{
  "fetched_at": "2026-10-24T16:46:26Z",
  "source_url": "https://www.kaggle.com/competitions/final22202/data",
  "pages": [
    {
      "name": "data-description",
      "content": "<h2>File descriptions</h2>\r\n<ul>\r\n<li><strong>training.csv</strong> - Training set of 250000 events, with an ID column, 30 feature columns, a weight column and a label column.</li>\r\n<li><strong>test.csv</strong> - Test set of 550000 events with an ID column and 30 feature columns.</li>\r\n<li><strong>random_submission</strong> - Sample submission file in the correct format. File format is described on the <a href=\"https://www.kaggle.com/c/higgs-boson/details/evaluation\">Evaluation</a> page.</li>\r\n<li><strong>HiggsBosonCompetition_AMSMetric</strong> - Python script to calculate the competition evaluation metric.</li>\r\n</ul>\r\n<p>For detailed information on the semantics of the features, labels, and weights, see the <a href=\"http://higgsml.lal.in2p3.fr/documentation\">technical documentation</a> from the <a href=\"https://higgsml.lal.in2p3.fr/\">LAL website</a> on the task.</p>\r\n<p>Some details to get started:</p>\r\n<ul>\r\n<li>all variables are floating point, except <strong style=\"font-size: 1em;\">PRI_jet_num</strong><span style=\"font-size: 1em;\"> which is integer</span></li>\r\n<li>variables prefixed with <strong style=\"font-size: 1em;\">PRI</strong><span style=\"font-size: 1em;\"> (for PRImitives) are “raw” quantities about the bunch collision as measured by the detector.</span></li>\r\n<li>variables prefixed with <strong style=\"font-size: 1em;\">DER</strong><span style=\"font-size: 1em;\"> (for DERived) are quantities computed from the primitive features, which were selected by the physicists of ATLAS</span></li>\r\n<li>it can happen that for some entries some variables are meaningless or cannot be computed; in this case, their value is −999.0, which is outside the normal range of all variables</li>\r\n</ul>",
      "isPublished": false,
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    {
      "name": "Description",
      "content": "<h2>Overview</h2>\r\n<p>Discovery of the long awaited Higgs Boson was announced July 4, 2012 and confirmed six months later. 2013 saw a number of prestigious awards, including a Nobel prize. But for physicists, the discovery of a new particle means the beginning of a long and difficult quest to measure its characteristics and determine if it fits the current model of nature.</p>\r\n<p>A key property of any particle is how often it decays into other particles. ATLAS is a particle physics experiment taking place at the Large Hadron Collider at CERN that searches for new particles and processes using head-on collisions of protons of extraordinarily high energy. The ATLAS experiment has recently observed a signal of the Higgs boson decaying into two tau particles, but this decay is a small signal buried in background noise.</p>\r\n<p>The goal of the Higgs Boson Machine Learning Challenge is to explore the potential of advanced machine learning methods to improve the discovery significance of the experiment. No knowledge of particle physics is required. Using simulated data with features characterizing events detected by ATLAS, your task is to classify events into \"tau tau decay of a Higgs boson\" versus \"background.\"</p>\r\n<p>The winning method may eventually be applied to real data and the winners may be invited to CERN to discuss their results with high energy physicists.</p>",
      "isPublished": false,
      "hasIsPublished": false,
      "postTitle": "",
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    {
      "name": "Evaluation",
      "content": "<p>The evaluation metric is the approximate median significance (AMS):</p>\r\n<div class=\"MathJax_Display\" style=\"text-align: center;\"><span class=\"MathJax\" id=\"MathJax-Element-1-Frame\" tabindex=\"0\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mtext&gt;AMS&lt;/mtext&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msqrt&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/msub&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;mo&gt;&amp;#x2061;&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mfrac&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mrow&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;&amp;#x2212;&lt;/mo&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msqrt&gt;&lt;/math&gt;\" role=\"presentation\" style=\"text-align: center; position: relative;\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-1\" style=\"width: 25.647em; display: inline-block;\"><strong><span style=\"display: inline-block; position: relative; width: 21.022em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(0.296em 1021.02em 3.633em -999.997em); top: -2.163em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-2\"><span class=\"mtext\" id=\"MathJax-Span-3\" style=\"font-family: MathJax_Main;\">AMS</span><span class=\"mo\" id=\"MathJax-Span-4\" style=\"font-family: MathJax_Main; padding-left: 0.296em;\">=</span><span class=\"msqrt\" id=\"MathJax-Span-5\" style=\"padding-left: 0.296em;\"><span style=\"display: inline-block; position: relative; width: 17.45em; height: 0px;\"><span style=\"position: absolute; clip: rect(2.345em 1016.22em 5.097em -999.997em); top: -3.978em; left: 0.998em;\"><span class=\"mrow\" id=\"MathJax-Span-6\"><span class=\"mn\" id=\"MathJax-Span-7\" style=\"font-family: MathJax_Main;\">2</span><span class=\"mrow\" id=\"MathJax-Span-8\" style=\"padding-left: 0.179em;\"><span class=\"mo\" id=\"MathJax-Span-9\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">(</span></span><span class=\"mrow\" id=\"MathJax-Span-10\"><span class=\"mo\" id=\"MathJax-Span-11\" style=\"font-family: MathJax_Main;\">(</span><span class=\"mi\" id=\"MathJax-Span-12\" style=\"font-family: MathJax_Math-italic;\">s</span><span class=\"mo\" id=\"MathJax-Span-13\" style=\"font-family: MathJax_Main; padding-left: 0.237em;\">+</span><span class=\"mi\" id=\"MathJax-Span-14\" style=\"font-family: MathJax_Math-italic; padding-left: 0.237em;\">b</span><span class=\"mo\" id=\"MathJax-Span-15\" style=\"font-family: