRegressionWithSGD</span><span class="o">.</span><span class="n">train</span><span class="o">(</span><span class="n">parsedData</span><span class="o">,</span> <span class="n">numIterations</span><span class="o">)</span> + +<span class="c1">// Evaluate model on training examples and compute training error</span> +<span class="k">val</span> <span class="n">valuesAndPreds</span> <span class="k">=</span> <span class="n">parsedData</span><span class="o">.</span><span class="n">map</span> <span class="o">{</span> <span class="n">point</span> <span class="k">=></span> + <span class="k">val</span> <span class="n">prediction</span> <span class="k">=</span> <span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="o">(</span><span class="n">point</span><span class="o">.</span><span class="n">features</span><span class="o">)</span> + <span class="o">(</span><span class="n">point</span><span class="o">.</span><span class="n">label</span><span class="o">,</span> <span class="n">prediction</span><span class="o">)</span> +<span class="o">}</span> +<span class="k">val</span> <span class="nc">MSE</span> <span class="k">=</span> <span class="n">valuesAndPreds</span><span class="o">.</span><span class="n">map</span><span class="o">{</span><span class="k">case</span><span class="o">(</span><span class="n">v</span><span class="o">,</span> <span class="n">p</span><span class="o">)</span> <span class="k">=></span> <span class="n">math</span><span class="o">.</span><span class="n">pow</span><span class="o">((</span><span class="n">v</span> <span class="o">-</span> <span class="n">p</span><span class="o">),</span> <span class="mi">2</span><span class="o">)}.</span><span class="n">mean</span><span class="o">()</span> +<span class="n">println</span><span class="o">(</span><span class="s">"training Mean Squared Error = "</span> <span class="o">+</span> <span class="nc">MSE</span><span class="o">)</span> +</code></pre></div> + + <p><a href="api/scala/index.html#org.apache.spark.mllib.regression.RidgeRegressionWithSGD"><code>RidgeRegressionWithSGD</code></a> +and <a href="api/scala/index.html#org.apache.spark.mllib.regression.LassoWithSGD"><code>LassoWithSGD</code></a> can be used in a similar fashion as <code>LinearRegressionWithSGD</code>.</p> + + </div> + +<div data-lang="java"> + <p>All of MLlib’s methods use Java-friendly types, so you can import and call them there the same +way you do in Scala. The only caveat is that the methods take Scala RDD objects, while the +Spark Java API uses a separate <code>JavaRDD</code> class. You can convert a Java RDD to a Scala one by +calling <code>.rdd()</code> on your <code>JavaRDD</code> object. The corresponding Java example to +the Scala snippet provided, is presented bellow:</p> + + <div class="highlight"><pre><code class="java"><span class="kn">import</span> <span class="nn">scala.Tuple2</span><span class="o">;</span> + +<span class="kn">import</span> <span class="nn">org.apache.spark.api.java.*</span><span class="o">;</span> +<span class="kn">import</span> <span class="nn">org.apache.spark.api.java.function.Function</span><span class="o">;</span> +<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vector</span><span class="o">;</span> +<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vectors</span><span class="o">;</span> +<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.regression.LabeledPoint</span><span class="o">;</span> +<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.regression.LinearRegressionModel</span><span class="o">;</span> +<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.regression.LinearRegressionWithSGD</span><span class="o">;</span> +<span class="kn">import</span> <span class="nn">org.apache.spark.SparkConf</span><span class="o">;</span> + +<span class="kd">public</span> <span class="kd">class</span> <span class="nc">LinearRegression</span> <span class="o">{</span> + <span class="kd">public</span> <span class="kd">static</span> <span class="kt">void</span> <span class="nf">main</span><span class="o">(</span><span class="n">String</span><span class="o">[]</span> <span class="n">args</span><span class="o">)</span> <span class="o">{</span> + <span class="n">SparkConf</span> <span class="n">conf</span> <span class="o">=</span> <span class="k">new</span> <span class="n">SparkConf</span><span class="o">().