[1803.08823] A high-bias, low-variance introduction to Machine Learning for physicists

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The purpose of this review is to provide an introduction to the core concepts and tools of machine learning in a manner easily understood and intuitive to physicists. The review begins by covering fundamental concepts in ML and modern statistics such as the bias-variance tradeoff, overfitting, regularization, generalization, and gradient descent before moving on to more advanced topics in both supervised and unsupervised learning. Topics covered in the review include ensemble models, deep learning and neural networks, clustering and data visualization, energy-based models (including MaxEnt models and Restricted Boltzmann Machines), and variational methods. Throughout, we emphasize the many natural connections between ML and statistical physics. A notable aspect of the review is the use of Python Jupyter notebooks to introduce modern ML/statistical packages to readers using physics-inspired datasets (the Ising Model and Monte-Carlo simulations of supersymmetric decays of proton-proton collisions). We conclude with an extended outlook discussing possible uses of machine learning for furthering our understanding of the physical world as well as open problems in ML where physicists may be able to contribute. (Notebooks are available at https://physics.bu.edu/~pankajm/MLnotebooks.html )"/> <meta name="twitter:site" content="@arxiv"/> <meta name="twitter:card" content="summary"/> <meta name="twitter:title" content="A high-bias, low-variance introduction to Machine Learning for physicists"/> <meta name="twitter:description" content="Machine Learning (ML) is one of the most exciting and dynamic areas of modern research and application. The purpose of this review is to provide an introduction to the core concepts and tools of..."/> <meta name="twitter:image" content="https://static.arxiv.org/icons/twitter/arxiv-logo-twitter-square.png"/> <meta name="twitter:image:alt" content="arXiv logo"/> <link rel="stylesheet" media="screen" type="text/css" href="/static/browse/0.3.4/css/tooltip.css"/><link rel="stylesheet" media="screen" type="text/css" href="https://static.arxiv.org/js/bibex-dev/bibex.css?20200709"/> <script src="/static/browse/0.3.4/js/mathjaxToggle.min.js" type="text/javascript"></script> <script src="//code.jquery.com/jquery-latest.min.js" type="text/javascript"></script> <script src="//cdn.jsdelivr.net/npm/js-cookie@2/src/js.cookie.min.js" type="text/javascript"></script> <script src="//cdn.jsdelivr.net/npm/dompurify@2.3.5/dist/purify.min.js"></script> <script src="/static/browse/0.3.4/js/toggle-labs.js?20241022" type="text/javascript"></script> <script src="/static/browse/0.3.4/js/cite.js" type="text/javascript"></script><meta name="citation_title" content="A high-bias, low-variance introduction to Machine Learning for physicists" /><meta name="citation_author" content="Mehta, Pankaj" /><meta name="citation_author" content="Bukov, Marin" /><meta name="citation_author" content="Wang, Ching-Hao" /><meta name="citation_author" content="Day, Alexandre G. R." /><meta name="citation_author" content="Richardson, Clint" /><meta name="citation_author" content="Fisher, Charles K." /><meta name="citation_author" content="Schwab, David J." /><meta name="citation_doi" content="10.1016/j.physrep.2019.03.001" /><meta name="citation_date" content="2018/03/23" /><meta name="citation_online_date" content="2019/05/27" /><meta name="citation_pdf_url" content="http://arxiv.org/pdf/1803.08823" /><meta name="citation_arxiv_id" content="1803.08823" /><meta name="citation_abstract" content="Machine Learning (ML) is one of the most exciting and dynamic areas of modern research and application. The purpose of this review is to provide an introduction to the core concepts and tools of machine learning in a manner easily understood and intuitive to physicists. The review begins by covering fundamental concepts in ML and modern statistics such as the bias-variance tradeoff, overfitting, regularization, generalization, and gradient descent before moving on to more advanced topics in both supervised and unsupervised learning. Topics covered in the review include ensemble models, deep learning and neural networks, clustering and data visualization, energy-based models (including MaxEnt models and Restricted Boltzmann Machines), and variational methods. Throughout, we emphasize the many natural connections between ML and statistical physics. A notable aspect of the review is the use of Python Jupyter notebooks to introduce modern ML/statistical packages to readers using physics-inspired datasets (the Ising Model and Monte-Carlo simulations of supersymmetric decays