MathJax_Main; padding-left: 0.237em;\">+</span><span class=\"msubsup\" id=\"MathJax-Span-16\" style=\"padding-left: 0.237em;\"><span style=\"display: inline-block; position: relative; width: 0.823em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.106em 1000.41em 4.16em -999.997em); top: -3.978em; left: 0em;\"><span class=\"mi\" id=\"MathJax-Span-17\" style=\"font-family: MathJax_Math-italic;\">b</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; top: -3.803em; left: 0.413em;\"><span class=\"mi\" id=\"MathJax-Span-18\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">r</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span><span class=\"mo\" id=\"MathJax-Span-19\" style=\"font-family: MathJax_Main;\">)</span><span class=\"mi\" id=\"MathJax-Span-20\" style=\"font-family: MathJax_Main; padding-left: 0.179em;\">log</span><span class=\"mo\" id=\"MathJax-Span-21\"></span><span class=\"mrow\" id=\"MathJax-Span-22\"><span class=\"mo\" id=\"MathJax-Span-23\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">(</span></span><span class=\"mrow\" id=\"MathJax-Span-24\"><span class=\"mn\" id=\"MathJax-Span-25\" style=\"font-family: MathJax_Main;\">1</span><span class=\"mo\" id=\"MathJax-Span-26\" style=\"font-family: MathJax_Main; padding-left: 0.237em;\">+</span><span class=\"mfrac\" id=\"MathJax-Span-27\" style=\"padding-left: 0.237em;\"><span style=\"display: inline-block; position: relative; width: 2.638em; height: 0px; margin-right: 0.12em; margin-left: 0.12em;\"><span style=\"position: absolute; clip: rect(3.34em 1000.41em 4.16em -999.997em); top: -4.681em; left: 50%; margin-left: -0.231em;\"><span class=\"mi\" id=\"MathJax-Span-28\" style=\"font-family: MathJax_Math-italic;\">s</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; clip: rect(3.106em 1002.52em 4.335em -999.997em); top: -3.276em; left: 50%; margin-left: -1.227em;\"><span class=\"mrow\" id=\"MathJax-Span-29\"><span class=\"mi\" id=\"MathJax-Span-30\" style=\"font-family: MathJax_Math-italic;\">b</span><span class=\"mo\" id=\"MathJax-Span-31\" style=\"font-family: MathJax_Main; padding-left: 0.237em;\">+</span><span class=\"msubsup\" id=\"MathJax-Span-32\" style=\"padding-left: 0.237em;\"><span style=\"display: inline-block; position: relative; width: 0.823em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.106em 1000.41em 4.16em -999.997em); top: -3.978em; left: 0em;\"><span class=\"mi\" id=\"MathJax-Span-33\" style=\"font-family: MathJax_Math-italic;\">b</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; top: -3.803em; left: 0.413em;\"><span class=\"mi\" id=\"MathJax-Span-34\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">r</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; clip: rect(0.823em 1002.64em 1.232em -999.997em); top: -1.285em; left: 0em;\"><span style=\"display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 2.638em; height: 0px;\"></span><span style=\"display: inline-block; width: 0px; height: 1.057em;\"></span></span></span></span></span><span class=\"mo\" id=\"MathJax-Span-35\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">)</span></span></span><span class=\"mo\" id=\"MathJax-Span-36\" style=\"font-family: MathJax_Main; padding-left: 0.237em;\">−</span><span class=\"mi\" id=\"MathJax-Span-37\" style=\"font-family: MathJax_Math-italic; padding-left: 0.237em;\">s</span></span><span class=\"mo\" id=\"MathJax-Span-38\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">)</span></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; clip: rect(3.516em 1016.46em 3.926em -999.997em); top: -5.383em; left: 0.998em;\"><span style=\"display: inline-block; position: relative; width: 16.455em; height: 0px;\"><span style=\"position: absolute; font-family: MathJax_Main; top: -3.978em; left: -0.056em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; font-family: MathJax_Main; top: -3.978em; left: 15.752em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 0.413em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 0.998em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 1.525em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 2.111em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 2.638em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 3.165em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 3.75em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 4.277em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 4.804em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 5.389em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 5.916em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 6.443em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 7.029em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 7.556em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 8.083em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 8.668em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 9.195em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 9.722em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 10.307em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 10.834em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 11.361em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 11.947em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 12.474em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 13.001em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 13.586em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 14.113em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 14.64em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"font-family: MathJax_Main; position: absolute; top: -3.978em; left: 15.225em;\">−<span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; clip: rect(2.052em 1001em 5.389em -999.997em); top: -3.978em; left: 0em;\"><span style=\"font-family: MathJax_Size4;\">√</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.169em;\"></span></span></span></strong><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.639em; border-left: 0px solid; width: 0px; height: 3.789em;\"></span></span></nobr><span