</span><span class="na">setAppName</span><span class="o">(</span><span class="s">"Linear Regression Example"</span><span class="o">);</span> + <span class="n">JavaSparkContext</span> <span class="n">sc</span> <span class="o">=</span> <span class="k">new</span> <span class="n">JavaSparkContext</span><span class="o">(</span><span class="n">conf</span><span class="o">);</span> + + <span class="c1">// Load and parse the data</span> + <span class="n">String</span> <span class="n">path</span> <span class="o">=</span> <span class="s">"data/mllib/ridge-data/lpsa.data"</span><span class="o">;</span> + <span class="n">JavaRDD</span><span class="o"><</span><span class="n">String</span><span class="o">></span> <span class="n">data</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="na">textFile</span><span class="o">(</span><span class="n">path</span><span class="o">);</span> + <span class="n">JavaRDD</span><span class="o"><</span><span class="n">LabeledPoint</span><span class="o">></span> <span class="n">parsedData</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="na">map</span><span class="o">(</span> + <span class="k">new</span> <span class="n">Function</span><span class="o"><</span><span class="n">String</span><span class="o">,</span> <span class="n">LabeledPoint</span><span class="o">>()</span> <span class="o">{</span> + <span class="kd">public</span> <span class="n">LabeledPoint</span> <span class="nf">call</span><span class="o">(</span><span class="n">String</span> <span class="n">line</span><span class="o">)</span> <span class="o">{</span> + <span class="n">String</span><span class="o">[]</span> <span class="n">parts</span> <span class="o">=</span> <span class="n">line</span><span class="o">.</span><span class="na">split</span><span class="o">(</span><span class="s">","</span><span class="o">);</span> + <span class="n">String</span><span class="o">[]</span> <span class="n">features</span> <span class="o">=</span> <span class="n">parts</span><span class="o">[</span><span class="mi">1</span><span class="o">].</span><span class="na">split</span><span class="o">(</span><span class="s">" "</span><span class="o">);</span> + <span class="kt">double</span><span class="o">[]</span> <span class="n">v</span> <span class="o">=</span> <span class="k">new</span> <span class="kt">double</span><span class="o">[</span><span class="n">features</span><span class="o">.</span><span class="na">length</span><span class="o">];</span> + <span class="k">for</span> <span class="o">(</span><span class="kt">int</span> <span class="n">i</span> <span class="o">=</span> <span class="mi">0</span><span class="o">;</span> <span class="n">i</span> <span class="o"><</span> <span class="n">features</span><span class="o">.</span><span class="na">length</span> <span class="o">-</span> <span class="mi">1</span><span class="o">;</span> <span class="n">i</span><span class="o">++)</span> + <span class="n">v</span><span class="o">[</span><span class="n">i</span><span class="o">]</span> <span class="o">=</span> <span class="n">Double</span><span class="o">.</span><span class="na">parseDouble</span><span class="o">(</span><span class="n">features</span><span class="o">[</span><span class="n">i</span><span class="o">]);</span> + <span class="k">return</span> <span class="k">new</span> <span class="nf">LabeledPoint</span><span class="o">(</span><span class="n">Double</span><span class="o">.</span><span class="na">parseDouble</span><span class="o">(</span><span class="n">parts</span><span class="o">[</span><span class="mi">0</span><span class="o">]),</span> <span class="n">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="n">v</span><span class="o">));</span> + <span class="o">}</span> + <span class="o">}</span> + <span class="o">);</span> + + <span class="c1">// Building the model</span> + <span class="kt">int</span> <span class="n">numIterations</span> <span class="o">=</span> <span class="mi">100</span><span class="o">;</span> + <span class="kd">final</span> <span class="n">LinearRegressionModel</span> <span class="n">model</span> <span class="o">=</span> + <span class="n">LinearRegressionWithSGD</span><span class="o">.</span><span class="na">train</span><span class="o">(</span><span class="n">JavaRDD</span><span class="o">.</span><span class="na">toRDD</span><span class="o">(</span><span class="n">parsedData</span><span class="o">),</span> <span class="n">numIterations</span><span class="o">);</span> + + <span class="c1">// Evaluate model on training examples and compute training error</span> + <span class="n">JavaRDD</span><span class="o"><</span><span class="n">Tuple2</span><span class="o"><</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">>></span> <span class="n">valuesAndPreds</span> <span class="o">=</span> <span class="n">parsedData</span><span class="o">.</span><span class="na">map</span><span class="o">(</span> + <span class="k">new</span> <span class="n">Function</span><span class="o"><</span><span class="n">LabeledPoint</span><span class="o">,</span> <span class="n">Tuple2</span><span class="o"><</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">>>()</span> <span class="o">{</span> + <span class="kd">public</span> <span class="n">Tuple2</span><span class="o"><</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">></span> <span class="n">call</span><span class="o">(</span><span class="n">LabeledPoint</span> <span class="n">point</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">point</span><span class="o">.