| <!DOCTYPE html><html><head><title>Choosing Evaluation Metrics</title><meta charset="utf-8"/><meta content="IE=edge,chrome=1" http-equiv="X-UA-Compatible"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><meta class="swiftype" name="title" data-type="string" content="Choosing Evaluation Metrics"/><link rel="canonical" href="https://docs.prediction.io/evaluation/metricchoose/"/><link href="/images/favicon/normal-b330020a.png" rel="shortcut icon"/><link href="/images/favicon/apple-c0febcf2.png" rel="apple-touch-icon"/><link href="//fonts.googleapis.com/css?family=Open+Sans:300italic,400italic,600italic,700italic,800italic,400,300,600,700,800" rel="stylesheet"/><link href="//maxcdn.bootstrapcdn.com/font-awesome/4.2.0/css/font-awesome.min.css" rel="stylesheet"/><link href="/stylesheets/application-3598c7d7.css" rel="stylesheet" type="text/css"/><!--[if lt IE 9]><script src="//cdnjs.cloudflare.com/ajax/libs/html5shiv/3.7.2/html5shiv.min.js"></script><![endif]--><script src="//cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script><script>(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){ |
| (i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o), |
| m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m) |
| })(window,document,'script','//www.google-analytics.com/analytics.js','ga'); |
| |
| ga('create', 'UA-38306178-1', 'auto'); |
| ga('require', 'linkid', 'linkid.js'); |
| ga('send', 'pageview');</script><script>!function(){var analytics=window.analytics=window.analytics||[];if(!analytics.initialize)if(analytics.invoked)window.console&&console.error&&console.error("Segment snippet included twice.");else{analytics.invoked=!0;analytics.methods=["trackSubmit","trackClick","trackLink","trackForm","pageview","identify","group","track","ready","alias","page","once","off","on"];analytics.factory=function(t){return function(){var e=Array.prototype.slice.call(arguments);e.unshift(t);analytics.push(e);return analytics}};for(var t=0;t<analytics.methods.length;t++){var e=analytics.methods[t];analytics[e]=analytics.factory(e)}analytics.load=function(t){var e=document.createElement("script");e.type="text/javascript";e.async=!0;e.src=("https:"===document.location.protocol?"https://":"http://")+"cdn.segment.com/analytics.js/v1/"+t+"/analytics.min.js";var n=document.getElementsByTagName("script")[0];n.parentNode.insertBefore(e,n)};analytics.SNIPPET_VERSION="3.0.1"; |
| analytics.load("YlF3updaI3DR96hnNgSGpR3PPBUGDzt8"); |
| analytics.page() |
| }}();</script><script>RCX_CUSTOM_LIB="https://cdn.recontext.com/staging/rcx.min.js"; |
| (function(b,d,a){b.RCX_OBJECT=a;a=b[a]||[];if(!a.snipV&&!a.libV){b.rcx=a;a.snipV="0.2.0";var g=function(a,b,c,d){a[b]=a[b]||function(){c.push([d].concat(Array.prototype.slice.call(arguments)))}};b="init page track identify link setUserProperty unsetUserProperty".split(" ");for(var f=0;f<b.length;f++){var e,c;e=b[f];c=e.split(".");2==c.length?(a[c[0]]=a[c[0]]||[],g(a[c[0]],c[1],a,e)):g(a,e,a,e)}a=d.createElement("script");a.type="text/javascript";a.async=!0;a.src="undefined"!==typeof RCX_CUSTOM_LIB? |
| RCX_CUSTOM_LIB:"https://cdn.recontext.com/rcx.min.js";d=d.getElementsByTagName("script")[0];d.parentNode.insertBefore(a,d)}})(window,document,"rcx"); |
| rcx.init("kTxFcI3IWdXYfRsh6uuYuej4qYl8m8LVMePM2hdIkM9YjHqkAFC6mqdqO9fpp8p9"); |
| rcx.page();</script><script>function t(e){analytics.identify(e); analytics.track("newsletter signup"); |
| rcx.track("newsletter signup", { '_email': e });}</script><script>!function(f,b,e,v,n,t,s){if(f.fbq)return;n=f.fbq=function(){n.callMethod? |
| n.callMethod.apply(n,arguments):n.queue.push(arguments)};if(!f._fbq)f._fbq=n; |
