| |
| <!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"> |
| <meta name="viewport" content="width=device-width, initial-scale=1.0"> |
| |
| <title>ML Pipelines - Spark 3.5.0 Documentation</title> |
| |
| |
| |
| |
| |
| <link rel="stylesheet" href="css/bootstrap.min.css"> |
| <link rel="preconnect" href="https://fonts.googleapis.com"> |
| <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin> |
| <link href="https://fonts.googleapis.com/css2?family=DM+Sans:ital,wght@0,400;0,500;0,700;1,400;1,500;1,700&Courier+Prime:wght@400;700&display=swap" rel="stylesheet"> |
| <link href="css/custom.css" rel="stylesheet"> |
| <script src="js/vendor/modernizr-2.6.1-respond-1.1.0.min.js"></script> |
| |
| <link rel="stylesheet" href="css/pygments-default.css"> |
| <link rel="stylesheet" href="css/docsearch.min.css" /> |
| <link rel="stylesheet" href="css/docsearch.css"> |
| |
| <!-- Matomo --> |
| <script type="text/javascript"> |
| var _paq = window._paq = window._paq || []; |
| /* tracker methods like "setCustomDimension" should be called before "trackPageView" */ |
| _paq.push(["disableCookies"]); |
| _paq.push(['trackPageView']); |
| _paq.push(['enableLinkTracking']); |
| (function() { |
| var u="https://analytics.apache.org/"; |
| _paq.push(['setTrackerUrl', u+'matomo.php']); |
| _paq.push(['setSiteId', '40']); |
| var d=document, g=d.createElement('script'), s=d.getElementsByTagName('script')[0]; |
| g.async=true; g.src=u+'matomo.js'; s.parentNode.insertBefore(g,s); |
| })(); |
| </script> |
| <!-- End Matomo Code --> |
| </head> |
| <body class="global"> |
| <!--[if lt IE 7]> |
| <p class="chromeframe">You are using an outdated browser. <a href="https://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 --> |
| |
| <nav class="navbar navbar-expand-lg navbar-dark p-0 px-4 fixed-top" style="background: #1d6890;" id="topbar"> |
| <div class="navbar-brand"><a href="index.html"> |
| <img src="img/spark-logo-rev.svg" width="141" height="72"/></a><span class="version">3.5.0</span> |
| </div> |
| <button class="navbar-toggler" type="button" data-toggle="collapse" |
| data-target="#navbarCollapse" aria-controls="navbarCollapse" |
| aria-expanded="false" aria-label="Toggle navigation"> |
| <span class="navbar-toggler-icon"></span> |
| </button> |
| <div class="collapse navbar-collapse" id="navbarCollapse"> |
| <ul class="navbar-nav me-auto"> |
| <li class="nav-item"><a href="index.html" class="nav-link">Overview</a></li> |
| |
| <li class="nav-item dropdown"> |
| <a href="#" class="nav-link dropdown-toggle" id="navbarQuickStart" role="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false">Programming Guides</a> |
| <div class="dropdown-menu" aria-labelledby="navbarQuickStart"> |
| <a class="dropdown-item" href="quick-start.html">Quick Start</a> |
| <a class="dropdown-item" href="rdd-programming-guide.html">RDDs, Accumulators, Broadcasts Vars</a> |
| <a class="dropdown-item" href="sql-programming-guide.html">SQL, DataFrames, and Datasets</a> |
| <a class="dropdown-item" href="structured-streaming-programming-guide.html">Structured Streaming</a> |
| <a class="dropdown-item" href="streaming-programming-guide.html">Spark Streaming (DStreams)</a> |
| <a class="dropdown-item" href="ml-guide.html">MLlib (Machine Learning)</a> |
| <a class="dropdown-item" href="graphx-programming-guide.html">GraphX (Graph Processing)</a> |
| <a class="dropdown-item" href="sparkr.html">SparkR (R on Spark)</a> |
| <a class="dropdown-item" href="api/python/getting_started/index.html">PySpark (Python on Spark)</a> |
| </div> |
| </li> |
| |
| <li class="nav-item dropdown"> |
| <a href="#" class="nav-link dropdown-toggle" id="navbarAPIDocs" role="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false">API Docs</a> |
| <div class="dropdown-menu" aria-labelledby="navbarAPIDocs"> |
| <a class="dropdown-item" href="api/scala/org/apache/spark/index.html">Scala</a> |
| <a class="dropdown-item" href="api/java/index.html">Java</a> |
| <a class="dropdown-item" href="api/python/index.html">Python</a> |
| <a class="dropdown-item" href="api/R/index.html">R</a> |
| <a class="dropdown-item" href="api/sql/index.html">SQL, Built-in Functions</a> |
| </div> |
| </li> |
| |
| <li class="nav-item dropdown"> |
| <a href="#" class="nav-link dropdown-toggle" id="navbarDeploying" role="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false">Deploying</a> |
| <div class="dropdown-menu" aria-labelledby="navbarDeploying"> |
| <a class="dropdown-item" href="cluster-overview.html">Overview</a> |
| <a class="dropdown-item" href="submitting-applications.html">Submitting Applications</a> |
| <div class="dropdown-divider"></div> |
| <a class="dropdown-item" href="spark-standalone.html">Spark Standalone</a> |
| <a class="dropdown-item" href="running-on-mesos.html">Mesos</a> |
| <a class="dropdown-item" href="running-on-yarn.html">YARN</a> |
| <a class="dropdown-item" href="running-on-kubernetes.html">Kubernetes</a> |
| </div> |
| </li> |
| |
| <li class="nav-item dropdown"> |
| <a href="#" class="nav-link dropdown-toggle" id="navbarMore" role="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false">More</a> |
| <div class="dropdown-menu" aria-labelledby="navbarMore"> |
| <a class="dropdown-item" href="configuration.html">Configuration</a> |
| <a class="dropdown-item" href="monitoring.html">Monitoring</a> |
| <a class="dropdown-item" href="tuning.html">Tuning Guide</a> |
| <a class="dropdown-item" href="job-scheduling.html">Job Scheduling</a> |
| <a class="dropdown-item" href="security.html">Security</a> |
| <a class="dropdown-item" href="hardware-provisioning.html">Hardware Provisioning</a> |
| <a class="dropdown-item" href="migration-guide.html">Migration Guide</a> |
| <div class="dropdown-divider"></div> |
| <a class="dropdown-item" href="building-spark.html">Building Spark</a> |
| <a class="dropdown-item" href="https://spark.apache.org/contributing.html">Contributing to Spark</a> |
| <a class="dropdown-item" href="https://spark.apache.org/third-party-projects.html">Third Party Projects</a> |
| </div> |
| </li> |
| |
| <li class="nav-item"> |
| <input type="text" id="docsearch-input" placeholder="Search the docs…"> |
| </li> |
| </ul> |
| <!--<span class="navbar-text navbar-right"><span class="version-text">v3.5.0</span></span>--> |
| </div> |
| </nav> |
| |
| |
| |
| <div class="container"> |
| |
| |
| |
| <div class="left-menu-wrapper"> |
| <div class="left-menu"> |
| <h3><a href="ml-guide.html">MLlib: Main Guide</a></h3> |
| |
| <ul> |
| |
| <li> |
| <a href="ml-statistics.html"> |
| |
| Basic statistics |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="ml-datasource.html"> |
| |
| Data sources |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="ml-pipeline.html"> |
| |
| Pipelines |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="ml-features.html"> |
| |
| Extracting, transforming and selecting features |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="ml-classification-regression.html"> |
| |
| Classification and Regression |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="ml-clustering.html"> |
| |
| Clustering |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="ml-collaborative-filtering.html"> |
| |
| Collaborative filtering |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="ml-frequent-pattern-mining.html"> |
| |
| Frequent Pattern Mining |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="ml-tuning.html"> |
| |
| Model selection and tuning |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="ml-advanced.html"> |
| |
| Advanced topics |
| |
| </a> |
| </li> |
| |
| |
| |
| </ul> |
| |
| <h3><a href="mllib-guide.html">MLlib: RDD-based API Guide</a></h3> |
| |
| <ul> |
| |
| <li> |
| <a href="mllib-data-types.html"> |
| |
| Data types |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="mllib-statistics.html"> |
| |
| Basic statistics |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="mllib-classification-regression.html"> |
| |
| Classification and regression |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="mllib-collaborative-filtering.html"> |
| |
| Collaborative filtering |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="mllib-clustering.html"> |
| |
| Clustering |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="mllib-dimensionality-reduction.html"> |
| |
| Dimensionality reduction |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="mllib-feature-extraction.html"> |
| |
| Feature extraction and transformation |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="mllib-frequent-pattern-mining.html"> |
| |
| Frequent pattern mining |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="mllib-evaluation-metrics.html"> |
| |
| Evaluation metrics |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="mllib-pmml-model-export.html"> |
| |
| PMML model export |
| |
| </a> |
| </li> |
| |
| |
| |
| <li> |
| <a href="mllib-optimization.html"> |
| |
| Optimization (developer) |
| |
| </a> |
| </li> |
| |
| |
| |
| </ul> |
| |
| </div> |
| </div> |
| |
| <input id="nav-trigger" class="nav-trigger" checked type="checkbox"> |
| <label for="nav-trigger"></label> |
| <div class="content-with-sidebar mr-3" id="content"> |
| |
| <h1 class="title">ML Pipelines</h1> |
| |
| |
| <p><code class="language-plaintext highlighter-rouge">\[ |
| \newcommand{\R}{\mathbb{R}} |
| \newcommand{\E}{\mathbb{E}} |
| \newcommand{\x}{\mathbf{x}} |
| \newcommand{\y}{\mathbf{y}} |
| \newcommand{\wv}{\mathbf{w}} |
| \newcommand{\av}{\mathbf{\alpha}} |
| \newcommand{\bv}{\mathbf{b}} |
| \newcommand{\N}{\mathbb{N}} |
| \newcommand{\id}{\mathbf{I}} |
| \newcommand{\ind}{\mathbf{1}} |
| \newcommand{\0}{\mathbf{0}} |
| \newcommand{\unit}{\mathbf{e}} |
| \newcommand{\one}{\mathbf{1}} |
| \newcommand{\zero}{\mathbf{0}} |
| \]</code></p> |
| |
| <p>In this section, we introduce the concept of <strong><em>ML Pipelines</em></strong>. |
| ML Pipelines provide a uniform set of high-level APIs built on top of |
| <a href="sql-programming-guide.html">DataFrames</a> that help users create and tune practical |
| machine learning pipelines.</p> |
| |
| <p><strong>Table of Contents</strong></p> |
| |
| <ul id="markdown-toc"> |
| <li><a href="#main-concepts-in-pipelines" id="markdown-toc-main-concepts-in-pipelines">Main concepts in Pipelines</a> <ul> |
| <li><a href="#dataframe" id="markdown-toc-dataframe">DataFrame</a></li> |
| <li><a href="#pipeline-components" id="markdown-toc-pipeline-components">Pipeline components</a> <ul> |
| <li><a href="#transformers" id="markdown-toc-transformers">Transformers</a></li> |
| <li><a href="#estimators" id="markdown-toc-estimators">Estimators</a></li> |
| <li><a href="#properties-of-pipeline-components" id="markdown-toc-properties-of-pipeline-components">Properties of pipeline components</a></li> |
| </ul> |
| </li> |
| <li><a href="#pipeline" id="markdown-toc-pipeline">Pipeline</a> <ul> |
| <li><a href="#how-it-works" id="markdown-toc-how-it-works">How it works</a></li> |
| <li><a href="#details" id="markdown-toc-details">Details</a></li> |
| </ul> |
| </li> |
| <li><a href="#parameters" id="markdown-toc-parameters">Parameters</a></li> |
| <li><a href="#ml-persistence-saving-and-loading-pipelines" id="markdown-toc-ml-persistence-saving-and-loading-pipelines">ML persistence: Saving and Loading Pipelines</a> <ul> |
| <li><a href="#backwards-compatibility-for-ml-persistence" id="markdown-toc-backwards-compatibility-for-ml-persistence">Backwards compatibility for ML persistence</a></li> |
| </ul> |
| </li> |
| </ul> |
| </li> |
| <li><a href="#code-examples" id="markdown-toc-code-examples">Code examples</a> <ul> |
| <li><a href="#example-estimator-transformer-and-param" id="markdown-toc-example-estimator-transformer-and-param">Example: Estimator, Transformer, and Param</a></li> |
| <li><a href="#example-pipeline" id="markdown-toc-example-pipeline">Example: Pipeline</a></li> |
| <li><a href="#model-selection-hyperparameter-tuning" id="markdown-toc-model-selection-hyperparameter-tuning">Model selection (hyperparameter tuning)</a></li> |