class=\"MJX_Assistive_MathML MJX_Assistive_MathML_Block\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"></math></span></span></div>\r\n<p>where</p>\r\n<ul>\r\n<li><span class=\"MathJax_Preview\" style=\"color: inherit; display: none;\"></span><strong><span class=\"MathJax\" id=\"MathJax-Element-2-Frame\" tabindex=\"0\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/math&gt;\" role=\"presentation\" style=\"position: relative;\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-39\" style=\"width: 1.642em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 1.35em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(1.291em 1001.35em 2.52em -999.997em); top: -2.163em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-40\"><span class=\"mi\" id=\"MathJax-Span-41\" style=\"font-family: MathJax_Math-italic;\">s</span><span class=\"mo\" id=\"MathJax-Span-42\" style=\"font-family: MathJax_Main;\">,</span><span class=\"mi\" id=\"MathJax-Span-43\" style=\"font-family: MathJax_Math-italic; padding-left: 0.179em;\">b</span></span><span style=\"display: inline-block; width: 0px; height: 2.169em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.218em;\"></span></span></nobr></span>:</strong> unnormalized true positive and false positive rates, respectively,</li>\r\n<li><span class=\"MathJax_Preview\" style=\"color: inherit; display: none;\"></span><span class=\"MathJax\" id=\"MathJax-Element-3-Frame\" tabindex=\"0\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msub&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;/math&gt;\" role=\"presentation\" style=\"position: relative;\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-44\" style=\"width: 3.867em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 3.165em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(1.291em 1003.11em 2.52em -999.997em); top: -2.163em; left: 0em;\"><strong><span class=\"mrow\" id=\"MathJax-Span-45\"><span class=\"msubsup\" id=\"MathJax-Span-46\"><span style=\"display: inline-block; position: relative; width: 0.823em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.106em 1000.41em 4.16em -999.997em); top: -3.978em; left: 0em;\"><span class=\"mi\" id=\"MathJax-Span-47\" style=\"font-family: MathJax_Math-italic;\">b</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; top: -3.803em; left: 0.413em;\"><span class=\"mi\" id=\"MathJax-Span-48\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">r</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span><span class=\"mo\" id=\"MathJax-Span-49\" style=\"font-family: MathJax_Main; padding-left: 0.296em;\">=</span><span class=\"mn\" id=\"MathJax-Span-50\" style=\"font-family: MathJax_Main; padding-left: 0.296em;\">10</span></span></strong><span style=\"display: inline-block; width: 0px; height: 2.169em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.282em; border-left: 0px solid; width: 0px; height: 1.218em;\"></span></span></nobr></span>is the constant regularization term,</li>\r\n<li><span class=\"MathJax_Preview\" style=\"color: inherit; display: none;\"></span><span class=\"MathJax\" id=\"MathJax-Element-28-Frame\" tabindex=\"0\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;log&lt;/mi&gt;&lt;/math&gt;\" role=\"presentation\" style=\"position: relative;\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-501\" style=\"width: 1.584em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 1.291em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(1.291em 1001.29em 2.579em -999.997em); top: -2.163em; left: 0em;\"><strong><span class=\"mrow\" id=\"MathJax-Span-502\"><span class=\"mi\" id=\"MathJax-Span-503\" style=\"font-family: MathJax_Main;\">log</span></span></strong><span style=\"display: inline-block; width: 0px; height: 2.169em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.354em; border-left: 0px solid; width: 0px; height: 1.218em;\"></span></span></nobr><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi> </mi></math></span></span>\r\n<script type=\"math/tex\" id=\"MathJax-Element-28\">// <![CDATA[\r\n\\log\r\n// ]]></script>\r\nis the natural log.</li>\r\n</ul>\r\n<p>More precisely, let <span class=\"MathJax_Preview\" style=\"color: inherit; display: none;\"></span><span class=\"MathJax\" id=\"MathJax-Element-5-Frame\" tabindex=\"0\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;&amp;#x2026;&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/msub&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;&amp;#x2208;&lt;/mo&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;{&lt;/mo&gt;&lt;mtext&gt;b&lt;/mtext&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mtext&gt;s&lt;/mtext&gt;&lt;msup&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;}&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/msup&gt;&lt;/math&gt;\" role=\"presentation\" style=\"position: relative;\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-54\" style=\"width: 11.186em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 9.136em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(1.232em 1009.14em 2.579em -999.997em); top: -2.163em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-55\"><span class=\"mo\" id=\"MathJax-Span-56\" style=\"font-family: MathJax_Main;\">(</span><span class=\"msubsup\" id=\"MathJax-Span-57\"><span style=\"display: inline-block; position: relative; width: 0.94em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.34em 1000.47em 4.394em -999.997em); top: -3.978em; left: 0em;\"><span class=\"mi\" id=\"MathJax-Span-58\" style=\"font-family: MathJax_Math-italic;\">y<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; top: -3.803em; left: 0.471em;\"><span class=\"mn\" id=\"MathJax-Span-59\" style=\"font-size: 70.7%; font-family: MathJax_Main;\">1</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span><span class=\"mo\" id=\"MathJax-Span-60\" style=\"font-family: MathJax_Main;\">,</span><span class=\"mo\" id=\"MathJax-Span-61\" style=\"font-family: MathJax_Main; padding-left: 0.179em;\">…</span><span class=\"mo\" id=\"MathJax-Span-62\" style=\"font-family: MathJax_Main; padding-left: 