| n.push=n;n.loaded=!0;n.version='2.0';n.queue=[];t=b.createElement(e);t.async=!0; |
| t.src=v;s=b.getElementsByTagName(e)[0];s.parentNode.insertBefore(t,s)}(window, |
| document,'script','//connect.facebook.net/en_US/fbevents.js'); |
| |
| fbq('init', '1073028432707778'); |
| fbq('track', "PageView");</script><script src="//use.typekit.net/mut4mjx.js"></script><script>try{Typekit.load();}catch(e){}</script></head><body><div id="global"><header><div class="container" id="header-wrapper"><div class="row"><div class="col-sm-12"><div id="logo-wrapper"><span id="drawer-toggle"></span><a href="#"></a><a href="http://prediction.io/"><img alt="PredictionIO" id="logo" src="/images/logos/logo-ee2b9bb3.png"/></a></div><div id="menu-wrapper"><div id="header-nav-options-wrapper"><ul><li><a href="/">Install & Doc</a></li> <li><a href="/support">Support</a></li> </ul></div><div id="pill-wrapper"><a class="pill left" href="//templates.prediction.io/">TEMPLATES</a> <a class="pill right" href="//github.com/PredictionIO/PredictionIO/">OPEN SOURCE</a></div></div><img class="mobile-search-bar-toggler hidden-md hidden-lg" src="/images/icons/search-glass-704bd4ff.png"/></div></div></div></header><div id="search-bar-row-wrapper"><div class="container-fluid" id="search-bar-row"><div class="row"><div class="col-md-9 col-sm-11 col-xs-11"><div class="hidden-md hidden-lg" id="mobile-page-heading-wrapper"><p>PredictionIO Docs</p><h4>Choosing Evaluation Metrics</h4></div><h4 class="hidden-sm hidden-xs">PredictionIO Docs</h4></div><div class="col-md-3 col-sm-1 col-xs-1 hidden-md hidden-lg"><img id="left-menu-indicator" src="/images/icons/down-arrow-dfe9f7fe.png"/></div><div class="col-md-3 col-sm-12 col-xs-12 swiftype-wrapper"><div class="swiftype"><form class="search-form"><img class="search-box-toggler hidden-xs hidden-sm" src="/images/icons/search-glass-704bd4ff.png"/><div class="search-box"><img src="/images/icons/search-glass-704bd4ff.png"/><input type="text" id="st-search-input" class="st-search-input" placeholder="Search Doc..."/></div><img class="swiftype-row-hider hidden-md hidden-lg" src="/images/icons/drawer-toggle-active-fcbef12a.png"/></form></div></div><div class="mobile-left-menu-toggler hidden-md hidden-lg"></div></div></div></div><div id="page" class="container-fluid"><div class="row"><div id="left-menu-wrapper" class="col-md-3"><nav id="nav-main"><ul><li class="level-1"><a class="expandible" href="/"><span>Apache PredictionIO (incubating) Documentation</span></a><ul><li class="level-2"><a class="final" href="/"><span>Welcome to Apache PredictionIO (incubating)</span></a></li></ul></li><li class="level-1"><a class="expandible" href="#"><span>Getting Started</span></a><ul><li class="level-2"><a class="final" href="/start/"><span>A Quick Intro</span></a></li><li class="level-2"><a class="final" href="/install/"><span>Installing Apache PredictionIO (incubating)</span></a></li><li class="level-2"><a class="final" href="/start/download/"><span>Downloading an Engine Template</span></a></li><li class="level-2"><a class="final" href="/start/deploy/"><span>Deploying Your First Engine</span></a></li><li class="level-2"><a class="final" href="/start/customize/"><span>Customizing the Engine</span></a></li></ul></li><li class="level-1"><a class="expandible" href="#"><span>Integrating with Your App</span></a><ul><li class="level-2"><a class="final" href="/appintegration/"><span>App Integration Overview</span></a></li><li class="level-2"><a class="expandible" href="/sdk/"><span>List of SDKs</span></a><ul><li class="level-3"><a class="final" href="/sdk/java/"><span>Java & Android SDK</span></a></li><li class="level-3"><a class="final" href="/sdk/php/"><span>PHP