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-<!DOCTYPE html><html><head><title>Building Evaluation Metrics</title><meta 
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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 
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Engine</span></a></li></ul></li><li class="level-1"><a class="expandible" 
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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 cla
 ss="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" 
 >href="/evaluation/metricchoose/"><span>Choosing Evaluation 
 >Metrics</span></a></
 li><li class="level-2"><a class="final active" 
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 
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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" 
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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 
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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" 
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 l-2"><a class="final" href="/resources/faq/"><span>FAQs</span></a></li><li 
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href="/support/"><span>Support</span></a></li></ul></li><li class="level-1"><a 
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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">&gt;</span></li><li><span class="last">Building Evaluation 
Metrics</span></li></ul></div><div id="page-title"><h1>Building Evaluation 
Metrics</h1></div></div><div id="table-of-content-wrapper"><h5>On t
 his page</h5><aside id="table-of-contents"><ul> <li> <a 
href="#overview">Overview</a> </li> <li> <a 
href="#example-1-accuracy-metric">Example 1: Accuracy Metric</a> </li> <li> <a 
href="#example-2-precision-metric">Example 2: Precision Metric</a> </li> </ul> 
</aside><hr/><a id="edit-page-link" 
href="https://github.com/apache/incubator-predictionio/tree/livedoc/docs/manual/source/evaluation/metricbuild.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">&gt;</span></li><li><span 
class="last">Building Evaluation Metrics</span></li></ul></div><div 
id="page-title"><h1>Building Evaluation Metrics</h1></div></div><div 
class="content"><p>PredictionIO enables developer to implement evaluation 
custom evaluation metric with just a few lines of code. We illustrate it with 
<a href="/templates/classif
 ication/quickstart/">the classification template</a>.</p><h2 id='overview' 
class='header-anchors'>Overview</h2><p>A simplistic form of metric is a 
function which takes a <code>(Query, PredictedResult, 
ActualResult)</code>-tuple (<em>QPA-tuple</em>) as input and return a score. 
Exploiting this properties allows us to implement custom metric with a single 
line of code (plus some boilerplates). We demonstate this with two metrics: 
accuracy and precision.</p> <h2 id='example-1:-accuracy-metric' 
class='header-anchors'>Example 1: Accuracy Metric</h2><p>Accuracy is a metric 
capturing the portion of correct prediction among all test data points. A way 
to model this is for each correct QPA-tuple, we give a score of 1.0 and 
otherwise 0.0, then we take an average of all tuple scores.</p><p>PredictionIO 
has a [[AverageMetric]] helper class which provides this feature. This class 
takes 4 type parameters, [[EvalInfo]], [[Query]], [[PredictedResult]], and 
[[ActualResult]], these types can be found
  from the engine&#39;s signature. Line 5 below is the custom 
calculation.</p><div class="highlight scala"><table style="border-spacing: 
0"><tbody><tr><td class="gutter gl" style="text-align: right"><pre 
class="lineno">1
+<!DOCTYPE html><html><head><title>Building Evaluation Metrics</title><meta 
charset="utf-8"/><meta content="IE=edge,chrome=1" 
http-equiv="X-UA-Compatible"/><meta name="viewport" 
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name="title" data-type="string" content="Building Evaluation Metrics"/><link 
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SOURCE</a></div></div><img class="mobile-search-bar-toggler hidden-md 
hidden-lg" 
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id="search-bar-row"><div class="row"><div class="col-md-9 col-sm-11 
col-xs-11"><div c
 lass="hidden-md hidden-lg" id="mobile-page-heading-wrapper"><p>PredictionIO 
Docs</p><h4>Building 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" 
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hidden-lg"></div></div></div></div><div id="page" class="container-fluid"><div 
class="row"><div id="left-menu-wrappe
 r" 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</s
 pan></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 c
 lass="level-2"><a class="final" href="/deploy/monitoring/"><span>Monitoring 
Engine</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 clas
 s="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" 
href="/evaluation/metricchoose/"><span>Choosing Evaluation Metrics</span></a></l
 i><li class="level-2"><a class="final active" 
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="/gallery/template-gallery/"><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 c
 lass="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" 
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Metrics</h1></div></div><div id="table-of-content-wrapper"><h5>On th
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</aside><hr/><a id="edit-page-link" 
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id="page-title"><h1>Building Evaluation Metrics</h1></div></div><div 
class="content"><p>PredictionIO enables developer to implement evaluation 
custom evaluation metric with just a few lines of code. We illustrate it with 
<a href="/templates/classifi
 cation/quickstart/">the classification template</a>.</p><h2 id='overview' 
class='header-anchors'>Overview</h2><p>A simplistic form of metric is a 
function which takes a <code>(Query, PredictedResult, 
ActualResult)</code>-tuple (<em>QPA-tuple</em>) as input and return a score. 
Exploiting this properties allows us to implement custom metric with a single 
line of code (plus some boilerplates). We demonstate this with two metrics: 
accuracy and precision.</p> <h2 id='example-1:-accuracy-metric' 
class='header-anchors'>Example 1: Accuracy Metric</h2><p>Accuracy is a metric 
capturing the portion of correct prediction among all test data points. A way 
to model this is for each correct QPA-tuple, we give a score of 1.0 and 
otherwise 0.0, then we take an average of all tuple scores.</p><p>PredictionIO 
has a [[AverageMetric]] helper class which provides this feature. This class 
takes 4 type parameters, [[EvalInfo]], [[Query]], [[PredictedResult]], and 
[[ActualResult]], these types can be found 
 from the engine&#39;s signature. Line 5 below is the custom 
calculation.</p><div class="highlight scala"><table style="border-spacing: 
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href="#">ML Tuning and Evaluation</a><span 
class="spacer">&gt;</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
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class="hidden-sm hidden xs"><ul><li><a href="#">ML Tuning and 
Evaluation</a><span class="spacer">&gt;</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&#39;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&#39;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 styl
 e="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 probl
 em 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 
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href="#">ML Tuning and Evaluation</a><span 
class="spacer">&gt;</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 t
 his 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 
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class="hidden-sm hidden xs"><ul><li><a href="#">ML Tuning and 
Evaluation</a><span class="spacer">&gt;</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&#39;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&#39;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 proble
 m 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><h
 3 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 
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