| </ul> |
| </li> |
| </ul> |
| |
| <h1 id="main-concepts-in-pipelines">Main concepts in Pipelines</h1> |
| |
| <p>MLlib standardizes APIs for machine learning algorithms to make it easier to combine multiple |
| algorithms into a single pipeline, or workflow. |
| This section covers the key concepts introduced by the Pipelines API, where the pipeline concept is |
| mostly inspired by the <a href="http://scikit-learn.org/">scikit-learn</a> project.</p> |
| |
| <ul> |
| <li> |
| <p><strong><a href="ml-pipeline.html#dataframe"><code class="language-plaintext highlighter-rouge">DataFrame</code></a></strong>: This ML API uses <code class="language-plaintext highlighter-rouge">DataFrame</code> from Spark SQL as an ML |
| dataset, which can hold a variety of data types. |
| E.g., a <code class="language-plaintext highlighter-rouge">DataFrame</code> could have different columns storing text, feature vectors, true labels, and predictions.</p> |
| </li> |
| <li> |
| <p><strong><a href="ml-pipeline.html#transformers"><code class="language-plaintext highlighter-rouge">Transformer</code></a></strong>: A <code class="language-plaintext highlighter-rouge">Transformer</code> is an algorithm which can transform one <code class="language-plaintext highlighter-rouge">DataFrame</code> into another <code class="language-plaintext highlighter-rouge">DataFrame</code>. |
| E.g., an ML model is a <code class="language-plaintext highlighter-rouge">Transformer</code> which transforms a <code class="language-plaintext highlighter-rouge">DataFrame</code> with features into a <code class="language-plaintext highlighter-rouge">DataFrame</code> with predictions.</p> |
| </li> |
| <li> |
| <p><strong><a href="ml-pipeline.html#estimators"><code class="language-plaintext highlighter-rouge">Estimator</code></a></strong>: An <code class="language-plaintext highlighter-rouge">Estimator</code> is an algorithm which can be fit on a <code class="language-plaintext highlighter-rouge">DataFrame</code> to produce a <code class="language-plaintext highlighter-rouge">Transformer</code>. |
| E.g., a learning algorithm is an <code class="language-plaintext highlighter-rouge">Estimator</code> which trains on a <code class="language-plaintext highlighter-rouge">DataFrame</code> and produces a model.</p> |
| </li> |
| <li> |
| <p><strong><a href="ml-pipeline.html#pipeline"><code class="language-plaintext highlighter-rouge">Pipeline</code></a></strong>: A <code class="language-plaintext highlighter-rouge">Pipeline</code> chains multiple <code class="language-plaintext highlighter-rouge">Transformer</code>s and <code class="language-plaintext highlighter-rouge">Estimator</code>s together to specify an ML workflow.</p> |
| </li> |
| <li> |
| <p><strong><a href="ml-pipeline.html#parameters"><code class="language-plaintext highlighter-rouge">Parameter</code></a></strong>: All <code class="language-plaintext highlighter-rouge">Transformer</code>s and <code class="language-plaintext highlighter-rouge">Estimator</code>s now share a common API for specifying parameters.</p> |
| </li> |
| </ul> |
| |
| <h2 id="dataframe">DataFrame</h2> |
| |
| <p>Machine learning can be applied to a wide variety of data types, such as vectors, text, images, and structured data. |
| This API adopts the <code class="language-plaintext highlighter-rouge">DataFrame</code> from Spark SQL in order to support a variety of data types.</p> |
| |
| <p><code class="language-plaintext highlighter-rouge">DataFrame</code> supports many basic and structured types; see the <a href="sql-ref-datatypes.html">Spark SQL datatype reference</a> for a list of supported types. |
| In addition to the types listed in the Spark SQL guide, <code class="language-plaintext highlighter-rouge">DataFrame</code> can use ML <a href="mllib-data-types.html#local-vector"><code class="language-plaintext highlighter-rouge">Vector</code></a> types.</p> |
| |
| <p>A <code class="language-plaintext highlighter-rouge">DataFrame</code> can be created either implicitly or explicitly from a regular <code class="language-plaintext highlighter-rouge">RDD</code>. See the code examples below and the <a href="sql-programming-guide.html">Spark SQL programming guide</a> for examples.</p> |
| |
| <p>Columns in a <code class="language-plaintext highlighter-rouge">DataFrame</code> are named. The code examples below use names such as “text”, “features”, and “label”.</p> |
| |
| <h2 id="pipeline-components">Pipeline components</h2> |
| |
| <h3 id="transformers">Transformers</h3> |
| |
| <p>A <code class="language-plaintext highlighter-rouge">Transformer</code> is an abstraction that includes feature transformers and learned models. |
| Technically, a <code class="language-plaintext highlighter-rouge">Transformer</code> implements a method <code class="language-plaintext highlighter-rouge">transform()</code>, which converts one <code class="language-plaintext highlighter-rouge">DataFrame</code> into |
| another, generally by appending one or more columns. |
| For example:</p> |
| |
| <ul> |
| <li>A feature transformer might take a <code class="language-plaintext highlighter-rouge">DataFrame</code>, read a column (e.g., text), map it into a new |
| column (e.g., feature vectors), and output a new <code class="language-plaintext highlighter-rouge">DataFrame</code> with the mapped column appended.</li> |
| <li>A learning model might take a <code class="language-plaintext highlighter-rouge">DataFrame</code>, read the column containing feature vectors, predict the |
| label for each feature vector, and output a new <code class="language-plaintext highlighter-rouge">DataFrame</code> with predicted labels appended as a |
| column.</li> |
| </ul> |
| |
| <h3 id="estimators">Estimators</h3> |
| |
| <p>An <code class="language-plaintext highlighter-rouge">Estimator</code> abstracts the concept of a learning algorithm or any algorithm that fits or trains on |
| data. |
| Technically, an <code class="language-plaintext highlighter-rouge">Estimator</code> implements a method <code class="language-plaintext highlighter-rouge">fit()</code>, which accepts a <code class="language-plaintext highlighter-rouge">DataFrame</code> and produces a |
| <code class="language-plaintext highlighter-rouge">Model</code>, which is a <code class="language-plaintext highlighter-rouge">Transformer</code>. |
| For example, a learning algorithm such as <code class="language-plaintext highlighter-rouge">LogisticRegression</code> is an <code class="language-plaintext highlighter-rouge">Estimator</code>, and calling |
| <code class="language-plaintext highlighter-rouge">fit()</code> trains a <code class="language-plaintext highlighter-rouge">LogisticRegressionModel</code>, which is a <code class="language-plaintext highlighter-rouge">Model</code> and hence a <code class="language-plaintext highlighter-rouge">Transformer</code>.</p> |
| |
| <h3 id="properties-of-pipeline-components">Properties of pipeline components</h3> |
| |
| <p><code class="language-plaintext highlighter-rouge">Transformer.transform()</code>s and <code class="language-plaintext highlighter-rouge">Estimator.fit()</code>s are both stateless. In the future, stateful algorithms may be supported via alternative concepts.</p> |
| |
| <p>Each instance of a <code class="language-plaintext highlighter-rouge">Transformer</code> or <code class="language-plaintext highlighter-rouge">Estimator</code> has a unique ID, which is useful in specifying parameters (discussed below).</p> |
| |
| <h2 id="pipeline">Pipeline</h2> |
| |
| <p>In machine learning, it is common to run a sequence of algorithms to process and learn from data. |
| E.g., a simple text document processing workflow might include several stages:</p> |
| |
| <ul> |
| <li>Split each document’s text into words.</li> |
| <li>Convert each document’s words into a numerical feature vector.</li> |
| <li>Learn a prediction model using the feature vectors and labels.</li> |
| </ul> |
| |
| <p>MLlib represents such a workflow as a <code class="language-plaintext highlighter-rouge">Pipeline</code>, which consists of a sequence of |
| <code class="language-plaintext highlighter-rouge">PipelineStage</code>s (<code class="language-plaintext highlighter-rouge">Transformer</code>s and <code class="language-plaintext highlighter-rouge">Estimator</code>s) to be run in a specific order. |
| We will use this simple workflow as a running example in this section.</p> |
| |
| <h3 id="how-it-works">How it works</h3> |
| |
| <p>A <code class="language-plaintext highlighter-rouge">Pipeline</code> is specified as a sequence of stages, and each stage is either a <code class="language-plaintext highlighter-rouge">Transformer</code> or an <code class="language-plaintext highlighter-rouge">Estimator</code>. |
| These stages are run in order, and the input <code class="language-plaintext highlighter-rouge">DataFrame</code> is transformed as it passes through each stage. |
| For <code class="language-plaintext highlighter-rouge">Transformer</code> stages, the <code class="language-plaintext highlighter-rouge">transform()</code> method is called on the <code class="language-plaintext highlighter-rouge">DataFrame</code>. |
| For <code class="language-plaintext highlighter-rouge">Estimator</code> stages, the <code class="language-plaintext highlighter-rouge">fit()</code> method is called to produce a <code class="language-plaintext highlighter-rouge">Transformer</code> (which becomes part of the <code class="language-plaintext highlighter-rouge">PipelineModel</code>, or fitted <code class="language-plaintext highlighter-rouge">Pipeline</code>), and that <code class="language-plaintext highlighter-rouge">Transformer</code>’s <code class="language-plaintext highlighter-rouge">transform()</code> method is called on the <code class="language-plaintext highlighter-rouge">DataFrame</code>.</p> |
| |
| <p>We illustrate this for the simple text document workflow. The figure below is for the <em>training time</em> usage of a <code class="language-plaintext highlighter-rouge">Pipeline</code>.</p> |
| |
| <p style="text-align: center;"> |
| <img src="img/ml-Pipeline.png" title="ML Pipeline Example" alt="ML Pipeline Example" width="80%" /> |
| </p> |
| |
| <p>Above, the top row represents a <code class="language-plaintext highlighter-rouge">Pipeline</code> with three stages. |
| The first two (<code class="language-plaintext highlighter-rouge">Tokenizer</code> and <code class="language-plaintext highlighter-rouge">HashingTF</code>) are <code class="language-plaintext highlighter-rouge">Transformer</code>s (blue), and the third (<code class="language-plaintext highlighter-rouge">LogisticRegression</code>) is an <code class="language-plaintext highlighter-rouge">Estimator</code> (red). |
| The bottom row represents data flowing through the pipeline, where cylinders indicate <code class="language-plaintext highlighter-rouge">DataFrame</code>s. |
| The <code class="language-plaintext highlighter-rouge">Pipeline.fit()</code> method is called on the original <code class="language-plaintext highlighter-rouge">DataFrame</code>, which has raw text documents and labels. |
| The <code class="language-plaintext highlighter-rouge">Tokenizer.transform()</code> method splits the raw text documents into words, adding a new column with words to the <code class="language-plaintext highlighter-rouge">DataFrame</code>. |
| The <code class="language-plaintext highlighter-rouge">HashingTF.transform()</code> method converts the words column into feature vectors, adding a new column with those vectors to the <code class="language-plaintext highlighter-rouge">DataFrame</code>. |
| Now, since <code class="language-plaintext highlighter-rouge">LogisticRegression</code> is an <code class="language-plaintext highlighter-rouge">Estimator</code>, the <code class="language-plaintext highlighter-rouge">Pipeline</code> first calls <code class="language-plaintext highlighter-rouge">LogisticRegression.fit()</code> to produce a <code class="language-plaintext highlighter-rouge">LogisticRegressionModel</code>. |