SDK</span></a></li><li class="level-3"><a class="final" href="/sdk/python/"><span>Python SDK</span></a></li><li class="level-3"><a class="final" href="/sdk/ruby/"><span>Ruby SDK</span></a></li><li class="level-3"><a class="final" href="/sdk/community/"><span>Community Powered SDKs</span></a></li></ul></li></ul></li><li class="level-1"><a class="expandible" href="#"><span>Deploying an Engine</span></a><ul><li class="level-2"><a class="final" href="/deploy/"><span>Deploying as a Web Service</span></a></li><li class="level-2"><a class="final" href="/cli/#engine-commands"><span>Engine Command-line Interface</span></a></li><li class="level-2"><a class="final" href="/deploy/engineparams/"><span>Setting Engine Parameters</span></a></li><li class="level-2"><a class="final" href="/deploy/enginevariants/"><span>Deploying Multiple Engine Variants</span></a></li></ul></li><li class="level-1"><a class="expandible" href="#"><span>Customizing an Engine</span></a><ul><li class="level-2"><a class="final" href="/customize/"><span>Learning DASE</span></a></li><li class="level-2"><a class="final" href="/customize/dase/"><span>Implement DASE</span></a></li><li class="level-2"><a class="final" href="/customize/troubleshooting/"><span>Troubleshooting Engine Development</span></a></li><li class="level-2"><a class="final" href="/api/current/#package"><span>Engine Scala APIs</span></a></li></ul></li><li class="level-1"><a class="expandible" href="#"><span>Collecting and Analyzing Data</span></a><ul><li class="level-2"><a class="final" href="/datacollection/"><span>Event Server Overview</span></a></li><li class="level-2"><a class="final" href="/cli/#event-server-commands"><span>Event Server Command-line Interface</span></a></li><li class="level-2"><a class="final" href="/datacollection/eventapi/"><span>Collecting Data with REST/SDKs</span></a></li><li class="level-2"><a class="final" href="/datacollection/eventmodel/"><span>Events Modeling</span></a></li><li class="level-2"><a class="final" href="/datacollection/webhooks/"><span>Unifying Multichannel Data with Webhooks</span></a></li><li class="level-2"><a class="final" href="/datacollection/channel/"><span>Channel</span></a></li><li class="level-2"><a class="final" href="/datacollection/batchimport/"><span>Importing Data in Batch</span></a></li><li class="level-2"><a class="final" href="/datacollection/analytics/"><span>Using Analytics Tools</span></a></li></ul></li><li class="level-1"><a class="expandible" href="#"><span>Choosing an Algorithm(s)</span></a><ul><li class="level-2"><a class="final" href="/algorithm/"><span>Built-in Algorithm Libraries</span></a></li><li class="level-2"><a class="final" href="/algorithm/switch/"><span>Switching to Another Algorithm</span></a></li><li class="level-2"><a class="final" href="/algorithm/multiple/"><span>Combining Multiple Algorithms</span></a></li><li class="level-2"><a class="final" href="/algorithm/custom/"><span>Adding Your Own Algorithms</span></a></li></ul></li><li class="level-1"><a class="expandible" href="#"><span>ML Tuning and Evaluation</span></a><ul><li class="level-2"><a class="final" href="/evaluation/"><span>Overview</span></a></li><li class="level-2"><a class="final" href="/evaluation/paramtuning/"><span>Hyperparameter Tuning</span></a></li><li class="level-2"><a class="final" href="/evaluation/evaluationdashboard/"><span>Evaluation Dashboard</span></a></li><li class="level-2"><a class="final active" href="/evaluation/metricchoose/"><span>Choosing Evaluation Metrics</span></a></li><li class="level-2"><a class="final" href="/evaluation/metricbuild/"><span>Building Evaluation Metrics</span></a></li></ul></li><li class="level-1"><a