</span><span class="na">features</span><span class="o">());</span> + <span class="k">return</span> <span class="k">new</span> <span class="n">Tuple2</span><span class="o"><</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">>(</span><span class="n">prediction</span><span class="o">,</span> <span class="n">point</span><span class="o">.</span><span class="na">label</span><span class="o">());</span> + <span class="o">}</span> + <span class="o">}</span> + <span class="o">);</span> + <span class="n">JavaRDD</span><span class="o"><</span><span class="n">Object</span><span class="o">></span> <span class="n">MSE</span> <span class="o">=</span> <span class="k">new</span> <span class="n">JavaDoubleRDD</span><span class="o">(</span><span class="n">valuesAndPreds</span><span class="o">.</span><span class="na">map</span><span class="o">(</span> + <span class="k">new</span> <span class="n">Function</span><span class="o"><</span><span class="n">Tuple2</span><span class="o"><</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">>,</span> <span class="n">Object</span><span class="o">>()</span> <span class="o">{</span> + <span class="kd">public</span> <span class="n">Object</span> <span class="nf">call</span><span class="o">(</span><span class="n">Tuple2</span><span class="o"><</span><span class="n">Double</span><span class="o">,</span> <span class="n">Double</span><span class="o">></span> <span class="n">pair</span><span class="o">)</span> <span class="o">{</span> + <span class="k">return</span> <span class="n">Math</span><span class="o">.</span><span class="na">pow</span><span class="o">(</span><span class="n">pair</span><span class="o">.</span><span class="na">_1</span><span class="o">()</span> <span class="o">-</span> <span class="n">pair</span><span class="o">.</span><span class="na">_2</span><span class="o">(),</span> <span class="mf">2.0</span><span class="o">);</span> + <span class="o">}</span> + <span class="o">}</span> + <span class="o">).</span><span class="na">rdd</span><span class="o">()).</span><span class="na">mean</span><span class="o">();</span> + <span class="n">System</span><span class="o">.</span><span class="na">out</span><span class="o">.</span><span class="na">println</span><span class="o">(</span><span class="s">"training Mean Squared Error = "</span> <span class="o">+</span> <span class="n">MSE</span><span class="o">);</span> + <span class="o">}</span> +<span class="o">}</span> +</code></pre></div> + + <p>In order to run the above standalone application, follow the instructions +provided in the <a href="quick-start.html#standalone-applications">Standalone +Applications</a> section of the Spark +quick-start guide. Be sure to also include <em>spark-mllib</em> to your build file as +a dependency.</p> + </div> + +<div data-lang="python"> + <p>The following example demonstrate how to load training data, parse it as an RDD of LabeledPoint. +The example then uses LinearRegressionWithSGD to build a simple linear model to predict label +values. We compute the mean squared error at the end to evaluate +<a href="http://en.wikipedia.org/wiki/Goodness_of_fit">goodness of fit</a>.</p> + + <div class="highlight"><pre><code class="python"><span class="kn">from</span> <span class="nn">pyspark.mllib.regression</span> <span class="kn">import</span> <span class="n">LabeledPoint</span><span class="p">,</span> <span class="n">LinearRegressionWithSGD</span> +<span class="kn">from</span> <span class="nn">numpy</span> <span class="kn">import</span> <span class="n">array</span> + +<span class="c"># Load and parse the data</span> +<span class="k">def</span> <span class="nf">parsePoint</span><span class="p">(</span><span class="n">line</span><span class="p">):</span> + <span class="n">values</span> <span class="o">=</span> <span class="p">[</span><span class="nb">float</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">line</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span><span class="s">','</span><span class="p">,</span> <span class="s">' '</span><span class="p">)</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="s">' '</span><span class="p">)]</span> + <span class="k">return</span> <span class="n">LabeledPoint</span><span class="p">(</span><span class="n">values</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">values</span><span class="p">[</span><span class="mi">1</span><span class="p">:])</span> + +<span class="n">data</span> <span class="o">=</span> <span class="n">sc</span><span class="o">.