| If the <code class="language-plaintext highlighter-rouge">Pipeline</code> had more <code class="language-plaintext highlighter-rouge">Estimator</code>s, it would call the <code class="language-plaintext highlighter-rouge">LogisticRegressionModel</code>’s <code class="language-plaintext highlighter-rouge">transform()</code> |
| method on the <code class="language-plaintext highlighter-rouge">DataFrame</code> before passing the <code class="language-plaintext highlighter-rouge">DataFrame</code> to the next stage.</p> |
| |
| <p>A <code class="language-plaintext highlighter-rouge">Pipeline</code> is an <code class="language-plaintext highlighter-rouge">Estimator</code>. |
| Thus, after a <code class="language-plaintext highlighter-rouge">Pipeline</code>’s <code class="language-plaintext highlighter-rouge">fit()</code> method runs, it produces a <code class="language-plaintext highlighter-rouge">PipelineModel</code>, which is a |
| <code class="language-plaintext highlighter-rouge">Transformer</code>. |
| This <code class="language-plaintext highlighter-rouge">PipelineModel</code> is used at <em>test time</em>; the figure below illustrates this usage.</p> |
| |
| <p style="text-align: center;"> |
| <img src="img/ml-PipelineModel.png" title="ML PipelineModel Example" alt="ML PipelineModel Example" width="80%" /> |
| </p> |
| |
| <p>In the figure above, the <code class="language-plaintext highlighter-rouge">PipelineModel</code> has the same number of stages as the original <code class="language-plaintext highlighter-rouge">Pipeline</code>, but all <code class="language-plaintext highlighter-rouge">Estimator</code>s in the original <code class="language-plaintext highlighter-rouge">Pipeline</code> have become <code class="language-plaintext highlighter-rouge">Transformer</code>s. |
| When the <code class="language-plaintext highlighter-rouge">PipelineModel</code>’s <code class="language-plaintext highlighter-rouge">transform()</code> method is called on a test dataset, the data are passed |
| through the fitted pipeline in order. |
| Each stage’s <code class="language-plaintext highlighter-rouge">transform()</code> method updates the dataset and passes it to the next stage.</p> |
| |
| <p><code class="language-plaintext highlighter-rouge">Pipeline</code>s and <code class="language-plaintext highlighter-rouge">PipelineModel</code>s help to ensure that training and test data go through identical feature processing steps.</p> |
| |
| <h3 id="details">Details</h3> |
| |
| <p><em>DAG <code class="language-plaintext highlighter-rouge">Pipeline</code>s</em>: A <code class="language-plaintext highlighter-rouge">Pipeline</code>’s stages are specified as an ordered array. The examples given here are all for linear <code class="language-plaintext highlighter-rouge">Pipeline</code>s, i.e., <code class="language-plaintext highlighter-rouge">Pipeline</code>s in which each stage uses data produced by the previous stage. It is possible to create non-linear <code class="language-plaintext highlighter-rouge">Pipeline</code>s as long as the data flow graph forms a Directed Acyclic Graph (DAG). This graph is currently specified implicitly based on the input and output column names of each stage (generally specified as parameters). If the <code class="language-plaintext highlighter-rouge">Pipeline</code> forms a DAG, then the stages must be specified in topological order.</p> |
| |
| <p><em>Runtime checking</em>: Since <code class="language-plaintext highlighter-rouge">Pipeline</code>s can operate on <code class="language-plaintext highlighter-rouge">DataFrame</code>s with varied types, they cannot use |
| compile-time type checking. |
| <code class="language-plaintext highlighter-rouge">Pipeline</code>s and <code class="language-plaintext highlighter-rouge">PipelineModel</code>s instead do runtime checking before actually running the <code class="language-plaintext highlighter-rouge">Pipeline</code>. |
| This type checking is done using the <code class="language-plaintext highlighter-rouge">DataFrame</code> <em>schema</em>, a description of the data types of columns in the <code class="language-plaintext highlighter-rouge">DataFrame</code>.</p> |
| |
| <p><em>Unique Pipeline stages</em>: A <code class="language-plaintext highlighter-rouge">Pipeline</code>’s stages should be unique instances. E.g., the same instance |
| <code class="language-plaintext highlighter-rouge">myHashingTF</code> should not be inserted into the <code class="language-plaintext highlighter-rouge">Pipeline</code> twice since <code class="language-plaintext highlighter-rouge">Pipeline</code> stages must have |
| unique IDs. However, different instances <code class="language-plaintext highlighter-rouge">myHashingTF1</code> and <code class="language-plaintext highlighter-rouge">myHashingTF2</code> (both of type <code class="language-plaintext highlighter-rouge">HashingTF</code>) |
| can be put into the same <code class="language-plaintext highlighter-rouge">Pipeline</code> since different instances will be created with different IDs.</p> |
| |
| <h2 id="parameters">Parameters</h2> |
| |
| <p>MLlib <code class="language-plaintext highlighter-rouge">Estimator</code>s and <code class="language-plaintext highlighter-rouge">Transformer</code>s use a uniform API for specifying parameters.</p> |
| |
| <p>A <code class="language-plaintext highlighter-rouge">Param</code> is a named parameter with self-contained documentation. |
| A <code class="language-plaintext highlighter-rouge">ParamMap</code> is a set of (parameter, value) pairs.</p> |
| |
| <p>There are two main ways to pass parameters to an algorithm:</p> |
| |
| <ol> |
| <li>Set parameters for an instance. E.g., if <code class="language-plaintext highlighter-rouge">lr</code> is an instance of <code class="language-plaintext highlighter-rouge">LogisticRegression</code>, one could |
| call <code class="language-plaintext highlighter-rouge">lr.setMaxIter(10)</code> to make <code class="language-plaintext highlighter-rouge">lr.fit()</code> use at most 10 iterations. |
| This API resembles the API used in <code class="language-plaintext highlighter-rouge">spark.mllib</code> package.</li> |
| <li>Pass a <code class="language-plaintext highlighter-rouge">ParamMap</code> to <code class="language-plaintext highlighter-rouge">fit()</code> or <code class="language-plaintext highlighter-rouge">transform()</code>. Any parameters in the <code class="language-plaintext highlighter-rouge">ParamMap</code> will override parameters previously specified via setter methods.</li> |
| </ol> |
| |
| <p>Parameters belong to specific instances of <code class="language-plaintext highlighter-rouge">Estimator</code>s and <code class="language-plaintext highlighter-rouge">Transformer</code>s. |
| For example, if we have two <code class="language-plaintext highlighter-rouge">LogisticRegression</code> instances <code class="language-plaintext highlighter-rouge">lr1</code> and <code class="language-plaintext highlighter-rouge">lr2</code>, then we can build a <code class="language-plaintext highlighter-rouge">ParamMap</code> with both <code class="language-plaintext highlighter-rouge">maxIter</code> parameters specified: <code class="language-plaintext highlighter-rouge">ParamMap(lr1.maxIter -> 10, lr2.maxIter -> 20)</code>. |
| This is useful if there are two algorithms with the <code class="language-plaintext highlighter-rouge">maxIter</code> parameter in a <code class="language-plaintext highlighter-rouge">Pipeline</code>.</p> |
| |
| <h2 id="ml-persistence-saving-and-loading-pipelines">ML persistence: Saving and Loading Pipelines</h2> |
| |
| <p>Often times it is worth it to save a model or a pipeline to disk for later use. In Spark 1.6, a model import/export functionality was added to the Pipeline API. |
| As of Spark 2.3, the DataFrame-based API in <code class="language-plaintext highlighter-rouge">spark.ml</code> and <code class="language-plaintext highlighter-rouge">pyspark.ml</code> has complete coverage.</p> |
| |
| <p>ML persistence works across Scala, Java and Python. However, R currently uses a modified format, |
| so models saved in R can only be loaded back in R; this should be fixed in the future and is |
| tracked in <a href="https://issues.apache.org/jira/browse/SPARK-15572">SPARK-15572</a>.</p> |
| |
| <h3 id="backwards-compatibility-for-ml-persistence">Backwards compatibility for ML persistence</h3> |
| |
| <p>In general, MLlib maintains backwards compatibility for ML persistence. I.e., if you save an ML |
| model or Pipeline in one version of Spark, then you should be able to load it back and use it in a |
| future version of Spark. However, there are rare exceptions, described below.</p> |
| |
| <p>Model persistence: Is a model or Pipeline saved using Apache Spark ML persistence in Spark |
| version X loadable by Spark version Y?</p> |
| |
| <ul> |
| <li>Major versions: No guarantees, but best-effort.</li> |
| <li>Minor and patch versions: Yes; these are backwards compatible.</li> |
| <li>Note about the format: There are no guarantees for a stable persistence format, but model loading itself is designed to be backwards compatible.</li> |
| </ul> |
| |
| <p>Model behavior: Does a model or Pipeline in Spark version X behave identically in Spark version Y?</p> |
| |
| <ul> |
| <li>Major versions: No guarantees, but best-effort.</li> |
| <li>Minor and patch versions: Identical behavior, except for bug fixes.</li> |
| </ul> |
| |
| <p>For both model persistence and model behavior, any breaking changes across a minor version or patch |
| version are reported in the Spark version release notes. If a breakage is not reported in release |
| notes, then it should be treated as a bug to be fixed.</p> |
| |
| <h1 id="code-examples">Code examples</h1> |
| |
| <p>This section gives code examples illustrating the functionality discussed above. |
| For more info, please refer to the API documentation |
| (<a href="api/scala/org/apache/spark/ml/package.html">Scala</a>, |
| <a href="api/java/org/apache/spark/ml/package-summary.html">Java</a>, |
| and <a href="api/python/reference/pyspark.ml.html">Python</a>).</p> |
| |
| <h2 id="example-estimator-transformer-and-param">Example: Estimator, Transformer, and Param</h2> |
| |
| <p>This example covers the concepts of <code class="language-plaintext highlighter-rouge">Estimator</code>, <code class="language-plaintext highlighter-rouge">Transformer</code>, and <code class="language-plaintext highlighter-rouge">Param</code>.</p> |
| |
| <div class="codetabs"> |
| |
| <div data-lang="python"> |
| |
| <p>Refer to the <a href="api/python/reference/api/pyspark.ml.Estimator.html"><code class="language-plaintext highlighter-rouge">Estimator</code> Python docs</a>, |
| the <a href="api/python/reference/api/pyspark.ml.Transformer.html"><code class="language-plaintext highlighter-rouge">Transformer</code> Python docs</a> and |
| the <a href="api/python/reference/api/pyspark.ml.param.Params.html"><code class="language-plaintext highlighter-rouge">Params</code> Python docs</a> for more details on the API.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="kn">from</span> <span class="nn">pyspark.ml.linalg</span> <span class="kn">import</span> <span class="n">Vectors</span> |
| <span class="kn">from</span> <span class="nn">pyspark.ml.classification</span> <span class="kn">import</span> <span class="n">LogisticRegression</span> |
| |
| <span class="c1"># Prepare training data from a list of (label, features) tuples. |
| </span><span class="n">training</span> <span class="o">=</span> <span class="n">spark</span><span class="p">.</span><span class="n">createDataFrame</span><span class="p">([</span> |
| <span class="p">(</span><span class="mf">1.0</span><span class="p">,</span> <span class="n">Vectors</span><span class="p">.</span><span class="n">dense</span><span class="p">([</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">1.1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">])),</span> |