class="expandible" href="#"><span>System Architecture</span></a><ul><li class="level-2"><a class="final" href="/system/"><span>Architecture Overview</span></a></li><li class="level-2"><a class="final" href="/system/anotherdatastore/"><span>Using Another Data Store</span></a></li></ul></li><li class="level-1"><a class="expandible" href="#"><span>Engine Template Gallery</span></a><ul><li class="level-2"><a class="final" href="http://templates.prediction.io"><span>Browse</span></a></li><li class="level-2"><a class="final" href="/community/submit-template/"><span>Submit your Engine as a Template</span></a></li></ul></li><li class="level-1"><a class="expandible" href="#"><span>Demo Tutorials</span></a><ul><li class="level-2"><a class="final" href="/demo/tapster/"><span>Comics Recommendation Demo</span></a></li><li class="level-2"><a class="final" href="/demo/community/"><span>Community Contributed Demo</span></a></li><li class="level-2"><a class="final" href="/demo/textclassification/"><span>Text Classification Engine Tutorial</span></a></li></ul></li><li class="level-1"><a class="expandible" href="/community/"><span>Getting Involved</span></a><ul><li class="level-2"><a class="final" href="/community/contribute-code/"><span>Contribute Code</span></a></li><li class="level-2"><a class="final" href="/community/contribute-documentation/"><span>Contribute Documentation</span></a></li><li class="level-2"><a class="final" href="/community/contribute-sdk/"><span>Contribute a SDK</span></a></li><li class="level-2"><a class="final" href="/community/contribute-webhook/"><span>Contribute a Webhook</span></a></li><li class="level-2"><a class="final" href="/community/projects/"><span>Community Projects</span></a></li></ul></li><li class="level-1"><a class="expandible" href="#"><span>Getting Help</span></a><ul><li class="level-2"><a class="final" href="/resources/faq/"><span>FAQs</span></a></li><li class="level-2"><a class="final" href="/support/"><span>Community Support</span></a></li><li class="level-2"><a class="final" href="/support/#enterprise-support"><span>Enterprise Support</span></a></li></ul></li><li class="level-1"><a class="expandible" href="#"><span>Resources</span></a><ul><li class="level-2"><a class="final" href="/resources/intellij/"><span>Developing Engines with IntelliJ IDEA</span></a></li><li class="level-2"><a class="final" href="/resources/upgrade/"><span>Upgrade Instructions</span></a></li><li class="level-2"><a class="final" href="/resources/glossary/"><span>Glossary</span></a></li></ul></li></ul></nav></div><div class="col-md-9 col-sm-12"><div class="content-header hidden-md hidden-lg"><div id="breadcrumbs" class="hidden-sm hidden xs"><ul><li><a href="#">ML Tuning and Evaluation</a><span class="spacer">></span></li><li><span class="last">Choosing Evaluation Metrics</span></li></ul></div><div id="page-title"><h1>Choosing Evaluation Metrics</h1></div></div><div id="table-of-content-wrapper"><h5>On this page</h5><aside id="table-of-contents"><ul> <li> <a href="#defining-metric">Defining Metric</a> </li> <li> <a href="#common-metrics">Common Metrics</a> </li> </ul> </aside><hr/><a id="edit-page-link" href="https://github.com/apache/incubator-predictionio/tree/livedoc/docs/manual/source/evaluation/metricchoose.html.md"><img src="/images/icons/edit-pencil-d6c1bb3d.png"/>Edit this page</a></div><div class="content-header hidden-sm hidden-xs"><div id="breadcrumbs" class="hidden-sm hidden xs"><ul><li><a href="#">ML Tuning and Evaluation</a><span class="spacer">></span></li><li><span class="last">Choosing Evaluation Metrics</span></li></ul></div><div id="page-title"><h1>Choosing Evaluation Metrics</h1></div></div><div class="content"><p>The <a href="/evaluation/paramtuning/">hyperparameter tuning module</a> allows us to select the optimal engine parameter defined by a <code>Metric</code>. <code>Metric</code> determines the quality of an engine variant. We have skimmmed through the process of choosing the right <code>Metric</code> in previous sections.