</span><span class="n">textFile</span><span class="p">(</span><span class="s">"data/mllib/ridge-data/lpsa.data"</span><span class="p">)</span> +<span class="n">parsedData</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="n">parsePoint</span><span class="p">)</span> + +<span class="c"># Build the model</span> +<span class="n">model</span> <span class="o">=</span> <span class="n">LinearRegressionWithSGD</span><span class="o">.</span><span class="n">train</span><span class="p">(</span><span class="n">parsedData</span><span class="p">)</span> + +<span class="c"># Evaluate the model on training data</span> +<span class="n">valuesAndPreds</span> <span class="o">=</span> <span class="n">parsedData</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="k">lambda</span> <span class="n">p</span><span class="p">:</span> <span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">label</span><span class="p">,</span> <span class="n">model</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">features</span><span class="p">)))</span> +<span class="n">MSE</span> <span class="o">=</span> <span class="n">valuesAndPreds</span><span class="o">.</span><span class="n">map</span><span class="p">(</span><span class="k">lambda</span> <span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">p</span><span class="p">):</span> <span class="p">(</span><span class="n">v</span> <span class="o">-</span> <span class="n">p</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">reduce</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">:</span> <span class="n">x</span> <span class="o">+</span> <span class="n">y</span><span class="p">)</span> <span class="o">/</span> <span class="n">valuesAndPreds</span><span class="o">.</span><span class="n">count</span><span class="p">()</span> +<span class="k">print</span><span class="p">(</span><span class="s">"Mean Squared Error = "</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">MSE</span><span class="p">))</span> +</code></pre></div> + + </div> +</div> + +<h2 id="streaming-linear-regression">Streaming linear regression</h2> + +<p>When data arrive in a streaming fashion, it is useful to fit regression models online, +updating the parameters of the model as new data arrives. MLlib currently supports +streaming linear regression using ordinary least squares. The fitting is similar +to that performed offline, except fitting occurs on each batch of data, so that +the model continually updates to reflect the data from the stream.</p> + +<h3 id="examples-2">Examples</h3> + +<p>The following example demonstrates how to load training and testing data from two different +input streams of text files, parse the streams as labeled points, fit a linear regression model +online to the first stream, and make predictions on the second stream.</p> + +<div class="codetabs"> + +<div data-lang="scala"> + + <p>First, we import the necessary classes for parsing our input data and creating the model. </p> + + <div class="highlight"><pre><code class="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.linalg.Vectors</span> +<span class="k">import</span> <span class="nn">org.apache.spark.mllib.regression.LabeledPoint</span> +<span class="k">import</span> <span class="nn">org.apache.spark.mllib.regression.StreamingLinearRegressionWithSGD</span> +</code></pre></div> + + <p>Then we make input streams for training and testing data. We assume a StreamingContext <code>ssc</code> +has already been created, see <a href="streaming-programming-guide.html#initializing">Spark Streaming Programming Guide</a> +for more info. For this example, we use labeled points in training and testing streams, +but in practice you will likely want to use unlabeled vectors for test data.</p> + + <div class="highlight"><pre><code class="scala"><span class="k">val</span> <span class="n">trainingData</span> <span class="k">=</span> <span class="n">ssc</span><span class="o">.</span><span class="n">textFileStream</span><span class="o">(</span><span class="err">'</span><span class="o">/</span><span class="n">training</span><span class="o">/</span><span class="n">data</span><span class="o">/</span><span class="n">dir</span><span class="err">'</span><span class="o">).</span><span class="n">map</span><span class="o">(</span><span class="nc">LabeledPoint</span><span class="o">.</span><span class="n">parse</span><span class="o">)</span> +<span class="k">val</span> <span class="n">testData</span> <span class="k">=</span> <span class="n">ssc</span><span class="o">.</span><span class="n">textFileStream</span><span class="o">(</span><span class="err">'</span><span class="o">/</span><span class="n">testing</span><span class="o">/</span><span class="n">data</span><span class="o">/</span><span class="n">dir</span><span class="err">'</span><span class="o">).</span><span class="n">map</span><span class="o">(</span><span class="nc">LabeledPoint</span><span class="o">.