| <span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">Vectors</span><span class="p">.</span><span class="n">dense</span><span class="p">([</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.0</span><span class="p">])),</span> |
| <span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">Vectors</span><span class="p">.</span><span class="n">dense</span><span class="p">([</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">1.3</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">])),</span> |
| <span class="p">(</span><span class="mf">1.0</span><span class="p">,</span> <span class="n">Vectors</span><span class="p">.</span><span class="n">dense</span><span class="p">([</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">1.2</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.5</span><span class="p">]))],</span> <span class="p">[</span><span class="s">"label"</span><span class="p">,</span> <span class="s">"features"</span><span class="p">])</span> |
| |
| <span class="c1"># Create a LogisticRegression instance. This instance is an Estimator. |
| </span><span class="n">lr</span> <span class="o">=</span> <span class="n">LogisticRegression</span><span class="p">(</span><span class="n">maxIter</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">regParam</span><span class="o">=</span><span class="mf">0.01</span><span class="p">)</span> |
| <span class="c1"># Print out the parameters, documentation, and any default values. |
| </span><span class="k">print</span><span class="p">(</span><span class="s">"LogisticRegression parameters:</span><span class="se">\n</span><span class="s">"</span> <span class="o">+</span> <span class="n">lr</span><span class="p">.</span><span class="n">explainParams</span><span class="p">()</span> <span class="o">+</span> <span class="s">"</span><span class="se">\n</span><span class="s">"</span><span class="p">)</span> |
| |
| <span class="c1"># Learn a LogisticRegression model. This uses the parameters stored in lr. |
| </span><span class="n">model1</span> <span class="o">=</span> <span class="n">lr</span><span class="p">.</span><span class="n">fit</span><span class="p">(</span><span class="n">training</span><span class="p">)</span> |
| |
| <span class="c1"># Since model1 is a Model (i.e., a transformer produced by an Estimator), |
| # we can view the parameters it used during fit(). |
| # This prints the parameter (name: value) pairs, where names are unique IDs for this |
| # LogisticRegression instance. |
| </span><span class="k">print</span><span class="p">(</span><span class="s">"Model 1 was fit using parameters: "</span><span class="p">)</span> |
| <span class="k">print</span><span class="p">(</span><span class="n">model1</span><span class="p">.</span><span class="n">extractParamMap</span><span class="p">())</span> |
| |
| <span class="c1"># We may alternatively specify parameters using a Python dictionary as a paramMap |
| </span><span class="n">paramMap</span> <span class="o">=</span> <span class="p">{</span><span class="n">lr</span><span class="p">.</span><span class="n">maxIter</span><span class="p">:</span> <span class="mi">20</span><span class="p">}</span> |
| <span class="n">paramMap</span><span class="p">[</span><span class="n">lr</span><span class="p">.</span><span class="n">maxIter</span><span class="p">]</span> <span class="o">=</span> <span class="mi">30</span> <span class="c1"># Specify 1 Param, overwriting the original maxIter. |
| # Specify multiple Params. |
| </span><span class="n">paramMap</span><span class="p">.</span><span class="n">update</span><span class="p">({</span><span class="n">lr</span><span class="p">.</span><span class="n">regParam</span><span class="p">:</span> <span class="mf">0.1</span><span class="p">,</span> <span class="n">lr</span><span class="p">.</span><span class="n">threshold</span><span class="p">:</span> <span class="mf">0.55</span><span class="p">})</span> <span class="c1"># type: ignore |
| </span> |
| <span class="c1"># You can combine paramMaps, which are python dictionaries. |
| # Change output column name |
| </span><span class="n">paramMap2</span> <span class="o">=</span> <span class="p">{</span><span class="n">lr</span><span class="p">.</span><span class="n">probabilityCol</span><span class="p">:</span> <span class="s">"myProbability"</span><span class="p">}</span> |
| <span class="n">paramMapCombined</span> <span class="o">=</span> <span class="n">paramMap</span><span class="p">.</span><span class="n">copy</span><span class="p">()</span> |
| <span class="n">paramMapCombined</span><span class="p">.</span><span class="n">update</span><span class="p">(</span><span class="n">paramMap2</span><span class="p">)</span> <span class="c1"># type: ignore |
| </span> |
| <span class="c1"># Now learn a new model using the paramMapCombined parameters. |
| # paramMapCombined overrides all parameters set earlier via lr.set* methods. |
| </span><span class="n">model2</span> <span class="o">=</span> <span class="n">lr</span><span class="p">.</span><span class="n">fit</span><span class="p">(</span><span class="n">training</span><span class="p">,</span> <span class="n">paramMapCombined</span><span class="p">)</span> |
| <span class="k">print</span><span class="p">(</span><span class="s">"Model 2 was fit using parameters: "</span><span class="p">)</span> |
| <span class="k">print</span><span class="p">(</span><span class="n">model2</span><span class="p">.</span><span class="n">extractParamMap</span><span class="p">())</span> |
| |
| <span class="c1"># Prepare test data |
| </span><span class="n">test</span> <span class="o">=</span> <span class="n">spark</span><span class="p">.</span><span class="n">createDataFrame</span><span class="p">([</span> |
| <span class="p">(</span><span class="mf">1.0</span><span class="p">,</span> <span class="n">Vectors</span><span class="p">.</span><span class="n">dense</span><span class="p">([</span><span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.5</span><span class="p">,</span> <span class="mf">1.3</span><span class="p">])),</span> |
| <span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">Vectors</span><span class="p">.</span><span class="n">dense</span><span class="p">([</span><span class="mf">3.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.1</span><span class="p">])),</span> |
| <span class="p">(</span><span class="mf">1.0</span><span class="p">,</span> <span class="n">Vectors</span><span class="p">.</span><span class="n">dense</span><span class="p">([</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">2.2</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.5</span><span class="p">]))],</span> <span class="p">[</span><span class="s">"label"</span><span class="p">,</span> <span class="s">"features"</span><span class="p">])</span> |
| |
| <span class="c1"># Make predictions on test data using the Transformer.transform() method. |
| # LogisticRegression.transform will only use the 'features' column. |
| # Note that model2.transform() outputs a "myProbability" column instead of the usual |
| # 'probability' column since we renamed the lr.probabilityCol parameter previously. |
| </span><span class="n">prediction</span> <span class="o">=</span> <span class="n">model2</span><span class="p">.</span><span class="n">transform</span><span class="p">(</span><span class="n">test</span><span class="p">)</span> |
| <span class="n">result</span> <span class="o">=</span> <span class="n">prediction</span><span class="p">.</span><span class="n">select</span><span class="p">(</span><span class="s">"features"</span><span class="p">,</span> <span class="s">"label"</span><span class="p">,</span> <span class="s">"myProbability"</span><span class="p">,</span> <span class="s">"prediction"</span><span class="p">)</span> \ |
| <span class="p">.</span><span class="n">collect</span><span class="p">()</span> |
| |
| <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">result</span><span class="p">:</span> |
| <span class="k">print</span><span class="p">(</span><span class="s">"features=%s, label=%s -> prob=%s, prediction=%s"</span> |
| <span class="o">%</span> <span class="p">(</span><span class="n">row</span><span class="p">.</span><span class="n">features</span><span class="p">,</span> <span class="n">row</span><span class="p">.</span><span class="n">label</span><span class="p">,</span> <span class="n">row</span><span class="p">.</span><span class="n">myProbability</span><span class="p">,</span> <span class="n">row</span><span class="p">.</span><span class="n">prediction</span><span class="p">))</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/python/ml/estimator_transformer_param_example.py" in the Spark repo.</small></div> |
| </div> |
| |
| <div data-lang="scala"> |
| |
| <p>Refer to the <a href="api/scala/org/apache/spark/ml/Estimator.html"><code class="language-plaintext highlighter-rouge">Estimator</code> Scala docs</a>, |
| the <a href="api/scala/org/apache/spark/ml/Transformer.html"><code class="language-plaintext highlighter-rouge">Transformer</code> Scala docs</a> and |
| the <a href="api/scala/org/apache/spark/ml/param/Params.html"><code class="language-plaintext highlighter-rouge">Params</code> Scala docs</a> for details on the API.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="k">import</span> <span class="nn">org.apache.spark.ml.classification.LogisticRegression</span> |
| <span class="k">import</span> <span class="nn">org.apache.spark.ml.linalg.</span><span class="o">{</span><span class="nc">Vector</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">}</span> |
| <span class="k">import</span> <span class="nn">org.apache.spark.ml.param.ParamMap</span> |
| <span class="k">import</span> <span class="nn">org.apache.spark.sql.Row</span> |
| |
| <span class="c1">// Prepare training data from a list of (label, features) tuples.</span> |
| <span class="k">val</span> <span class="nv">training</span> <span class="k">=</span> <span class="nv">spark</span><span class="o">.</span><span class="py">createDataFrame</span><span class="o">(</span><span class="nc">Seq</span><span class="o">(</span> |
| <span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="nv">Vectors</span><span class="o">.</span><span class="py">dense</span><span class="o">(</span><span class="mf">0.0</span><span class="o">,</span> <span class="mf">1.1</span><span class="o">,</span> <span class="mf">0.1</span><span class="o">)),</span> |
| <span class="o">(</span><span class="mf">0.0</span><span class="o">,</span> <span class="nv">Vectors</span><span class="o">.</span><span class="py">dense</span><span class="o">(</span><span class="mf">2.0</span><span class="o">,</span> <span class="mf">1.0</span><span class="o">,</span> <span class="o">-</span><span class="mf">1.0</span><span class="o">)),</span> |
| <span class="o">(</span><span class="mf">0.0</span><span class="o">,</span> <span class="nv">Vectors</span><span class="o">.</span><span class="py">dense</span><span class="o">(</span><span class="mf">2.0</span><span class="o">,</span> <span class="mf">1.3</span><span class="o">,</span> <span class="mf">1.0</span><span class="o">)),</span> |
| <span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="nv">Vectors</span><span class="o">.</span><span class="py">dense</span><span class="o">(</span><span class="mf">0.0</span><span class="o">,</span> <span class="mf">1.2</span><span class="o">,</span> <span class="o">-</span><span class="mf">0.5</span><span class="o">))</span> |
| <span class="o">)).</span><span class="py">toDF</span><span class="o">(</span><span class="s">"label"</span><span class="o">,</span> <span class="s">"features"</span><span class="o">)</span> |
| |
| <span class="c1">// Create a LogisticRegression instance. This instance is an Estimator.</span> |
| <span class="k">val</span> <span class="nv">lr</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">LogisticRegression</span><span class="o">()</span> |