</p><p>This secion discusses basic evaluation metrics commonly used for classification problems. If you are more interested in knowing how to <em>implement</em> a custom metric, please skip to <a href="/evaluation/metricbuild/">the next section</a>.</p><h2 id='defining-metric' class='header-anchors'>Defining Metric</h2><p>Metric evaluates the quality of an engine by comparing engine's output (predicted result) with the original label (actual result). A engine serving better prediction should yield a higher metric score, the tuning module returns the engine parameter with the highest score. It is sometimes called <a href="http://en.wikipedia.org/wiki/Loss_function"><em>loss function</em></a> in literature, where the goal is to minimize the loss function. </p><p>During tuning, it is important for us to understand the definition of the metric, to make sure it is aligned with the prediction engine's goal.</p><p>In the classificaiton template, we use <em>Accuracy</em> as our metric. <em>Accuracy</em> is defined as: the percentage of queries which the engine is able to predict the correct label. </p><h2 id='common-metrics' class='header-anchors'>Common Metrics</h2><p>We illustrate the choice of metric with the following confusion matrix. Row represents the engine predicted label, column represents the acutal label. The second row means that of the 200 testing data points, the engine predicted 60 (15 + 35 + 10) of them as label 2.0, among which 35 are correct prediction (i.e. actual label is 2.0, matches with the prediction), and 25 are wrong.</p> <table><thead> <tr> <th style="text-align: center"></th> <th style="text-align: center">Actual = 1.0</th> <th style="text-align: center">Actual = 2.0</th> <th style="text-align: center">Actual = 3.0</th> </tr> </thead><tbody> <tr> <td style="text-align: center"><strong>Predicted = 1.0</strong></td> <td style="text-align: center">30</td> <td style="text-align: center">0</td> <td style="text-align: center">60</td> </tr> <tr> <td style="text-align: center"><strong>Predicted = 2.0</strong></td> <td style="text-align: center">15</td> <td style="text-align: center">35</td> <td style="text-align: center">10</td> </tr> <tr> <td style="text-align: center"><strong>Predicted = 3.0</strong></td> <td style="text-align: center">0</td> <td style="text-align: center">0</td> <td style="text-align: center">50</td> </tr> </tbody></table> <h3 id='accuracy' class='header-anchors'>Accuracy</h3><p>Accuracy means that how many data points are predicted correctly. It is one of the simplest form of evaluation metrics. The accuracy score is # of correct points / # total = (30 + 35 + 50) / 200 = 0.575.</p><h3 id='precision' class='header-anchors'>Precision</h3><p>Precision is a metric for binary classifier which measures the correctness among all positive labels. A binary classifier gives only two output values (i.e. positive and negative). For problem where there are multiple values (3 in our example), we first have to tranform our problem into a binary classification problem. For example, we can have problem whether label = 1.0. The confusion matrix now becomes:</p> <table><thead> <tr> <th style="text-align: center"></th> <th style="text-align: center">Actual = 1.0</th> <th style="text-align: center">Actual != 1.0</th> </tr> </thead><tbody> <tr> <td style="text-align: center"><strong>Predicted = 1.0</strong></td> <td style="text-align: center">30</td> <td style="text-align: center">60</td> </tr> <tr> <td style="text-align: center"><strong>Predicted != 1.0</strong></td> <td style="text-align: center">15</td> <td style="text-align: center">95</td> </tr> </tbody></table> <p>Precision is the ratio between the number of correct positive answer (true positive) and the sum of correct positive answer (true positive) and wrong but positively labeled answer (false positive). In this case, the precision is 30 / (30 + 60) = ~0.3333.