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author | Patrick Wendell <pwendell@apache.org> | 2015-03-13 02:30:55 +0000 |
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committer | Patrick Wendell <pwendell@apache.org> | 2015-03-13 02:30:55 +0000 |
commit | aaf670598f15d47784d8b91b34dd614d0f8162af (patch) | |
tree | d86a329b056b3e9e9e79591d5b5bc3ee1781386b /site/docs/1.3.0/mllib-isotonic-regression.html | |
parent | 0d484ac791630a4f0ca7e82002113d94c931a1e7 (diff) | |
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Spark 1.3.0 docs
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diff --git a/site/docs/1.3.0/mllib-isotonic-regression.html b/site/docs/1.3.0/mllib-isotonic-regression.html new file mode 100644 index 000000000..ca5c76713 --- /dev/null +++ b/site/docs/1.3.0/mllib-isotonic-regression.html @@ -0,0 +1,299 @@ +<!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>Naive Bayes - MLlib - Spark 1.3.0 Documentation</title> + + + + + <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"> + + + + </head> + <body> + <!--[if lt IE 7]> + <p class="chromeframe">You are using an outdated browser. <a href="http://browsehappy.com/">Upgrade your browser today</a> or <a href="http://www.google.com/chromeframe/?redirect=true">install Google Chrome Frame</a> to better experience this site.</p> + <![endif]--> + + <!-- This code is taken from http://twitter.github.com/bootstrap/examples/hero.html --> + + <div class="navbar navbar-fixed-top" id="topbar"> + <div class="navbar-inner"> + <div class="container"> + <div class="brand"><a href="index.html"> + <img src="img/spark-logo-hd.png" style="height:50px;"/></a><span class="version">1.3.0</span> + </div> + <ul class="nav"> + <!--TODO(andyk): Add class="active" attribute to li some how.--> + <li><a href="index.html">Overview</a></li> + + <li class="dropdown"> + <a href="#" class="dropdown-toggle" data-toggle="dropdown">Programming Guides<b class="caret"></b></a> + <ul class="dropdown-menu"> + <li><a href="quick-start.html">Quick Start</a></li> + <li><a href="programming-guide.html">Spark Programming Guide</a></li> + <li class="divider"></li> + <li><a href="streaming-programming-guide.html">Spark Streaming</a></li> + <li><a href="sql-programming-guide.html">DataFrames and SQL</a></li> + <li><a href="mllib-guide.html">MLlib (Machine Learning)</a></li> + <li><a href="graphx-programming-guide.html">GraphX (Graph Processing)</a></li> + <li><a href="bagel-programming-guide.html">Bagel (Pregel on Spark)</a></li> + </ul> + </li> + + <li class="dropdown"> + <a href="#" class="dropdown-toggle" data-toggle="dropdown">API Docs<b class="caret"></b></a> + <ul class="dropdown-menu"> + <li><a href="api/scala/index.html#org.apache.spark.package">Scala</a></li> + <li><a href="api/java/index.html">Java</a></li> + <li><a href="api/python/index.html">Python</a></li> + </ul> + </li> + + <li class="dropdown"> + <a href="#" class="dropdown-toggle" data-toggle="dropdown">Deploying<b class="caret"></b></a> + <ul class="dropdown-menu"> + <li><a href="cluster-overview.html">Overview</a></li> + <li><a href="submitting-applications.html">Submitting Applications</a></li> + <li class="divider"></li> + <li><a href="spark-standalone.html">Spark Standalone</a></li> + <li><a href="running-on-mesos.html">Mesos</a></li> + <li><a href="running-on-yarn.html">YARN</a></li> + <li class="divider"></li> + <li><a href="ec2-scripts.html">Amazon EC2</a></li> + </ul> + </li> + + <li class="dropdown"> + <a href="api.html" class="dropdown-toggle" data-toggle="dropdown">More<b class="caret"></b></a> + <ul class="dropdown-menu"> + <li><a href="configuration.html">Configuration</a></li> + <li><a href="monitoring.html">Monitoring</a></li> + <li><a href="tuning.html">Tuning Guide</a></li> + <li><a href="job-scheduling.html">Job Scheduling</a></li> + <li><a href="security.html">Security</a></li> + <li><a href="hardware-provisioning.html">Hardware Provisioning</a></li> + <li><a href="hadoop-third-party-distributions.html">3<sup>rd</sup>-Party Hadoop Distros</a></li> + <li class="divider"></li> + <li><a href="building-spark.html">Building Spark</a></li> + <li><a href="https://cwiki.apache.org/confluence/display/SPARK/Contributing+to+Spark">Contributing to Spark</a></li> + <li><a href="https://cwiki.apache.org/confluence/display/SPARK/Supplemental+Spark+Projects">Supplemental Projects</a></li> + </ul> + </li> + </ul> + <!--<p class="navbar-text pull-right"><span class="version-text">v1.3.0</span></p>--> + </div> + </div> + </div> + + <div class="container" id="content"> + + <h1 class="title"><a href="mllib-guide.html">MLlib</a> - Regression</h1> + + + <h2 id="isotonic-regression">Isotonic regression</h2> +<p><a href="http://en.wikipedia.org/wiki/Isotonic_regression">Isotonic regression</a> +belongs to the family of regression algorithms. Formally isotonic regression is a problem where +given a finite set of real numbers <code>$Y = {y_1, y_2, ..., y_n}$</code> representing observed responses +and <code>$X = {x_1, x_2, ..., x_n}$</code> the unknown response values to be fitted +finding a function that minimises</p> + +<p><code>\begin{equation} + f(x) = \sum_{i=1}^n w_i (y_i - x_i)^2 +\end{equation}</code></p> + +<p>with respect to complete order subject to +<code>$x_1\le x_2\le ...\le x_n$</code> where <code>$w_i$</code> are positive weights. +The resulting function is called isotonic regression and it is unique. +It can be viewed as least squares problem under order restriction. +Essentially isotonic regression is a +<a href="http://en.wikipedia.org/wiki/Monotonic_function">monotonic function</a> +best fitting the original data points.