| <span class="c1">// Print out the parameters, documentation, and any default values.</span> |
| <span class="nf">println</span><span class="o">(</span><span class="n">s</span><span class="s">"LogisticRegression parameters:\n ${lr.explainParams()}\n"</span><span class="o">)</span> |
| |
| <span class="c1">// We may set parameters using setter methods.</span> |
| <span class="nv">lr</span><span class="o">.</span><span class="py">setMaxIter</span><span class="o">(</span><span class="mi">10</span><span class="o">)</span> |
| <span class="o">.</span><span class="py">setRegParam</span><span class="o">(</span><span class="mf">0.01</span><span class="o">)</span> |
| |
| <span class="c1">// Learn a LogisticRegression model. This uses the parameters stored in lr.</span> |
| <span class="k">val</span> <span class="nv">model1</span> <span class="k">=</span> <span class="nv">lr</span><span class="o">.</span><span class="py">fit</span><span class="o">(</span><span class="n">training</span><span class="o">)</span> |
| <span class="c1">// Since model1 is a Model (i.e., a Transformer produced by an Estimator),</span> |
| <span class="c1">// we can view the parameters it used during fit().</span> |
| <span class="c1">// This prints the parameter (name: value) pairs, where names are unique IDs for this</span> |
| <span class="c1">// LogisticRegression instance.</span> |
| <span class="nf">println</span><span class="o">(</span><span class="n">s</span><span class="s">"Model 1 was fit using parameters: ${model1.parent.extractParamMap}"</span><span class="o">)</span> |
| |
| <span class="c1">// We may alternatively specify parameters using a ParamMap,</span> |
| <span class="c1">// which supports several methods for specifying parameters.</span> |
| <span class="k">val</span> <span class="nv">paramMap</span> <span class="k">=</span> <span class="nc">ParamMap</span><span class="o">(</span><span class="nv">lr</span><span class="o">.</span><span class="py">maxIter</span> <span class="o">-></span> <span class="mi">20</span><span class="o">)</span> |
| <span class="o">.</span><span class="py">put</span><span class="o">(</span><span class="nv">lr</span><span class="o">.</span><span class="py">maxIter</span><span class="o">,</span> <span class="mi">30</span><span class="o">)</span> <span class="c1">// Specify 1 Param. This overwrites the original maxIter.</span> |
| <span class="o">.</span><span class="py">put</span><span class="o">(</span><span class="nv">lr</span><span class="o">.</span><span class="py">regParam</span> <span class="o">-></span> <span class="mf">0.1</span><span class="o">,</span> <span class="nv">lr</span><span class="o">.</span><span class="py">threshold</span> <span class="o">-></span> <span class="mf">0.55</span><span class="o">)</span> <span class="c1">// Specify multiple Params.</span> |
| |
| <span class="c1">// One can also combine ParamMaps.</span> |
| <span class="k">val</span> <span class="nv">paramMap2</span> <span class="k">=</span> <span class="nc">ParamMap</span><span class="o">(</span><span class="nv">lr</span><span class="o">.</span><span class="py">probabilityCol</span> <span class="o">-></span> <span class="s">"myProbability"</span><span class="o">)</span> <span class="c1">// Change output column name.</span> |
| <span class="k">val</span> <span class="nv">paramMapCombined</span> <span class="k">=</span> <span class="n">paramMap</span> <span class="o">++</span> <span class="n">paramMap2</span> |
| |
| <span class="c1">// Now learn a new model using the paramMapCombined parameters.</span> |
| <span class="c1">// paramMapCombined overrides all parameters set earlier via lr.set* methods.</span> |
| <span class="k">val</span> <span class="nv">model2</span> <span class="k">=</span> <span class="nv">lr</span><span class="o">.</span><span class="py">fit</span><span class="o">(</span><span class="n">training</span><span class="o">,</span> <span class="n">paramMapCombined</span><span class="o">)</span> |
| <span class="nf">println</span><span class="o">(</span><span class="n">s</span><span class="s">"Model 2 was fit using parameters: ${model2.parent.extractParamMap}"</span><span class="o">)</span> |
| |
| <span class="c1">// Prepare test data.</span> |
| <span class="k">val</span> <span class="nv">test</span> <span class="k">=</span> <span class="nv">spark</span><span class="o">.</span><span class="py">createDataFrame</span><span class="o">(</span><span class="nc">Seq</span><span class="o">(</span> |
| <span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="nv">Vectors</span><span class="o">.</span><span class="py">dense</span><span class="o">(-</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">1.5</span><span class="o">,</span> <span class="mf">1.3</span><span class="o">)),</span> |
| <span class="o">(</span><span class="mf">0.0</span><span class="o">,</span> <span class="nv">Vectors</span><span class="o">.</span><span class="py">dense</span><span class="o">(</span><span class="mf">3.0</span><span class="o">,</span> <span class="mf">2.0</span><span class="o">,</span> <span class="o">-</span><span class="mf">0.1</span><span class="o">)),</span> |
| <span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="nv">Vectors</span><span class="o">.</span><span class="py">dense</span><span class="o">(</span><span class="mf">0.0</span><span class="o">,</span> <span class="mf">2.2</span><span class="o">,</span> <span class="o">-</span><span class="mf">1.5</span><span class="o">))</span> |
| <span class="o">)).</span><span class="py">toDF</span><span class="o">(</span><span class="s">"label"</span><span class="o">,</span> <span class="s">"features"</span><span class="o">)</span> |
| |
| <span class="c1">// Make predictions on test data using the Transformer.transform() method.</span> |
| <span class="c1">// LogisticRegression.transform will only use the 'features' column.</span> |
| <span class="c1">// Note that model2.transform() outputs a 'myProbability' column instead of the usual</span> |
| <span class="c1">// 'probability' column since we renamed the lr.probabilityCol parameter previously.</span> |
| <span class="nv">model2</span><span class="o">.</span><span class="py">transform</span><span class="o">(</span><span class="n">test</span><span class="o">)</span> |
| <span class="o">.</span><span class="py">select</span><span class="o">(</span><span class="s">"features"</span><span class="o">,</span> <span class="s">"label"</span><span class="o">,</span> <span class="s">"myProbability"</span><span class="o">,</span> <span class="s">"prediction"</span><span class="o">)</span> |
| <span class="o">.</span><span class="py">collect</span><span class="o">()</span> |
| <span class="o">.</span><span class="py">foreach</span> <span class="o">{</span> <span class="k">case</span> <span class="nc">Row</span><span class="o">(</span><span class="n">features</span><span class="k">:</span> <span class="kt">Vector</span><span class="o">,</span> <span class="n">label</span><span class="k">:</span> <span class="kt">Double</span><span class="o">,</span> <span class="n">prob</span><span class="k">:</span> <span class="kt">Vector</span><span class="o">,</span> <span class="n">prediction</span><span class="k">:</span> <span class="kt">Double</span><span class="o">)</span> <span class="k">=></span> |
| <span class="nf">println</span><span class="o">(</span><span class="n">s</span><span class="s">"($features, $label) -> prob=$prob, prediction=$prediction"</span><span class="o">)</span> |
| <span class="o">}</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/EstimatorTransformerParamExample.scala" in the Spark repo.</small></div> |
| </div> |
| |
| <div data-lang="java"> |
| |
| <p>Refer to the <a href="api/java/org/apache/spark/ml/Estimator.html"><code class="language-plaintext highlighter-rouge">Estimator</code> Java docs</a>, |
| the <a href="api/java/org/apache/spark/ml/Transformer.html"><code class="language-plaintext highlighter-rouge">Transformer</code> Java docs</a> and |
| the <a href="api/java/org/apache/spark/ml/param/Params.html"><code class="language-plaintext highlighter-rouge">Params</code> Java docs</a> for details on the API.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="kn">import</span> <span class="nn">java.util.Arrays</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">java.util.List</span><span class="o">;</span> |
| |
| <span class="kn">import</span> <span class="nn">org.apache.spark.ml.classification.LogisticRegression</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.ml.classification.LogisticRegressionModel</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.ml.linalg.VectorUDT</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.ml.linalg.Vectors</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.ml.param.ParamMap</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.sql.Dataset</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.sql.Row</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.sql.RowFactory</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.sql.types.DataTypes</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.sql.types.Metadata</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.sql.types.StructField</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.sql.types.StructType</span><span class="o">;</span> |
| |
| <span class="c1">// Prepare training data.</span> |
| <span class="nc">List</span><span class="o"><</span><span class="nc">Row</span><span class="o">></span> <span class="n">dataTraining</span> <span class="o">=</span> <span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span> |
| <span class="nc">RowFactory</span><span class="o">.</span><span class="na">create</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">0.0</span><span class="o">,</span> <span class="mf">1.1</span><span class="o">,</span> <span class="mf">0.1</span><span class="o">)),</span> |
| <span class="nc">RowFactory</span><span class="o">.</span><span class="na">create</span><span class="o">(</span><span class="mf">0.0</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">2.0</span><span class="o">,</span> <span class="mf">1.0</span><span class="o">,</span> <span class="o">-</span><span class="mf">1.0</span><span class="o">)),</span> |
| <span class="nc">RowFactory</span><span class="o">.</span><span class="na">create</span><span class="o">(</span><span class="mf">0.0</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">2.0</span><span class="o">,</span> <span class="mf">1.3</span><span class="o">,</span> <span class="mf">1.0</span><span class="o">)),</span> |
| <span class="nc">RowFactory</span><span class="o">.</span><span class="na">create</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">0.0</span><span class="o">,</span> <span class="mf">1.2</span><span class="o">,</span> <span class="o">-</span><span class="mf">0.5</span><span class="o">))</span> |
| <span class="o">);</span> |
| <span class="nc">StructType</span> <span class="n">schema</span> <span class="o">=</span> <span class="k">new</span> <span class="nc">StructType</span><span class="o">(</span><span class="k">new</span> <span class="nc">StructField</span><span class="o">[]{</span> |
| <span class="k">new</span> <span class="nf">StructField</span><span class="o">(</span><span class="s">"label"</span><span class="o">,</span> <span class="nc">DataTypes</span><span class="o">.</span><span class="na">DoubleType</span><span class="o">,</span> <span class="kc">false</span><span class="o">,</span> <span class="nc">Metadata</span><span class="o">.</span><span class="na">empty</span><span class="o">()),</span> |
| <span class="k">new</span> <span class="nf">StructField</span><span class="o">(</span><span class="s">"features"</span><span class="o">,</span> <span class="k">new</span> <span class="nc">VectorUDT</span><span class="o">(),</span> <span class="kc">false</span><span class="o">,</span> <span class="nc">Metadata</span><span class="o">.</span><span class="na">empty</span><span class="o">())</span> |
| <span class="o">});</span> |