</p><h3 id='recall' class='header-anchors'>Recall</h3><p>Recall is a metric for binary classifier which measures how many positive labels are successfully predicted amongst all positive labels. Formally, it is the ratio between the number of correct positive answer (true positive) and the sum of correct positive answer (true positive) and wrongly negatively labeled asnwer (false negative). In this case, the recall is 30 / (30 + 15) = ~0.6667.</p><p>As we have discussed several common metrics for classification problem, we can implement them using the <code>Metric</code> class in <a href="/evaluation/metricbuild">the next section</a>.</p></div></div></div></div><footer><div class="container"><div class="seperator"></div><div class="row"><div class="col-md-4 col-md-push-8 col-xs-12"><div class="subscription-form-wrapper"><h4>Subscribe to our Newsletter</h4><form class="ajax-form" id="subscribe-form" method="POST" action="https://script.google.com/macros/s/AKfycbwhzeKCQJjQ52eVAqNT_vcklH07OITUO7wzOMDXvK6EGAWgaZgF/exec"><input class="required underlined-input" type="email" placeholder="Your email address" name="subscription_email" id="subscription_email"/><input class="pill-button" value="SUBSCRIBE" type="submit" data-state-normal="SUBSCRIBE" data-state-sucess="SUBSCRIBED!" data-state-loading="SENDING..." onclick="t($('#subscription_email').val());"/><p class="result"></p></form></div></div><div class="col-md-2 col-md-pull-4 col-xs-6 footer-link-column"><div class="footer-link-column-row"><h4>Community</h4><ul><li><a href="//docs.prediction.io/install/" target="blank">Download</a></li><li><a href="//docs.prediction.io/" target="blank">Docs</a></li><li><a href="//github.com/PredictionIO/PredictionIO" target="blank">GitHub</a></li><li><a href="//groups.google.com/forum/#!forum/predictionio-user" target="blank">Support Forum</a></li><li><a href="//stackoverflow.com/questions/tagged/predictionio" target="blank">Stackoverflow</a></li><li><a href="mailto:support@prediction.io" target="blank">Contact Us</a></li></ul></div></div><div class="col-md-2 col-md-pull-4 col-xs-6 footer-link-column"><div class="footer-link-column-row"><h4>Contribute</h4><ul><li><a href="//docs.prediction.io/community/contribute-code/" target="blank">Contribute</a></li><li><a href="//github.com/PredictionIO/PredictionIO" target="blank">Source Code</a></li><li><a href="//predictionio.atlassian.net/secure/Dashboard.jspa" target="blank">Bug Tracker</a></li><li><a href="//groups.google.com/forum/#!forum/predictionio-dev" target="blank">Contributors’ Forum</a></li><li><a href="//prediction.io/cla">Contributor Agreement</a></li><li><a href="//predictionio.uservoice.com/forums/219398-general/filters/top">Request Features</a></li></ul></div></div><div class="col-md-2 col-md-pull-4 col-xs-6 footer-link-column"><div class="footer-link-column-row"><h4>Enterprise</h4><ul><li><a href="//docs.prediction.io/support/" target="blank">Support</a></li><li><a href="//prediction.io/enterprise">Enterprise</a></li><li><a href="//prediction.io/products/predictionio-enterprise">Services</a></li></ul></div><div class="footer-link-column-row"><h4>Connect</h4><ul><li><a