</p> + +<p>MLlib supports a +<a href="http://doi.org/10.1198/TECH.2010.10111">pool adjacent violators algorithm</a> +which uses an approach to +<a href="http://doi.org/10.1007/978-3-642-99789-1_10">parallelizing isotonic regression</a>. +The training input is a RDD of tuples of three double values that represent +label, feature and weight in this order. Additionally IsotonicRegression algorithm has one +optional parameter called $isotonic$ defaulting to true. +This argument specifies if the isotonic regression is +isotonic (monotonically increasing) or antitonic (monotonically decreasing).</p> + +<p>Training returns an IsotonicRegressionModel that can be used to predict +labels for both known and unknown features. The result of isotonic regression +is treated as piecewise linear function. The rules for prediction therefore are:</p> + +<ul> + <li>If the prediction input exactly matches a training feature +then associated prediction is returned. In case there are multiple predictions with the same +feature then one of them is returned. Which one is undefined +(same as java.util.Arrays.binarySearch).</li> + <li>If the prediction input is lower or higher than all training features +then prediction with lowest or highest feature is returned respectively. +In case there are multiple predictions with the same feature +then the lowest or highest is returned respectively.</li> + <li>If the prediction input falls between two training features then prediction is treated +as piecewise linear function and interpolated value is calculated from the +predictions of the two closest features. In case there are multiple values +with the same feature then the same rules as in previous point are used.</li> +</ul> + +<h3 id="examples">Examples</h3> + +<div class="codetabs"> +<div data-lang="scala"> + <p>Data are read from a file where each line has a format label,feature +i.e. 4710.28,500.00. The data are split to training and testing set. +Model is created using the training set and a mean squared error is calculated from the predicted +labels and real labels in the test set.</p> + + <div class="highlight"><pre><code class="language-scala" data-lang="scala"><span class="k">import</span> <span class="nn">org.apache.spark.mllib.regression.IsotonicRegression</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/sample_isotonic_regression_data.txt"</span><span class="o">)</span> + +<span class="c1">// Create label, feature, weight tuples from input data with weight set to default value 1.0.</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="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="n">parts</span><span class="o">(</span><span class="mi">0</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="mf">1.0</span><span class="o">)</span> +<span class="o">}</span> + +<span class="c1">// Split data into training (60%) and test (40%) sets.</span> +<span class="k">val</span> <span class="n">splits</span> <span class="k">=</span> <span class="n">parsedData</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="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">// Create isotonic regression model from training data.</span> +<span class="c1">// Isotonic parameter defaults to true so it is only shown for demonstration</span> +<span class="k">val</span> <span class="n">model</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">IsotonicRegression</span><span class="o">().</span><span class="n">setIsotonic</span><span class="o">(</span><span class="kc">true</span><span class="o">).</span><span class="n">run</span><span class="o">(</span><span class="n">training</span><span class="o">)</span> + +<span class="c1">// Create tuples of predicted and real labels.</span> +<span class="k">val</span> <span class="n">predictionAndLabel</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">predictedLabel</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">_2</span><span class="o">)</span> + <span class="o">(</span><span class="n">predictedLabel</span><span class="o">,</span> <span class="n">point</span><span class="o">.</span><span class="n">_1</span><span class="o">)</span> +<span class="o">}</span> + +<span class="c1">// Calculate mean squared error between predicted and real labels.</span> +<span class="k">val</span> <span class="n">meanSquaredError</span> <span class="k">=</span> <span class="n">predictionAndLabel</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">p</span><span class="o">,</span> <span class="n">l</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">p</span> <span class="o">-</span> <span class="n">l</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">"Mean Squared Error = "</span> <span class="o">+</span> <span class="n">meanSquaredError</span><span class="o">)</span></code></pre></div> + + </div> + +<div data-lang="java"> + <p>Data are read from a file where each line has a format label,feature +i.e. 4710.28,500.00. The data are split to training and testing set. +Model is created using the training set and a mean squared error is calculated from the predicted +labels and real labels in the test set.