| <span class="nc">Dataset</span><span class="o"><</span><span class="nc">Row</span><span class="o">></span> <span class="n">training</span> <span class="o">=</span> <span class="n">spark</span><span class="o">.</span><span class="na">createDataFrame</span><span class="o">(</span><span class="n">dataTraining</span><span class="o">,</span> <span class="n">schema</span><span class="o">);</span> |
| |
| <span class="c1">// Create a LogisticRegression instance. This instance is an Estimator.</span> |
| <span class="nc">LogisticRegression</span> <span class="n">lr</span> <span class="o">=</span> <span class="k">new</span> <span class="nc">LogisticRegression</span><span class="o">();</span> |
| <span class="c1">// Print out the parameters, documentation, and any default values.</span> |
| <span class="nc">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">"LogisticRegression parameters:\n"</span> <span class="o">+</span> <span class="n">lr</span><span class="o">.</span><span class="na">explainParams</span><span class="o">()</span> <span class="o">+</span> <span class="s">"\n"</span><span class="o">);</span> |
| |
| <span class="c1">// We may set parameters using setter methods.</span> |
| <span class="n">lr</span><span class="o">.</span><span class="na">setMaxIter</span><span class="o">(</span><span class="mi">10</span><span class="o">).</span><span class="na">setRegParam</span><span class="o">(</span><span class="mf">0.01</span><span class="o">);</span> |
| |
| <span class="c1">// Learn a LogisticRegression model. This uses the parameters stored in lr.</span> |
| <span class="nc">LogisticRegressionModel</span> <span class="n">model1</span> <span class="o">=</span> <span class="n">lr</span><span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">training</span><span class="o">);</span> |
| <span class="c1">// Since model1 is a Model (i.e., a Transformer produced by an Estimator),</span> |
| <span class="c1">// we can view the parameters it used during fit().</span> |
| <span class="c1">// This prints the parameter (name: value) pairs, where names are unique IDs for this</span> |
| <span class="c1">// LogisticRegression instance.</span> |
| <span class="nc">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">"Model 1 was fit using parameters: "</span> <span class="o">+</span> <span class="n">model1</span><span class="o">.</span><span class="na">parent</span><span class="o">().</span><span class="na">extractParamMap</span><span class="o">());</span> |
| |
| <span class="c1">// We may alternatively specify parameters using a ParamMap.</span> |
| <span class="nc">ParamMap</span> <span class="n">paramMap</span> <span class="o">=</span> <span class="k">new</span> <span class="nc">ParamMap</span><span class="o">()</span> |
| <span class="o">.</span><span class="na">put</span><span class="o">(</span><span class="n">lr</span><span class="o">.</span><span class="na">maxIter</span><span class="o">().</span><span class="na">w</span><span class="o">(</span><span class="mi">20</span><span class="o">))</span> <span class="c1">// Specify 1 Param.</span> |
| <span class="o">.</span><span class="na">put</span><span class="o">(</span><span class="n">lr</span><span class="o">.</span><span class="na">maxIter</span><span class="o">(),</span> <span class="mi">30</span><span class="o">)</span> <span class="c1">// This overwrites the original maxIter.</span> |
| <span class="o">.</span><span class="na">put</span><span class="o">(</span><span class="n">lr</span><span class="o">.</span><span class="na">regParam</span><span class="o">().</span><span class="na">w</span><span class="o">(</span><span class="mf">0.1</span><span class="o">),</span> <span class="n">lr</span><span class="o">.</span><span class="na">threshold</span><span class="o">().</span><span class="na">w</span><span class="o">(</span><span class="mf">0.55</span><span class="o">));</span> <span class="c1">// Specify multiple Params.</span> |
| |
| <span class="c1">// One can also combine ParamMaps.</span> |
| <span class="nc">ParamMap</span> <span class="n">paramMap2</span> <span class="o">=</span> <span class="k">new</span> <span class="nc">ParamMap</span><span class="o">()</span> |
| <span class="o">.</span><span class="na">put</span><span class="o">(</span><span class="n">lr</span><span class="o">.</span><span class="na">probabilityCol</span><span class="o">().</span><span class="na">w</span><span class="o">(</span><span class="s">"myProbability"</span><span class="o">));</span> <span class="c1">// Change output column name</span> |
| <span class="nc">ParamMap</span> <span class="n">paramMapCombined</span> <span class="o">=</span> <span class="n">paramMap</span><span class="o">.</span><span class="n">$plus$plus</span><span class="o">(</span><span class="n">paramMap2</span><span class="o">);</span> |
| |
| <span class="c1">// Now learn a new model using the paramMapCombined parameters.</span> |
| <span class="c1">// paramMapCombined overrides all parameters set earlier via lr.set* methods.</span> |
| <span class="nc">LogisticRegressionModel</span> <span class="n">model2</span> <span class="o">=</span> <span class="n">lr</span><span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">training</span><span class="o">,</span> <span class="n">paramMapCombined</span><span class="o">);</span> |
| <span class="nc">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">"Model 2 was fit using parameters: "</span> <span class="o">+</span> <span class="n">model2</span><span class="o">.</span><span class="na">parent</span><span class="o">().</span><span class="na">extractParamMap</span><span class="o">());</span> |
| |
| <span class="c1">// Prepare test documents.</span> |
| <span class="nc">List</span><span class="o"><</span><span class="nc">Row</span><span class="o">></span> <span class="n">dataTest</span> <span class="o">=</span> <span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span> |
| <span class="nc">RowFactory</span><span class="o">.</span><span class="na">create</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(-</span><span class="mf">1.0</span><span class="o">,</span> <span class="mf">1.5</span><span class="o">,</span> <span class="mf">1.3</span><span class="o">)),</span> |
| <span class="nc">RowFactory</span><span class="o">.</span><span class="na">create</span><span class="o">(</span><span class="mf">0.0</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">3.0</span><span class="o">,</span> <span class="mf">2.0</span><span class="o">,</span> <span class="o">-</span><span class="mf">0.1</span><span class="o">)),</span> |
| <span class="nc">RowFactory</span><span class="o">.</span><span class="na">create</span><span class="o">(</span><span class="mf">1.0</span><span class="o">,</span> <span class="nc">Vectors</span><span class="o">.</span><span class="na">dense</span><span class="o">(</span><span class="mf">0.0</span><span class="o">,</span> <span class="mf">2.2</span><span class="o">,</span> <span class="o">-</span><span class="mf">1.5</span><span class="o">))</span> |
| <span class="o">);</span> |
| <span class="nc">Dataset</span><span class="o"><</span><span class="nc">Row</span><span class="o">></span> <span class="n">test</span> <span class="o">=</span> <span class="n">spark</span><span class="o">.</span><span class="na">createDataFrame</span><span class="o">(</span><span class="n">dataTest</span><span class="o">,</span> <span class="n">schema</span><span class="o">);</span> |
| |
| <span class="c1">// Make predictions on test documents using the Transformer.transform() method.</span> |
| <span class="c1">// LogisticRegression.transform will only use the 'features' column.</span> |
| <span class="c1">// Note that model2.transform() outputs a 'myProbability' column instead of the usual</span> |
| <span class="c1">// 'probability' column since we renamed the lr.probabilityCol parameter previously.</span> |
| <span class="nc">Dataset</span><span class="o"><</span><span class="nc">Row</span><span class="o">></span> <span class="n">results</span> <span class="o">=</span> <span class="n">model2</span><span class="o">.</span><span class="na">transform</span><span class="o">(</span><span class="n">test</span><span class="o">);</span> |
| <span class="nc">Dataset</span><span class="o"><</span><span class="nc">Row</span><span class="o">></span> <span class="n">rows</span> <span class="o">=</span> <span class="n">results</span><span class="o">.</span><span class="na">select</span><span class="o">(</span><span class="s">"features"</span><span class="o">,</span> <span class="s">"label"</span><span class="o">,</span> <span class="s">"myProbability"</span><span class="o">,</span> <span class="s">"prediction"</span><span class="o">);</span> |
| <span class="k">for</span> <span class="o">(</span><span class="nc">Row</span> <span class="nl">r:</span> <span class="n">rows</span><span class="o">.</span><span class="na">collectAsList</span><span class="o">())</span> <span class="o">{</span> |
| <span class="nc">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">"("</span> <span class="o">+</span> <span class="n">r</span><span class="o">.</span><span class="na">get</span><span class="o">(</span><span class="mi">0</span><span class="o">)</span> <span class="o">+</span> <span class="s">", "</span> <span class="o">+</span> <span class="n">r</span><span class="o">.</span><span class="na">get</span><span class="o">(</span><span class="mi">1</span><span class="o">)</span> <span class="o">+</span> <span class="s">") -> prob="</span> <span class="o">+</span> <span class="n">r</span><span class="o">.</span><span class="na">get</span><span class="o">(</span><span class="mi">2</span><span class="o">)</span> |
| <span class="o">+</span> <span class="s">", prediction="</span> <span class="o">+</span> <span class="n">r</span><span class="o">.</span><span class="na">get</span><span class="o">(</span><span class="mi">3</span><span class="o">));</span> |
| <span class="o">}</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaEstimatorTransformerParamExample.java" in the Spark repo.</small></div> |
| </div> |
| |
| </div> |
| |
| <h2 id="example-pipeline">Example: Pipeline</h2> |
| |
| <p>This example follows the simple text document <code class="language-plaintext highlighter-rouge">Pipeline</code> illustrated in the figures above.</p> |
| |
| <div class="codetabs"> |
| |
| <div data-lang="python"> |
| |
| <p>Refer to the <a href="api/python/reference/api/pyspark.ml.Pipeline.html"><code class="language-plaintext highlighter-rouge">Pipeline</code> Python docs</a> for more details on the API.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="kn">from</span> <span class="nn">pyspark.ml</span> <span class="kn">import</span> <span class="n">Pipeline</span> |
| <span class="kn">from</span> <span class="nn">pyspark.ml.classification</span> <span class="kn">import</span> <span class="n">LogisticRegression</span> |
| <span class="kn">from</span> <span class="nn">pyspark.ml.feature</span> <span class="kn">import</span> <span class="n">HashingTF</span><span class="p">,</span> <span class="n">Tokenizer</span> |
| |
| <span class="c1"># Prepare training documents from a list of (id, text, label) tuples. |
| </span><span class="n">training</span> <span class="o">=</span> <span class="n">spark</span><span class="p">.</span><span class="n">createDataFrame</span><span class="p">([</span> |
| <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="s">"a b c d e spark"</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">),</span> |
| <span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="s">"b d"</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">),</span> |
| <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="s">"spark f g h"</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">),</span> |
| <span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="s">"hadoop mapreduce"</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">)</span> |