0.179em;\">,</span><span class=\"msubsup\" id=\"MathJax-Span-63\" style=\"padding-left: 0.179em;\"><span style=\"display: inline-block; position: relative; width: 0.998em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.34em 1000.47em 4.394em -999.997em); top: -3.978em; left: 0em;\"><span class=\"mi\" id=\"MathJax-Span-64\" style=\"font-family: MathJax_Math-italic;\">y<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; top: -3.803em; left: 0.471em;\"><span class=\"mi\" id=\"MathJax-Span-65\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">n</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span><span class=\"mo\" id=\"MathJax-Span-66\" style=\"font-family: MathJax_Main;\">)</span><span class=\"mo\" id=\"MathJax-Span-67\" style=\"font-family: MathJax_Main; padding-left: 0.296em;\">∈</span><span class=\"mo\" id=\"MathJax-Span-68\" style=\"font-family: MathJax_Main; padding-left: 0.296em;\">{</span><span class=\"mtext\" id=\"MathJax-Span-69\" style=\"font-family: MathJax_Main;\">b</span><span class=\"mo\" id=\"MathJax-Span-70\" style=\"font-family: MathJax_Main;\">,</span><span class=\"mtext\" id=\"MathJax-Span-71\" style=\"font-family: MathJax_Main; padding-left: 0.179em;\">s</span><span class=\"msubsup\" id=\"MathJax-Span-72\"><span style=\"display: inline-block; position: relative; width: 0.998em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.047em 1000.41em 4.394em -999.997em); top: -3.978em; left: 0em;\"><span class=\"mo\" id=\"MathJax-Span-73\" style=\"font-family: MathJax_Main;\">}</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; top: -4.33em; left: 0.53em;\"><span class=\"mi\" id=\"MathJax-Span-74\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">n</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.169em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.354em; border-left: 0px solid; width: 0px; height: 1.361em;\"></span></span></nobr></span>be the vector of true test labels, let <span class=\"MathJax_Preview\" style=\"color: inherit; display: none;\"></span><span class=\"MathJax\" id=\"MathJax-Element-6-Frame\" tabindex=\"0\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x005E;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;&amp;#x2026;&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x005E;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/msub&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;&amp;#x2208;&lt;/mo&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;{&lt;/mo&gt;&lt;mtext&gt;b&lt;/mtext&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mtext&gt;s&lt;/mtext&gt;&lt;msup&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;}&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/msup&gt;&lt;/math&gt;\" role=\"presentation\" style=\"position: relative;\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-75\" style=\"width: 11.361em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 9.312em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(1.232em 1009.31em 2.579em -999.997em); top: -2.163em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-76\"><span class=\"mo\" id=\"MathJax-Span-77\" style=\"font-family: MathJax_Main;\">(</span><span class=\"msubsup\" id=\"MathJax-Span-78\"><span style=\"display: inline-block; position: relative; width: 0.998em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.047em 1000.53em 4.394em -999.997em); top: -3.978em; left: 0em;\"><span class=\"texatom\" id=\"MathJax-Span-79\"><span class=\"mrow\" id=\"MathJax-Span-80\"><span class=\"munderover\" id=\"MathJax-Span-81\"><span style=\"display: inline-block; position: relative; width: 0.588em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.34em 1000.47em 4.394em -999.997em); top: -3.978em; left: 0.003em;\"><span class=\"mi\" id=\"MathJax-Span-82\" style=\"font-family: MathJax_Math-italic;\">y<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; clip: rect(3.106em 1000.41em 3.633em -999.997em); top: -4.037em; left: 0.061em;\"><span class=\"mo\" id=\"MathJax-Span-83\" style=\"font-family: MathJax_Main;\">^</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; top: -3.744em; left: 0.588em;\"><span class=\"mn\" id=\"MathJax-Span-84\" style=\"font-size: 70.7%; font-family: MathJax_Main;\">1</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span><span class=\"mo\" id=\"MathJax-Span-85\" style=\"font-family: MathJax_Main;\">,</span><span class=\"mo\" id=\"MathJax-Span-86\" style=\"font-family: MathJax_Main; padding-left: 0.179em;\">…</span><span class=\"mo\" id=\"MathJax-Span-87\" style=\"font-family: MathJax_Main; padding-left: 0.179em;\">,</span><span class=\"msubsup\" id=\"MathJax-Span-88\" style=\"padding-left: 0.179em;\"><span style=\"display: inline-block; position: relative; width: 1.115em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.047em 1000.53em 4.394em -999.997em); top: -3.978em; left: 0em;\"><span class=\"texatom\" id=\"MathJax-Span-89\"><span class=\"mrow\" id=\"MathJax-Span-90\"><span class=\"munderover\" id=\"MathJax-Span-91\"><span style=\"display: inline-block; position: relative; width: 0.588em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.34em 1000.47em 4.394em -999.997em); top: -3.978em; left: 0.003em;\"><span class=\"mi\" id=\"MathJax-Span-92\" style=\"font-family: MathJax_Math-italic;\">y<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; clip: rect(3.106em 1000.41em 3.633em -999.997em); top: -4.037em; left: 0.061em;\"><span class=\"mo\" id=\"MathJax-Span-93\" style=\"font-family: MathJax_Main;\">^</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; top: -3.744em; left: 0.588em;\"><span class=\"mi\" id=\"MathJax-Span-94\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">n</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span><span class=\"mo\" id=\"MathJax-Span-95\" style=\"font-family: MathJax_Main;\">)</span><span class=\"mo\" id=\"MathJax-Span-96\" style=\"font-family: MathJax_Main; padding-left: 0.296em;\">∈</span><span class=\"mo\" id=\"MathJax-Span-97\" style=\"font-family: MathJax_Main; padding-left: 0.296em;\">{</span><span class=\"mtext\" id=\"MathJax-Span-98\" style=\"font-family: MathJax_Main;\">b</span><span class=\"mo\" id=\"MathJax-Span-99\" style=\"font-family: MathJax_Main;\">,</span><span class=\"mtext\" id=\"MathJax-Span-100\" style=\"font-family: MathJax_Main; padding-left: 0.179em;\">s</span><span class=\"msubsup\" id=\"MathJax-Span-101\"><span style=\"display: inline-block; position: relative; width: 0.998em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.047em 1000.41em 4.394em -999.997em); top: -3.978em; left: 0em;\"><span class=\"mo\" id=\"MathJax-Span-102\" style=\"font-family: MathJax_Main;\">}</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; top: -4.33em; left: 0.53em;\"><span class=\"mi\" id=\"MathJax-Span-103\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">n</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.169em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.354em; border-left: 0px solid; width: 0px; height: 1.361em;\"></span></span></nobr></span>be the vector of predicted (submitted) test labels, and let <span class=\"MathJax_Preview\" style=\"color: inherit; display: none;\"></span><span class=\"MathJax\" id=\"MathJax-Element-7-Frame\" tabindex=\"0\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo stretchy=&quot;false&quot;&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;&amp;#x2026;&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/msub&gt;&lt;mo stretchy=&quot;false&quot;&gt;)&lt;/mo&gt;&lt;mo&gt;&amp;#x2208;&lt;/mo&gt;&lt;msup&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;msup&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi mathvariant=&quot;double-struck&quot;&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/msup&gt;&lt;/math&gt;\" role=\"presentation\" style=\"position: relative;\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-104\" style=\"width: 10.424em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 8.551em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(1.115em 1008.55em 2.579em -999.997em); top: -2.163em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-105\"><span class=\"mo\" id=\"MathJax-Span-106\" style=\"font-family: MathJax_Main;\">(</span><span class=\"msubsup\" id=\"MathJax-Span-107\"><span style=\"display: inline-block; position: relative; width: 1.174em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.34em 1000.71em 4.16em -999.997em); top: -3.978em; left: 0em;\"><span class=\"mi\" id=\"MathJax-Span-108\" style=\"font-family: MathJax_Math-italic;\">w</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; top: -3.803em; left: 0.706em;\"><span class=\"mn\" id=\"MathJax-Span-109\" style=\"font-size: 70.7%; font-family: MathJax_Main;\">1</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span><span class=\"mo\" id=\"MathJax-Span-110\" style=\"font-family: MathJax_Main;\">,</span><span class=\"mo\" id=\"MathJax-Span-111\" style=\"font-family: MathJax_Main; padding-left: 0.179em;\">…</span><span class=\"mo\" id=\"MathJax-Span-112\" style=\"font-family: MathJax_Main; padding-left: 0.179em;\">,</span><span class=\"msubsup\" id=\"MathJax-Span-113\" style=\"padding-left: 0.179em;\"><span style=\"display: inline-block; position: relative; width: 1.232em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.34em 1000.71em 4.16em -999.997em); top: -3.978em; left: 0em;\"><span class=\"mi\" id=\"MathJax-Span-114\" style=\"font-family: MathJax_Math-italic;\">w</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; top: -3.803em; left: 0.706em;\"><span class=\"mi\" id=\"MathJax-Span-115\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">n</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span><span class=\"mo\" id=\"MathJax-Span-116\" style=\"font-family: MathJax_Main;\">)</span><span class=\"mo\" id=\"MathJax-Span-117\" style=\"font-family: MathJax_Main; padding-left: 0.296em;\">∈</span><span class=\"msubsup\" id=\"MathJax-Span-118\" style=\"padding-left: 0.296em;\"><span style=\"display: inline-block; position: relative; width: 1.876em; height: 0px;\"><span style=\"position: absolute; clip: rect(2.989em 1001.35em 4.16em -999.997em); top: -3.978em; left: 0em;\"><span class=\"texatom\" id=\"MathJax-Span-119\"><span class=\"mrow\" id=\"MathJax-Span-120\"><span class=\"msubsup\" id=\"MathJax-Span-121\"><span style=\"display: inline-block; position: relative; width: 1.35em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.106em 1000.71em 4.16em -999.997em); top: -3.978em; left: 0em;\"><span class=\"texatom\" id=\"MathJax-Span-122\"><span class=\"mrow\" id=\"MathJax-Span-123\"><span class=\"mi\" id=\"MathJax-Span-124\" style=\"font-family: MathJax_AMS;\">R</span></span></span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; top: -4.388em; left: 0.706em;\"><span class=\"mo\" id=\"MathJax-Span-125\" style=\"font-size: 70.7%; font-family: MathJax_Main;\">+</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; top: -4.505em; left: 1.35em;\"><span class=\"mi\" id=\"MathJax-Span-126\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">n</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.169em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.354em; border-left: 0px solid; width: 0px; height: 1.504em;\"></span></span></nobr></span>be the vector of weights. Then</p>\r\n<div class=\"MathJax_Display\" style=\"text-align: center;\"><span class=\"MathJax\" id=\"MathJax-Element-8-Frame\" tabindex=\"0\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;munderover&gt;&lt;mo&gt;&amp;#x2211;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/munderover&gt;&lt;msub&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/msub&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mn mathvariant=&quot;double-struck&quot;&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mtext&gt;s&lt;/mtext&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;}&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mn mathvariant=&quot;double-struck&quot;&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x005E;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mtext&gt;s&lt;/mtext&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;}&lt;/mo&gt;&lt;/math&gt;\" role=\"presentation\" style=\"text-align: center; position: relative;\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-127\" style=\"width: 15.577em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 12.766em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(0.413em 1012.71em 3.516em -999.997em); top: -2.163em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-128\"><span class=\"mi\" id=\"MathJax-Span-129\" style=\"font-family: MathJax_Math-italic;\">s</span><span class=\"mo\" id=\"MathJax-Span-130\" style=\"font-family: MathJax_Main; padding-left: 0.296em;\">=</span><span class=\"munderover\" id=\"MathJax-Span-131\" style=\"padding-left: 0.296em;\"><span style=\"display: inline-block; position: relative; width: 1.467em; height: 0px;\"><span style=\"position: absolute; clip: rect(2.872em 1001.41em 4.628em -999.997em); top: -3.978em; left: 0em;\"><span class=\"mo\" id=\"MathJax-Span-132\" style=\"font-family: MathJax_Size2; vertical-align: 0em;\">∑</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; clip: rect(3.34em 1001.12em 4.277em -999.997em); top: -2.866em; left: 0.179em;\"><span class=\"texatom\" id=\"MathJax-Span-133\"><span class=\"mrow\" id=\"MathJax-Span-134\"><span class=\"mi\" id=\"MathJax-Span-135\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">i</span><span class=\"mo\" id=\"MathJax-Span-136\" style=\"font-size: 70.7%; font-family: MathJax_Main;\">=</span><span class=\"mn\" id=\"MathJax-Span-137\" style=\"font-size: 70.7%; font-family: MathJax_Main;\">1</span></span></span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; clip: rect(3.399em 1000.41em 4.16em -999.997em); top: -5.149em; left: 0.53em;\"><span class=\"mi\" id=\"MathJax-Span-138\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">n</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span><span class=\"msubsup\" id=\"MathJax-Span-139\" style=\"padding-left: 0.179em;\"><span style=\"display: inline-block; position: relative; width: 1.057em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.34em 1000.71em 4.16em -999.997em); top: -3.978em; left: 0em;\"><span class=\"mi\" id=\"MathJax-Span-140\" style=\"font-family: MathJax_Math-italic;\">w</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; top: -3.803em; left: 0.706em;\"><span class=\"mi\" id=\"MathJax-Span-141\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">i</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span><span class=\"texatom\" id=\"MathJax-Span-142\"><span class=\"mrow\" id=\"MathJax-Span-143\"><span class=\"mn\" id=\"MathJax-Span-144\" style=\"font-family: MathJax_Main;\">1</span></span></span><span class=\"mo\" id=\"MathJax-Span-145\" style=\"font-family: MathJax_Main;\">{</span><span class=\"msubsup\" id=\"MathJax-Span-146\"><span style=\"display: inline-block; position: relative; width: 0.823em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.34em 1000.47em 4.394em -999.997em); top: -3.978em; left: 0em;\"><span class=\"mi\" id=\"MathJax-Span-147\" style=\"font-family: MathJax_Math-italic;\">y<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; top: -3.803em; left: 0.471em;\"><span class=\"mi\" id=\"MathJax-Span-148\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">i</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span><span class=\"mo\" id=\"MathJax-Span-149\" style=\"font-family: MathJax_Main; padding-left: 0.296em;\">=</span><span class=\"mtext\" id=\"MathJax-Span-150\" style=\"font-family: MathJax_Main; padding-left: 0.296em;\">s</span><span class=\"mo\" id=\"MathJax-Span-151\" style=\"font-family: MathJax_Main;\">}</span><span class=\"texatom\" id=\"MathJax-Span-152\"><span class=\"mrow\" id=\"MathJax-Span-153\"><span class=\"mn\" id=\"MathJax-Span-154\" style=\"font-family: MathJax_Main;\">1</span></span></span><span class=\"mo\" id=\"MathJax-Span-155\" style=\"font-family: MathJax_Main;\">{</span><span class=\"msubsup\" id=\"MathJax-Span-156\"><span style=\"display: inline-block; position: relative; width: 0.881em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.047em 1000.53em 4.394em -999.997em); top: -3.978em; left: 0em;\"><span class=\"texatom\" id=\"MathJax-Span-157\"><span class=\"mrow\" id=\"MathJax-Span-158\"><span class=\"munderover\" id=\"MathJax-Span-159\"><span style=\"display: inline-block; position: relative; width: 0.588em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.34em 1000.47em 4.394em -999.997em); top: -3.978em; left: 0.003em;\"><span class=\"mi\" id=\"MathJax-Span-160\" style=\"font-family: MathJax_Math-italic;\">y<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; clip: rect(3.106em 1000.41em 3.633em -999.997em); top: -4.037em; left: 0.061em;\"><span class=\"mo\" id=\"MathJax-Span-161\" style=\"font-family: MathJax_Main;\">^</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; top: -3.744em; left: 0.588em;\"><span class=\"mi\" id=\"MathJax-Span-162\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">i</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span><span class=\"mo\" id=\"MathJax-Span-163\" style=\"font-family: MathJax_Main; padding-left: 0.296em;\">=</span><span class=\"mtext\" id=\"MathJax-Span-164\" style=\"font-family: MathJax_Main; padding-left: 0.296em;\">s</span><span class=\"mo\" id=\"MathJax-Span-165\" style=\"font-family: MathJax_Main;\">}</span></span><span style=\"display: inline-block; width: 0px; height: 2.169em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.496em; border-left: 0px solid; width: 0px; height: 3.504em;\"></span></span></nobr><span class=\"MJX_Assistive_MathML MJX_Assistive_MathML_Block\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"></math><br /></span></span></div>\r\n<div class=\"MathJax_Display\" style=\"text-align: center;\"></div>\r\n<p>\r\n<script type=\"math/tex; mode=display\" id=\"MathJax-Element-8\">// <![CDATA[\r\ns = \\sum_{i=1}^n w_i\\mathbb{1}\\{y_i = \\text{s}\\} \\mathbb{1}\\{\\hat{y}_i = \\text{s}\\}\r\n// ]]></script>\r\n</p>\r\n<p>and</p>\r\n<div class=\"MathJax_Display\" style=\"text-align: center;\"><span