</span><span class="n">parse</span><span class="o">)</span> +</code></pre></div> + + <p>We create our model by initializing the weights to 0</p> + + <div class="highlight"><pre><code class="scala"><span class="k">val</span> <span class="n">numFeatures</span> <span class="k">=</span> <span class="mi">3</span> +<span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">StreamingLinearRegressionWithSGD</span><span class="o">()</span> + <span class="o">.</span><span class="n">setInitialWeights</span><span class="o">(</span><span class="nc">Vectors</span><span class="o">.</span><span class="n">zeros</span><span class="o">(</span><span class="n">numFeatures</span><span class="o">))</span> +</code></pre></div> + + <p>Now we register the streams for training and testing and start the job. +Printing predictions alongside true labels lets us easily see the result.</p> + + <div class="highlight"><pre><code class="scala"><span class="n">model</span><span class="o">.</span><span class="n">trainOn</span><span class="o">(</span><span class="n">trainingData</span><span class="o">)</span> +<span class="n">model</span><span class="o">.</span><span class="n">predictOnValues</span><span class="o">(</span><span class="n">testData</span><span class="o">.</span><span class="n">map</span><span class="o">(</span><span class="n">lp</span> <span class="k">=></span> <span class="o">(</span><span class="n">lp</span><span class="o">.</span><span class="n">label</span><span class="o">,</span> <span class="n">lp</span><span class="o">.</span><span class="n">features</span><span class="o">))).</span><span class="n">print</span><span class="o">()</span> + +<span class="n">ssc</span><span class="o">.</span><span class="n">start</span><span class="o">()</span> +<span class="n">ssc</span><span class="o">.</span><span class="n">awaitTermination</span><span class="o">()</span> + +</code></pre></div> + + <p>We can now save text files with data to the training or testing folders. +Each line should be a data point formatted as <code>(y,[x1,x2,x3])</code> where <code>y</code> is the label +and <code>x1,x2,x3</code> are the features. Anytime a text file is placed in <code>/training/data/dir</code> +the model will update. Anytime a text file is placed in <code>/testing/data/dir</code> you will see predictions. +As you feed more data to the training directory, the predictions +will get better!</p> + + </div> + +</div> + +<h2 id="implementation-developer">Implementation (developer)</h2> + +<p>Behind the scene, MLlib implements a simple distributed version of stochastic gradient descent +(SGD), building on the underlying gradient descent primitive (as described in the <a href="mllib-optimization.html">optimization</a> section). All provided algorithms take as input a +regularization parameter (<code>regParam</code>) along with various parameters associated with stochastic +gradient descent (<code>stepSize</code>, <code>numIterations</code>, <code>miniBatchFraction</code>). For each of them, we support +all three possible regularizations (none, L1 or L2).</p> + +<p>Algorithms are all implemented in Scala:</p> + +<ul> + <li><a href="api/scala/index.html#org.apache.spark.mllib.classification.SVMWithSGD">SVMWithSGD</a></li> + <li><a href="api/scala/index.html#org.apache.spark.mllib.classification.LogisticRegressionWithSGD">LogisticRegressionWithSGD</a></li> + <li><a href="api/scala/index.html#org.apache.spark.mllib.regression.LinearRegressionWithSGD">LinearRegressionWithSGD</a></li> + <li><a href="api/scala/index.html#org.apache.spark.mllib.regression.RidgeRegressionWithSGD">RidgeRegressionWithSGD</a></li> + <li><a href="api/scala/index.html#org.apache.spark.mllib.regression.LassoWithSGD">LassoWithSGD</a></li> +</ul> + +<p>Python calls the Scala implementation via +<a href="api/scala/index.html#org.apache.spark.mllib.api.python.PythonMLLibAPI">PythonMLLibAPI</a>.</p> + + + </div> <!-- /container --> + + <script src="js/vendor/jquery-1.8.0.min.js"></script> + <script src="js/vendor/bootstrap.min.js"></script> + <script src="js/main.js"></script> + + <!-- MathJax Section --> + <script type="text/x-mathjax-config"> + MathJax.Hub.Config({ + TeX: { equationNumbers: { autoNumber: "AMS" } } + }); + </script> + <script> + // Note that we load MathJax this way to work with local file (file://), HTTP and HTTPS. + // We could use "//cdn.mathjax...", but that won't support "file://". + (function(d, script) { + script = d.createElement('script'); + script.type = 'text/javascript'; + script.async = true; + script.onload = function(){ + MathJax.Hub.Config({ + tex2jax: { + inlineMath: [ ["$", "$"], ["\\\\(","\\\\)"] ], + displayMath: [ ["$$","$$"], ["\\[", "\\]"] ], + processEscapes: true, + skipTags: ['script', 'noscript', 'style', 'textarea', 'pre'] + } + }); + }; + script.src = ('https:' == document.location.protocol ? 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