| <span class="p">],</span> <span class="p">[</span><span class="s">"id"</span><span class="p">,</span> <span class="s">"text"</span><span class="p">,</span> <span class="s">"label"</span><span class="p">])</span> |
| |
| <span class="c1"># Configure an ML pipeline, which consists of three stages: tokenizer, hashingTF, and lr. |
| </span><span class="n">tokenizer</span> <span class="o">=</span> <span class="n">Tokenizer</span><span class="p">(</span><span class="n">inputCol</span><span class="o">=</span><span class="s">"text"</span><span class="p">,</span> <span class="n">outputCol</span><span class="o">=</span><span class="s">"words"</span><span class="p">)</span> |
| <span class="n">hashingTF</span> <span class="o">=</span> <span class="n">HashingTF</span><span class="p">(</span><span class="n">inputCol</span><span class="o">=</span><span class="n">tokenizer</span><span class="p">.</span><span class="n">getOutputCol</span><span class="p">(),</span> <span class="n">outputCol</span><span class="o">=</span><span class="s">"features"</span><span class="p">)</span> |
| <span class="n">lr</span> <span class="o">=</span> <span class="n">LogisticRegression</span><span class="p">(</span><span class="n">maxIter</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">regParam</span><span class="o">=</span><span class="mf">0.001</span><span class="p">)</span> |
| <span class="n">pipeline</span> <span class="o">=</span> <span class="n">Pipeline</span><span class="p">(</span><span class="n">stages</span><span class="o">=</span><span class="p">[</span><span class="n">tokenizer</span><span class="p">,</span> <span class="n">hashingTF</span><span class="p">,</span> <span class="n">lr</span><span class="p">])</span> |
| |
| <span class="c1"># Fit the pipeline to training documents. |
| </span><span class="n">model</span> <span class="o">=</span> <span class="n">pipeline</span><span class="p">.</span><span class="n">fit</span><span class="p">(</span><span class="n">training</span><span class="p">)</span> |
| |
| <span class="c1"># Prepare test documents, which are unlabeled (id, text) tuples. |
| </span><span class="n">test</span> <span class="o">=</span> <span class="n">spark</span><span class="p">.</span><span class="n">createDataFrame</span><span class="p">([</span> |
| <span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="s">"spark i j k"</span><span class="p">),</span> |
| <span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="s">"l m n"</span><span class="p">),</span> |
| <span class="p">(</span><span class="mi">6</span><span class="p">,</span> <span class="s">"spark hadoop spark"</span><span class="p">),</span> |
| <span class="p">(</span><span class="mi">7</span><span class="p">,</span> <span class="s">"apache hadoop"</span><span class="p">)</span> |
| <span class="p">],</span> <span class="p">[</span><span class="s">"id"</span><span class="p">,</span> <span class="s">"text"</span><span class="p">])</span> |
| |
| <span class="c1"># Make predictions on test documents and print columns of interest. |
| </span><span class="n">prediction</span> <span class="o">=</span> <span class="n">model</span><span class="p">.</span><span class="n">transform</span><span class="p">(</span><span class="n">test</span><span class="p">)</span> |
| <span class="n">selected</span> <span class="o">=</span> <span class="n">prediction</span><span class="p">.</span><span class="n">select</span><span class="p">(</span><span class="s">"id"</span><span class="p">,</span> <span class="s">"text"</span><span class="p">,</span> <span class="s">"probability"</span><span class="p">,</span> <span class="s">"prediction"</span><span class="p">)</span> |
| <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">selected</span><span class="p">.</span><span class="n">collect</span><span class="p">():</span> |
| <span class="n">rid</span><span class="p">,</span> <span class="n">text</span><span class="p">,</span> <span class="n">prob</span><span class="p">,</span> <span class="n">prediction</span> <span class="o">=</span> <span class="n">row</span> |
| <span class="k">print</span><span class="p">(</span> |
| <span class="s">"(%d, %s) --> prob=%s, prediction=%f"</span> <span class="o">%</span> <span class="p">(</span> |
| <span class="n">rid</span><span class="p">,</span> <span class="n">text</span><span class="p">,</span> <span class="nb">str</span><span class="p">(</span><span class="n">prob</span><span class="p">),</span> <span class="n">prediction</span> <span class="c1"># type: ignore |
| </span> <span class="p">)</span> |
| <span class="p">)</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/python/ml/pipeline_example.py" in the Spark repo.</small></div> |
| </div> |
| |
| <div data-lang="scala"> |
| |
| <p>Refer to the <a href="api/scala/org/apache/spark/ml/Pipeline.html"><code class="language-plaintext highlighter-rouge">Pipeline</code> Scala docs</a> for details on the API.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="k">import</span> <span class="nn">org.apache.spark.ml.</span><span class="o">{</span><span class="nc">Pipeline</span><span class="o">,</span> <span class="nc">PipelineModel</span><span class="o">}</span> |
| <span class="k">import</span> <span class="nn">org.apache.spark.ml.classification.LogisticRegression</span> |
| <span class="k">import</span> <span class="nn">org.apache.spark.ml.feature.</span><span class="o">{</span><span class="nc">HashingTF</span><span class="o">,</span> <span class="nc">Tokenizer</span><span class="o">}</span> |
| <span class="k">import</span> <span class="nn">org.apache.spark.ml.linalg.Vector</span> |
| <span class="k">import</span> <span class="nn">org.apache.spark.sql.Row</span> |
| |
| <span class="c1">// Prepare training documents from a list of (id, text, label) tuples.</span> |
| <span class="k">val</span> <span class="nv">training</span> <span class="k">=</span> <span class="nv">spark</span><span class="o">.</span><span class="py">createDataFrame</span><span class="o">(</span><span class="nc">Seq</span><span class="o">(</span> |
| <span class="o">(</span><span class="mi">0L</span><span class="o">,</span> <span class="s">"a b c d e spark"</span><span class="o">,</span> <span class="mf">1.0</span><span class="o">),</span> |
| <span class="o">(</span><span class="mi">1L</span><span class="o">,</span> <span class="s">"b d"</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">),</span> |
| <span class="o">(</span><span class="mi">2L</span><span class="o">,</span> <span class="s">"spark f g h"</span><span class="o">,</span> <span class="mf">1.0</span><span class="o">),</span> |
| <span class="o">(</span><span class="mi">3L</span><span class="o">,</span> <span class="s">"hadoop mapreduce"</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">)</span> |
| <span class="o">)).</span><span class="py">toDF</span><span class="o">(</span><span class="s">"id"</span><span class="o">,</span> <span class="s">"text"</span><span class="o">,</span> <span class="s">"label"</span><span class="o">)</span> |
| |
| <span class="c1">// Configure an ML pipeline, which consists of three stages: tokenizer, hashingTF, and lr.</span> |
| <span class="k">val</span> <span class="nv">tokenizer</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">Tokenizer</span><span class="o">()</span> |
| <span class="o">.</span><span class="py">setInputCol</span><span class="o">(</span><span class="s">"text"</span><span class="o">)</span> |
| <span class="o">.</span><span class="py">setOutputCol</span><span class="o">(</span><span class="s">"words"</span><span class="o">)</span> |
| <span class="k">val</span> <span class="nv">hashingTF</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">HashingTF</span><span class="o">()</span> |
| <span class="o">.</span><span class="py">setNumFeatures</span><span class="o">(</span><span class="mi">1000</span><span class="o">)</span> |
| <span class="o">.</span><span class="py">setInputCol</span><span class="o">(</span><span class="nv">tokenizer</span><span class="o">.</span><span class="py">getOutputCol</span><span class="o">)</span> |
| <span class="o">.</span><span class="py">setOutputCol</span><span class="o">(</span><span class="s">"features"</span><span class="o">)</span> |
| <span class="k">val</span> <span class="nv">lr</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">LogisticRegression</span><span class="o">()</span> |
| <span class="o">.</span><span class="py">setMaxIter</span><span class="o">(</span><span class="mi">10</span><span class="o">)</span> |
| <span class="o">.</span><span class="py">setRegParam</span><span class="o">(</span><span class="mf">0.001</span><span class="o">)</span> |
| <span class="k">val</span> <span class="nv">pipeline</span> <span class="k">=</span> <span class="k">new</span> <span class="nc">Pipeline</span><span class="o">()</span> |
| <span class="o">.</span><span class="py">setStages</span><span class="o">(</span><span class="nc">Array</span><span class="o">(</span><span class="n">tokenizer</span><span class="o">,</span> <span class="n">hashingTF</span><span class="o">,</span> <span class="n">lr</span><span class="o">))</span> |
| |
| <span class="c1">// Fit the pipeline to training documents.</span> |
| <span class="k">val</span> <span class="nv">model</span> <span class="k">=</span> <span class="nv">pipeline</span><span class="o">.</span><span class="py">fit</span><span class="o">(</span><span class="n">training</span><span class="o">)</span> |
| |
| <span class="c1">// Now we can optionally save the fitted pipeline to disk</span> |
| <span class="nv">model</span><span class="o">.</span><span class="py">write</span><span class="o">.</span><span class="py">overwrite</span><span class="o">().</span><span class="py">save</span><span class="o">(</span><span class="s">"/tmp/spark-logistic-regression-model"</span><span class="o">)</span> |
| |
| <span class="c1">// We can also save this unfit pipeline to disk</span> |
| <span class="nv">pipeline</span><span class="o">.</span><span class="py">write</span><span class="o">.</span><span class="py">overwrite</span><span class="o">().</span><span class="py">save</span><span class="o">(</span><span class="s">"/tmp/unfit-lr-model"</span><span class="o">)</span> |
| |
| <span class="c1">// And load it back in during production</span> |
| <span class="k">val</span> <span class="nv">sameModel</span> <span class="k">=</span> <span class="nv">PipelineModel</span><span class="o">.</span><span class="py">load</span><span class="o">(</span><span class="s">"/tmp/spark-logistic-regression-model"</span><span class="o">)</span> |
| |
| <span class="c1">// Prepare test documents, which are unlabeled (id, text) tuples.</span> |
| <span class="k">val</span> <span class="nv">test</span> <span class="k">=</span> <span class="nv">spark</span><span class="o">.</span><span class="py">createDataFrame</span><span class="o">(</span><span class="nc">Seq</span><span class="o">(</span> |
| <span class="o">(</span><span class="mi">4L</span><span class="o">,</span> <span class="s">"spark i j k"</span><span class="o">),</span> |
| <span class="o">(</span><span class="mi">5L</span><span class="o">,</span> <span class="s">"l m n"</span><span class="o">),</span> |
| <span class="o">(</span><span class="mi">6L</span><span class="o">,</span> <span class="s">"spark hadoop spark"</span><span class="o">),</span> |
| <span class="o">(</span><span class="mi">7L</span><span class="o">,</span> <span class="s">"apache hadoop"</span><span class="o">)</span> |
| <span class="o">)).</span><span class="py">toDF</span><span class="o">(</span><span class="s">"id"</span><span class="o">,</span> <span class="s">"text"</span><span class="o">)</span> |
| |
| <span class="c1">// Make predictions on test documents.</span> |
| <span class="nv">model</span><span class="o">.</span><span class="py">transform</span><span class="o">(</span><span class="n">test</span><span class="o">)</span> |