class=\"MathJax\" id=\"MathJax-Element-9-Frame\" tabindex=\"0\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;munderover&gt;&lt;mo&gt;&amp;#x2211;&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;/munderover&gt;&lt;msub&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/msub&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mn mathvariant=&quot;double-struck&quot;&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mtext&gt;b&lt;/mtext&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;}&lt;/mo&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mn mathvariant=&quot;double-struck&quot;&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;{&lt;/mo&gt;&lt;msub&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mover&gt;&lt;mi&gt;y&lt;/mi&gt;&lt;mo stretchy=&quot;false&quot;&gt;&amp;#x005E;&lt;/mo&gt;&lt;/mover&gt;&lt;/mrow&gt;&lt;mi&gt;i&lt;/mi&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mtext&gt;s&lt;/mtext&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;}&lt;/mo&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/math&gt;\" role=\"presentation\" style=\"text-align: center; position: relative;\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-166\" style=\"width: 16.045em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 13.118em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(0.413em 1013.06em 3.516em -999.997em); top: -2.163em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-167\"><span class=\"mi\" id=\"MathJax-Span-168\" style=\"font-family: MathJax_Math-italic;\">b</span><span class=\"mo\" id=\"MathJax-Span-169\" style=\"font-family: MathJax_Main; padding-left: 0.296em;\">=</span><span class=\"munderover\" id=\"MathJax-Span-170\" style=\"padding-left: 0.296em;\"><span style=\"display: inline-block; position: relative; width: 1.467em; height: 0px;\"><span style=\"position: absolute; clip: rect(2.872em 1001.41em 4.628em -999.997em); top: -3.978em; left: 0em;\"><span class=\"mo\" id=\"MathJax-Span-171\" style=\"font-family: MathJax_Size2; vertical-align: 0em;\">∑</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; clip: rect(3.34em 1001.12em 4.277em -999.997em); top: -2.866em; left: 0.179em;\"><span class=\"texatom\" id=\"MathJax-Span-172\"><span class=\"mrow\" id=\"MathJax-Span-173\"><span class=\"mi\" id=\"MathJax-Span-174\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">i</span><span class=\"mo\" id=\"MathJax-Span-175\" style=\"font-size: 70.7%; font-family: MathJax_Main;\">=</span><span class=\"mn\" id=\"MathJax-Span-176\" style=\"font-size: 70.7%; font-family: MathJax_Main;\">1</span></span></span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; clip: rect(3.399em 1000.41em 4.16em -999.997em); top: -5.149em; left: 0.53em;\"><span class=\"mi\" id=\"MathJax-Span-177\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">n</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span><span class=\"msubsup\" id=\"MathJax-Span-178\" style=\"padding-left: 0.179em;\"><span style=\"display: inline-block; position: relative; width: 1.057em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.34em 1000.71em 4.16em -999.997em); top: -3.978em; left: 0em;\"><span class=\"mi\" id=\"MathJax-Span-179\" style=\"font-family: MathJax_Math-italic;\">w</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; top: -3.803em; left: 0.706em;\"><span class=\"mi\" id=\"MathJax-Span-180\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">i</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span><span class=\"texatom\" id=\"MathJax-Span-181\"><span class=\"mrow\" id=\"MathJax-Span-182\"><span class=\"mn\" id=\"MathJax-Span-183\" style=\"font-family: MathJax_Main;\">1</span></span></span><span class=\"mo\" id=\"MathJax-Span-184\" style=\"font-family: MathJax_Main;\">{</span><span class=\"msubsup\" id=\"MathJax-Span-185\"><span style=\"display: inline-block; position: relative; width: 0.823em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.34em 1000.47em 4.394em -999.997em); top: -3.978em; left: 0em;\"><span class=\"mi\" id=\"MathJax-Span-186\" style=\"font-family: MathJax_Math-italic;\">y<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; top: -3.803em; left: 0.471em;\"><span class=\"mi\" id=\"MathJax-Span-187\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">i</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span><span class=\"mo\" id=\"MathJax-Span-188\" style=\"font-family: MathJax_Main; padding-left: 0.296em;\">=</span><span class=\"mtext\" id=\"MathJax-Span-189\" style=\"font-family: MathJax_Main; padding-left: 0.296em;\">b</span><span class=\"mo\" id=\"MathJax-Span-190\" style=\"font-family: MathJax_Main;\">}</span><span class=\"texatom\" id=\"MathJax-Span-191\"><span class=\"mrow\" id=\"MathJax-Span-192\"><span class=\"mn\" id=\"MathJax-Span-193\" style=\"font-family: MathJax_Main;\">1</span></span></span><span class=\"mo\" id=\"MathJax-Span-194\" style=\"font-family: MathJax_Main;\">{</span><span class=\"msubsup\" id=\"MathJax-Span-195\"><span style=\"display: inline-block; position: relative; width: 0.881em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.047em 1000.53em 4.394em -999.997em); top: -3.978em; left: 0em;\"><span class=\"texatom\" id=\"MathJax-Span-196\"><span class=\"mrow\" id=\"MathJax-Span-197\"><span class=\"munderover\" id=\"MathJax-Span-198\"><span style=\"display: inline-block; position: relative; width: 0.588em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.34em 1000.47em 4.394em -999.997em); top: -3.978em; left: 0.003em;\"><span class=\"mi\" id=\"MathJax-Span-199\" style=\"font-family: MathJax_Math-italic;\">y<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; clip: rect(3.106em 1000.41em 3.633em -999.997em); top: -4.037em; left: 0.061em;\"><span class=\"mo\" id=\"MathJax-Span-200\" style=\"font-family: MathJax_Main;\">^</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span><span style=\"position: absolute; top: -3.744em; left: 0.588em;\"><span class=\"mi\" id=\"MathJax-Span-201\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">i</span><span style=\"display: inline-block; width: 0px; height: 3.984em;\"></span></span></span></span><span