</p> + + <div class="highlight"><pre><code class="language-java" data-lang="java"><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.api.java.JavaDoubleRDD</span><span class="o">;</span> +<span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaPairRDD</span><span class="o">;</span> +<span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaRDD</span><span class="o">;</span> +<span class="kn">import</span> <span class="nn">org.apache.spark.api.java.JavaSparkContext</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.api.java.function.PairFunction</span><span class="o">;</span> +<span class="kn">import</span> <span class="nn">org.apache.spark.mllib.regression.IsotonicRegressionModel</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">scala.Tuple3</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="s">"data/mllib/sample_isotonic_regression_data.txt"</span><span class="o">);</span> + +<span class="c1">// Create label, feature, weight tuples from input data with weight set to default value 1.0.</span> +<span class="n">JavaRDD</span><span class="o"><</span><span class="n">Tuple3</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">Double</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">Tuple3</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">Double</span><span class="o">>>()</span> <span class="o">{</span> + <span class="kd">public</span> <span class="n">Tuple3</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">Double</span><span class="o">></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="k">return</span> <span class="k">new</span> <span class="n">Tuple3</span><span class="o"><>(</span><span class="k">new</span> <span class="nf">Double</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="k">new</span> <span class="nf">Double</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="mf">1.0</span><span class="o">);</span> + <span class="o">}</span> + <span class="o">}</span> +<span class="o">);</span> + +<span class="c1">// Split data into training (60%) and test (40%) sets.</span> +<span class="n">JavaRDD</span><span class="o"><</span><span class="n">Tuple3</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">Double</span><span class="o">>>[]</span> <span class="n">splits</span> <span class="o">=</span> <span class="n">parsedData</span><span class="o">.</span><span class="na">randomSplit</span><span class="o">(</span><span class="k">new</span> <span class="kt">double</span><span class="o">[]</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="mi">11L</span><span class="o">);</span> +<span class="n">JavaRDD</span><span class="o"><</span><span class="n">Tuple3</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">Double</span><span class="o">>></span> <span class="n">training</span> <span class="o">=</span> <span class="n">splits</span><span class="o">[</span><span class="mi">0</span><span class="o">];</span> +<span class="n">JavaRDD</span><span class="o"><</span><span class="n">Tuple3</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">Double</span><span class="o">>></span> <span class="n">test</span> <span class="o">=</span> <span class="n">splits</span><span class="o">[</span><span class="mi">1</span><span class="o">];</span> + +<span class="c1">// Create isotonic regression model from training data.</span> +<span class="c1">// Isotonic parameter defaults to true so it is only shown for demonstration</span> +<span class="n">IsotonicRegressionModel</span> <span class="n">model</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">IsotonicRegression</span><span class="o">().</span><span class="na">setIsotonic</span><span class="o">(</span><span class="kc">true</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="c1">// Create tuples of predicted and real labels.</span> +<span class="n">JavaPairRDD</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">predictionAndLabel</span> <span class="o">=</span> <span class="n">test</span><span class="o">.</span><span class="na">mapToPair</span><span class="o">(</span> + <span class="k">new</span> <span class="n">PairFunction</span><span class="o"><</span><span class="n">Tuple3</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">Double</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="nd">@Override</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="nf">call</span><span class="o">(</span><span class="n">Tuple3</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">Double</span><span class="o">></span> <span class="n">point</span><span class="o">)</span> <span class="o">{</span> + <span class="n">Double</span> <span class="n">predictedLabel</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">_2</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">predictedLabel</span><span class="o">,</span> <span class="n">point</span><span class="o">.</span><span class="na">_1</span><span class="o">());</span> + <span class="o">}</span> + <span class="o">}</span> +<span class="o">);</span> + +<span class="c1">// Calculate mean squared error between predicted and real labels.</span> +<span class="n">Double</span> <span class="n">meanSquaredError</span> <span class="o">=</span> <span class="k">new</span> <span class="nf">JavaDoubleRDD</span><span class="o">(</span><span class="n">predictionAndLabel</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="nd">@Override</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">pl</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">pl</span><span class="o">.</span><span class="na">_1</span><span class="o">()</span> <span class="o">-</span> <span class="n">pl</span><span class="o">.</span><span class="na">_2</span><span class="o">(),</span> <span class="mi">2</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">"Mean Squared Error = "</span> <span class="o">+</span> <span class="n">meanSquaredError</span><span class="o">);</span></code></pre></div> + + </div> +</div> + + + </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 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