| <span class="o">.</span><span class="py">select</span><span class="o">(</span><span class="s">"id"</span><span class="o">,</span> <span class="s">"text"</span><span class="o">,</span> <span class="s">"probability"</span><span class="o">,</span> <span class="s">"prediction"</span><span class="o">)</span> |
| <span class="o">.</span><span class="py">collect</span><span class="o">()</span> |
| <span class="o">.</span><span class="py">foreach</span> <span class="o">{</span> <span class="k">case</span> <span class="nc">Row</span><span class="o">(</span><span class="n">id</span><span class="k">:</span> <span class="kt">Long</span><span class="o">,</span> <span class="n">text</span><span class="k">:</span> <span class="kt">String</span><span class="o">,</span> <span class="n">prob</span><span class="k">:</span> <span class="kt">Vector</span><span class="o">,</span> <span class="n">prediction</span><span class="k">:</span> <span class="kt">Double</span><span class="o">)</span> <span class="k">=></span> |
| <span class="nf">println</span><span class="o">(</span><span class="n">s</span><span class="s">"($id, $text) --> prob=$prob, prediction=$prediction"</span><span class="o">)</span> |
| <span class="o">}</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/scala/org/apache/spark/examples/ml/PipelineExample.scala" in the Spark repo.</small></div> |
| </div> |
| |
| <div data-lang="java"> |
| |
| <p>Refer to the <a href="api/java/org/apache/spark/ml/Pipeline.html"><code class="language-plaintext highlighter-rouge">Pipeline</code> Java docs</a> for details on the API.</p> |
| |
| <div class="highlight"><pre class="codehilite"><code><span class="kn">import</span> <span class="nn">java.util.Arrays</span><span class="o">;</span> |
| |
| <span class="kn">import</span> <span class="nn">org.apache.spark.ml.Pipeline</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.ml.PipelineModel</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.ml.PipelineStage</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.ml.classification.LogisticRegression</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.ml.feature.HashingTF</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.ml.feature.Tokenizer</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.sql.Dataset</span><span class="o">;</span> |
| <span class="kn">import</span> <span class="nn">org.apache.spark.sql.Row</span><span class="o">;</span> |
| |
| <span class="c1">// Prepare training documents, which are labeled.</span> |
| <span class="nc">Dataset</span><span class="o"><</span><span class="nc">Row</span><span class="o">></span> <span class="n">training</span> <span class="o">=</span> <span class="n">spark</span><span class="o">.</span><span class="na">createDataFrame</span><span class="o">(</span><span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span> |
| <span class="k">new</span> <span class="nf">JavaLabeledDocument</span><span class="o">(</span><span class="mi">0L</span><span class="o">,</span> <span class="s">"a b c d e spark"</span><span class="o">,</span> <span class="mf">1.0</span><span class="o">),</span> |
| <span class="k">new</span> <span class="nf">JavaLabeledDocument</span><span class="o">(</span><span class="mi">1L</span><span class="o">,</span> <span class="s">"b d"</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">),</span> |
| <span class="k">new</span> <span class="nf">JavaLabeledDocument</span><span class="o">(</span><span class="mi">2L</span><span class="o">,</span> <span class="s">"spark f g h"</span><span class="o">,</span> <span class="mf">1.0</span><span class="o">),</span> |
| <span class="k">new</span> <span class="nf">JavaLabeledDocument</span><span class="o">(</span><span class="mi">3L</span><span class="o">,</span> <span class="s">"hadoop mapreduce"</span><span class="o">,</span> <span class="mf">0.0</span><span class="o">)</span> |
| <span class="o">),</span> <span class="nc">JavaLabeledDocument</span><span class="o">.</span><span class="na">class</span><span class="o">);</span> |
| |
| <span class="c1">// Configure an ML pipeline, which consists of three stages: tokenizer, hashingTF, and lr.</span> |
| <span class="nc">Tokenizer</span> <span class="n">tokenizer</span> <span class="o">=</span> <span class="k">new</span> <span class="nc">Tokenizer</span><span class="o">()</span> |
| <span class="o">.</span><span class="na">setInputCol</span><span class="o">(</span><span class="s">"text"</span><span class="o">)</span> |
| <span class="o">.</span><span class="na">setOutputCol</span><span class="o">(</span><span class="s">"words"</span><span class="o">);</span> |
| <span class="nc">HashingTF</span> <span class="n">hashingTF</span> <span class="o">=</span> <span class="k">new</span> <span class="nc">HashingTF</span><span class="o">()</span> |
| <span class="o">.</span><span class="na">setNumFeatures</span><span class="o">(</span><span class="mi">1000</span><span class="o">)</span> |
| <span class="o">.</span><span class="na">setInputCol</span><span class="o">(</span><span class="n">tokenizer</span><span class="o">.</span><span class="na">getOutputCol</span><span class="o">())</span> |
| <span class="o">.</span><span class="na">setOutputCol</span><span class="o">(</span><span class="s">"features"</span><span class="o">);</span> |
| <span class="nc">LogisticRegression</span> <span class="n">lr</span> <span class="o">=</span> <span class="k">new</span> <span class="nc">LogisticRegression</span><span class="o">()</span> |
| <span class="o">.</span><span class="na">setMaxIter</span><span class="o">(</span><span class="mi">10</span><span class="o">)</span> |
| <span class="o">.</span><span class="na">setRegParam</span><span class="o">(</span><span class="mf">0.001</span><span class="o">);</span> |
| <span class="nc">Pipeline</span> <span class="n">pipeline</span> <span class="o">=</span> <span class="k">new</span> <span class="nc">Pipeline</span><span class="o">()</span> |
| <span class="o">.</span><span class="na">setStages</span><span class="o">(</span><span class="k">new</span> <span class="nc">PipelineStage</span><span class="o">[]</span> <span class="o">{</span><span class="n">tokenizer</span><span class="o">,</span> <span class="n">hashingTF</span><span class="o">,</span> <span class="n">lr</span><span class="o">});</span> |
| |
| <span class="c1">// Fit the pipeline to training documents.</span> |
| <span class="nc">PipelineModel</span> <span class="n">model</span> <span class="o">=</span> <span class="n">pipeline</span><span class="o">.</span><span class="na">fit</span><span class="o">(</span><span class="n">training</span><span class="o">);</span> |
| |
| <span class="c1">// Prepare test documents, which are unlabeled.</span> |
| <span class="nc">Dataset</span><span class="o"><</span><span class="nc">Row</span><span class="o">></span> <span class="n">test</span> <span class="o">=</span> <span class="n">spark</span><span class="o">.</span><span class="na">createDataFrame</span><span class="o">(</span><span class="nc">Arrays</span><span class="o">.</span><span class="na">asList</span><span class="o">(</span> |
| <span class="k">new</span> <span class="nf">JavaDocument</span><span class="o">(</span><span class="mi">4L</span><span class="o">,</span> <span class="s">"spark i j k"</span><span class="o">),</span> |
| <span class="k">new</span> <span class="nf">JavaDocument</span><span class="o">(</span><span class="mi">5L</span><span class="o">,</span> <span class="s">"l m n"</span><span class="o">),</span> |
| <span class="k">new</span> <span class="nf">JavaDocument</span><span class="o">(</span><span class="mi">6L</span><span class="o">,</span> <span class="s">"spark hadoop spark"</span><span class="o">),</span> |
| <span class="k">new</span> <span class="nf">JavaDocument</span><span class="o">(</span><span class="mi">7L</span><span class="o">,</span> <span class="s">"apache hadoop"</span><span class="o">)</span> |
| <span class="o">),</span> <span class="nc">JavaDocument</span><span class="o">.</span><span class="na">class</span><span class="o">);</span> |
| |
| <span class="c1">// Make predictions on test documents.</span> |
| <span class="nc">Dataset</span><span class="o"><</span><span class="nc">Row</span><span class="o">></span> <span class="n">predictions</span> <span class="o">=</span> <span class="n">model</span><span class="o">.</span><span class="na">transform</span><span class="o">(</span><span class="n">test</span><span class="o">);</span> |
| <span class="k">for</span> <span class="o">(</span><span class="nc">Row</span> <span class="n">r</span> <span class="o">:</span> <span class="n">predictions</span><span class="o">.</span><span class="na">select</span><span class="o">(</span><span class="s">"id"</span><span class="o">,</span> <span class="s">"text"</span><span class="o">,</span> <span class="s">"probability"</span><span class="o">,</span> <span class="s">"prediction"</span><span class="o">).</span><span class="na">collectAsList</span><span class="o">())</span> <span class="o">{</span> |
| <span class="nc">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">"("</span> <span class="o">+</span> <span class="n">r</span><span class="o">.</span><span class="na">get</span><span class="o">(</span><span class="mi">0</span><span class="o">)</span> <span class="o">+</span> <span class="s">", "</span> <span class="o">+</span> <span class="n">r</span><span class="o">.</span><span class="na">get</span><span class="o">(</span><span class="mi">1</span><span class="o">)</span> <span class="o">+</span> <span class="s">") --> prob="</span> <span class="o">+</span> <span class="n">r</span><span class="o">.</span><span class="na">get</span><span class="o">(</span><span class="mi">2</span><span class="o">)</span> |
| <span class="o">+</span> <span class="s">", prediction="</span> <span class="o">+</span> <span class="n">r</span><span class="o">.</span><span class="na">get</span><span class="o">(</span><span class="mi">3</span><span class="o">));</span> |
| <span class="o">}</span></code></pre></div> |
| <div><small>Find full example code at "examples/src/main/java/org/apache/spark/examples/ml/JavaPipelineExample.java" in the Spark repo.</small></div> |
| </div> |
| |
| </div> |
| |
| <h2 id="model-selection-hyperparameter-tuning">Model selection (hyperparameter tuning)</h2> |
| |
| <p>A big benefit of using ML Pipelines is hyperparameter optimization. See the <a href="ml-tuning.html">ML Tuning Guide</a> for more information on automatic model selection.</p> |
| |
| |
| </div> |
| |
| <!-- /container --> |
| </div> |
| |
| <script src="js/vendor/jquery-3.5.1.min.js"></script> |
| <script src="js/vendor/bootstrap.bundle.min.js"></script> |
| |
| <script src="js/vendor/anchor.min.js"></script> |
| <script src="js/main.js"></script> |
| |
| <script type="text/javascript" src="js/vendor/docsearch.min.js"></script> |
| <script type="text/javascript"> |
| // DocSearch is entirely free and automated. DocSearch is built in two parts: |
| // 1. a crawler which we run on our own infrastructure every 24 hours. It follows every link |
| // in your website and extract content from every page it traverses. It then pushes this |
| // content to an Algolia index. |
| // 2. a JavaScript snippet to be inserted in your website that will bind this Algolia index |
| // to your search input and display its results in a dropdown UI. If you want to find more |
| // details on how works DocSearch, check the docs of DocSearch. |
| docsearch({ |
| apiKey: 'd62f962a82bc9abb53471cb7b89da35e', |
| appId: 'RAI69RXRSK', |
| indexName: 'apache_spark', |
| inputSelector: '#docsearch-input', |
| enhancedSearchInput: true, |
| algoliaOptions: { |
| 'facetFilters': ["version:3.5.0"] |
| }, |
| debug: false // Set debug to true if you want to inspect the dropdown |
| }); |
| |
| </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 ? 'https://' : 'http://') + |
| 'cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js' + |
| '?config=TeX-AMS-MML_HTMLorMML'; |
| d.getElementsByTagName('head')[0].appendChild(script); |
| }(document)); |
| </script> |
| </body> |
| </html> |