class=\"mo\" id=\"MathJax-Span-202\" style=\"font-family: MathJax_Main; padding-left: 0.296em;\">=</span><span class=\"mtext\" id=\"MathJax-Span-203\" style=\"font-family: MathJax_Main; padding-left: 0.296em;\">s</span><span class=\"mo\" id=\"MathJax-Span-204\" style=\"font-family: MathJax_Main;\">}</span><span class=\"mo\" id=\"MathJax-Span-205\" style=\"font-family: MathJax_Main;\">,</span></span><span style=\"display: inline-block; width: 0px; height: 2.169em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.496em; border-left: 0px solid; width: 0px; height: 3.504em;\"></span></span></nobr><span class=\"MJX_Assistive_MathML MJX_Assistive_MathML_Block\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"></math><br /></span></span></div>\r\n<div class=\"MathJax_Display\" style=\"text-align: center;\"></div>\r\n<p>\r\n<script type=\"math/tex; mode=display\" id=\"MathJax-Element-9\">// <![CDATA[\r\nb = \\sum_{i=1}^n w_i\\mathbb{1}\\{y_i = \\text{b}\\} \\mathbb{1}\\{\\hat{y}_i = \\text{s}\\},\r\n// ]]></script>\r\n</p>\r\n<p>where the indicator function <span class=\"MathJax_Preview\" style=\"color: inherit; display: none;\"></span><span class=\"MathJax\" id=\"MathJax-Element-10-Frame\" tabindex=\"0\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mrow class=&quot;MJX-TeXAtom-ORD&quot;&gt;&lt;mn mathvariant=&quot;double-struck&quot;&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;{&lt;/mo&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;mo fence=&quot;false&quot; stretchy=&quot;false&quot;&gt;}&lt;/mo&gt;&lt;/math&gt;\" role=\"presentation\" style=\"position: relative;\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-206\" style=\"width: 2.755em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 2.228em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(1.232em 1002.17em 2.579em -999.997em); top: -2.163em; left: 0em;\"><strong><span class=\"mrow\" id=\"MathJax-Span-207\"><span class=\"texatom\" id=\"MathJax-Span-208\"><span class=\"mrow\" id=\"MathJax-Span-209\"><span class=\"mn\" id=\"MathJax-Span-210\" style=\"font-family: MathJax_Main;\">1</span></span></span><span class=\"mo\" id=\"MathJax-Span-211\" style=\"font-family: MathJax_Main;\">{</span><span class=\"mi\" id=\"MathJax-Span-212\" style=\"font-family: MathJax_Math-italic;\">A</span><span class=\"mo\" id=\"MathJax-Span-213\" style=\"font-family: MathJax_Main;\">}</span></span></strong><span style=\"display: inline-block; width: 0px; height: 2.169em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.354em; border-left: 0px solid; width: 0px; height: 1.361em;\"></span></span></nobr></span> 1 if its argument <span class=\"MathJax_Preview\" style=\"color: inherit; display: none;\"></span><span class=\"MathJax\" id=\"MathJax-Element-11-Frame\" tabindex=\"0\" data-mathml=\"&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/math&gt;\" role=\"presentation\" style=\"position: relative;\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-214\" style=\"width: 0.94em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 0.764em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(1.174em 1000.76em 2.228em -999.997em); top: -2.046em; left: 0em;\"><strong><span class=\"mrow\" id=\"MathJax-Span-215\"><span class=\"mi\" id=\"MathJax-Span-216\" style=\"font-family: MathJax_Math-italic;\">A</span></span></strong><span style=\"display: inline-block; width: 0px; height: 2.052em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.068em; border-left: 0px solid; width: 0px; height: 1.004em;\"></span></span></nobr><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>  </mi></math></span></span>\r\n<script type=\"math/tex\" id=\"MathJax-Element-11\">// <![CDATA[\r\nA\r\n// ]]></script>\r\nis true and 0 otherwise.</p>\r\n<p>For more information on the statistical model and the derivation of the metric, see the <a href=\"http://higgsml.lal.in2p3.fr/documentation/\">technical documentation</a>. We have provided python code for the metric is available from the <a href=\"https://www.kaggle.com/c/higgs-boson/data\">Data</a> page and a Python <a href=\"https://higgsml.lal.in2p3.fr/software/starting-kit/\">starting kit</a>.</p>\r\n<p>Submission Instructions</p>\r\n<p>The submission file format is</p>\r\n<pre>EventId,Class<br />1,b<br />2,s<br />3,b<br />4,b<br />5,s</pre>\r\n<ul>\r\n<li><strong>EventId</strong> is a unique identifier for each event. The list of EventIds must correspond to the exact list of EventIds in test.csv, but the ordering can be arbitrary.</li>\r\n<li><strong>Class</strong> is either \"b\" or \"s\", and it indicates if your prediction (y^iy^i above in the formal definition) for the event is background or signal. <strong>The AMS will be calculated based on the (hidden) weights of events that you mark \"s\".</strong></li>\r\n</ul>",
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    {
      "name": "rules",
      "content": "<!-- Begin Base Rules -->\r\n<h3>One account per participant</h3>\r\n<p>You cannot sign up to Kaggle from multiple accounts and therefore you cannot submit from multiple accounts.</p>\r\n<h3>No private sharing outside teams</h3>\r\n<p>Privately sharing code or data outside of teams is not permitted. It's okay to share code if made available to all participants on the forums.</p>\r\n<h3>Team Mergers</h3>\r\n<p>Team mergers are not allowed in this competition.</p>\r\n<h3>Team Limits</h3>\r\n<p>There is no maximum team size.</p>\r\n<h3>Submission Limits</h3>\r\n<p>You may submit a maximum of 2 entries per day.</p>\r\n<p>You may select up to 2 final submissions for judging.</p>\r\n<h3>Competition Timeline</h3>\r\n<p>Start Date: <strong>TBA</strong></p>\r\n<p>Merger Deadline: <strong>None</strong></p>\r\n<p>Entry Deadline: <strong>None</strong></p>\r\n<p>End Date: <strong>2/1/2014 12:00 AM UTC</strong></p>\r\n<!-- End Base Rules -->\r\n<p>The rules page is a bit special: it will auto-update the text based on the parameters of the competition. The rules you need to add here are any additional rules relating to dataset usage. You may also put grading information here.</p>",
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}