href="//blog.prediction.io/" target="blank">Blog</a></li><li><a href="//predictionio.theresumator.com/" target="blank">Careers</a></li></ul></div></div><div class="col-md-2 col-md-pull-4 col-xs-6 footer-link-column"><div class="footer-link-column-row"><h4>Partnership</h4><ul><li><a href="//prediction.io/partners/program">Partner Program</a></li></ul></div></div></div></div><div id="footer-bottom"><div class="container"><div class="row"><div class="col-md-12"><div id="footer-logo-wrapper"><img alt="PredictionIO" src="/images/logos/logo-white-d1e9c6e6.png"/></div><div id="social-icons-wrapper"><a class="github-button" href="https://github.com/PredictionIO/PredictionIO" data-style="mega" data-count-href="/PredictionIO/PredictionIO/stargazers" data-count-api="/repos/PredictionIO/PredictionIO#stargazers_count" data-count-aria-label="# stargazers on GitHub" aria-label="Star PredictionIO/PredictionIO on GitHub">Star</a> <a class="github-button" href="https://github.com/PredictionIO/PredictionIO/fork" data-icon="octicon-git-branch" data-style="mega" data-count-href="/PredictionIO/PredictionIO/network" data-count-api="/repos/PredictionIO/PredictionIO#forks_count" data-count-aria-label="# forks on GitHub" aria-label="Fork PredictionIO/PredictionIO on GitHub">Fork</a> <script id="github-bjs" async="" defer="" src="https://buttons.github.io/buttons.js"></script><a href="//www.facebook.com/predictionio" target="blank"><img alt="PredictionIO on Twitter" src="/images/icons/twitter-ea9dc152.png"/></a> <a href="//twitter.com/predictionio" target="blank"><img alt="PredictionIO on Facebook" src="/images/icons/facebook-5c57939c.png"/></a> </div></div></div></div></div></footer></div><script>(function(w,d,t,u,n,s,e){w['SwiftypeObject']=n;w[n]=w[n]||function(){ |
| (w[n].q=w[n].q||[]).push(arguments);};s=d.createElement(t); |
| e=d.getElementsByTagName(t)[0];s.async=1;s.src=u;e.parentNode.insertBefore(s,e); |
| })(window,document,'script','//s.swiftypecdn.com/install/v1/st.js','_st'); |
| |
| _st('install','HaUfpXXV87xoB_zzCQ45');</script><script>var _qevents = _qevents || []; |
| (function() { |
| var elem = document.createElement('script'); |
| elem.src = (document.location.protocol == "https:" ? "https://secure" : "http://edge") + ".quantserve.com/quant.js"; |
| elem.async = true; |
| elem.type = "text/javascript"; |
| var scpt = document.getElementsByTagName('script')[0]; |
| scpt.parentNode.insertBefore(elem, scpt); |
| })(); |
| _qevents.push({ |
| qacct:"p-stVMxuw8H5EPX" |
| });</script><noscript><div style="display:none;"><img src="//pixel.quantserve.com/pixel/p-stVMxuw8H5EPX.gif" border="0" height="1" width="1" alt="Quantcast"/></div></noscript><script>adroll_adv_id = "CPSSMJFFZ5DDHITC2STA54"; |
| adroll_pix_id = "UWX4N2WIMJADVHJGOFTM44"; |
| (function () { |
| var _onload = function(){ |
| if (document.readyState && !/loaded|complete/.test(document.readyState)){setTimeout(_onload, 10);return} |
| if (!window.__adroll_loaded){__adroll_loaded=true;setTimeout(_onload, 50);return} |
| var scr = document.createElement("script"); |
| var host = (("https:" == document.location.protocol) ? "https://s.adroll.com" : "http://a.adroll.com"); |
| scr.setAttribute('async', 'true'); |
| scr.type = "text/javascript"; |
| scr.src = host + "/j/roundtrip.js"; |
| ((document.getElementsByTagName('head') || [null])[0] || |
| document.getElementsByTagName('script')[0].parentNode).appendChild(scr); |
| }; |
| if (window.addEventListener) {window.addEventListener('load', _onload, false);} |
| else {window.attachEvent('onload', _onload)} |
| }());</script><script src="/javascripts/application-5a24945b.js"></script></body></html> |