of proton-proton collisions). We conclude with an extended outlook discussing possible uses of machine learning for furthering our understanding of the physical world as well as open problems in ML where physicists may be able to contribute. (Notebooks are available at https://physics.bu.edu/~pankajm/MLnotebooks.html )" /> </head> <body class="with-cu-identity"> <div class="flex-wrap-footer"> <header> <a href="#content" class="is-sr-only">Skip to main content</a>  <div class="columns is-vcentered is-hidden-mobile" id="cu-identity"> <div class="column" id="cu-logo"> <a href="https://www.cornell.edu/"><img src="/static/browse/0.3.4/images/icons/cu/cornell-reduced-white-SMALL.svg" alt="Cornell University" /></a> </div><div class="column" id="support-ack"> <span id="support-ack-url">We gratefully acknowledge support from the Simons Foundation, <a href="https://info.arxiv.org/about/ourmembers.html">member institutions</a>, and all contributors.</span> <a href="https://info.arxiv.org/about/donate.html" class="btn-header-donate">Donate</a> </div> </div> <div id="header" class="is-hidden-mobile"> <a aria-hidden="true" href="{url_path('ignore_me')}"></a> <div class="header-breadcrumbs is-hidden-mobile"> <a href="/"><img 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href="https://arxiv.org/search/physics?searchtype=author&query=Mehta,+P" rel="nofollow">Pankaj Mehta</a>, <a href="https://arxiv.org/search/physics?searchtype=author&query=Bukov,+M" rel="nofollow">Marin Bukov</a>, <a href="https://arxiv.org/search/physics?searchtype=author&query=Wang,+C" rel="nofollow">Ching-Hao Wang</a>, <a href="https://arxiv.org/search/physics?searchtype=author&query=Day,+A+G" rel="nofollow">Alexandre G.R. Day</a>, <a href="https://arxiv.org/search/physics?searchtype=author&query=Richardson,+C" rel="nofollow">Clint Richardson</a>, <a href="https://arxiv.org/search/physics?searchtype=author&query=Fisher,+C+K" rel="nofollow">Charles K. Fisher</a>, <a href="https://arxiv.org/search/physics?searchtype=author&query=Schwab,+D+J" rel="nofollow">David J. Schwab</a></div> <div id="download-button-info" hidden>View a PDF of the paper titled A high-bias, low-variance introduction to Machine Learning for physicists, by Pankaj Mehta and 6 other authors</div> <a class="mobile-submission-download" href="/pdf/1803.08823">View PDF</a> <blockquote class="abstract mathjax"> <span class="descriptor">Abstract:</span>Machine Learning (ML) is one of the most exciting and dynamic areas of modern research and application. The purpose of this review is to provide an introduction to the core concepts and tools of machine learning in a manner easily understood and intuitive to physicists. The review begins by covering fundamental concepts in ML and modern statistics such as the bias-variance tradeoff, overfitting, regularization, generalization, and gradient descent before moving on to more advanced topics in both supervised and unsupervised learning. Topics covered in the review include ensemble models, deep learning and neural networks, clustering and data visualization, energy-based models (including MaxEnt models and Restricted Boltzmann Machines), and variational methods. Throughout, we emphasize the many natural connections between ML and statistical physics. A notable aspect of the review is the use of Python Jupyter notebooks to introduce modern ML/statistical packages to readers using physics-inspired datasets (the Ising Model and Monte-Carlo simulations of supersymmetric decays of proton-proton collisions). We conclude with an extended outlook discussing possible uses of machine learning for furthering our understanding of the physical world as well as open problems in ML where physicists may be able to contribute. (Notebooks are available at <a href="https://physics.bu.edu/~pankajm/MLnotebooks.html" rel="external noopener nofollow" class="link-external link-https">this https URL</a> ) </blockquote>  <div class="metatable"> <table summary="Additional metadata"> <tr> <td class="tablecell label">Comments:</td> <td class="tablecell comments mathjax">Notebooks have been updated. 122 pages, 78 figures, 20 Python notebooks</td> </tr> <tr> <td class="tablecell label">Subjects:</td> <td class="tablecell subjects"> <span class="primary-subject">Computational Physics (physics.comp-ph)</span>; Statistical Mechanics (cond-mat.stat-mech); Machine Learning (cs.LG); Machine Learning (stat.ML)</td> </tr><tr> <td class="tablecell label">Cite as:</td> <td class="tablecell arxivid"><span class="arxivid"><a href="https://arxiv.org/abs/1803.08823">arXiv:1803.08823</a> [physics.comp-ph]</span></td> </tr> <tr> <td class="tablecell label"> </td> <td class="tablecell arxividv">(or <span class="arxivid"> <a href="https://arxiv.org/abs/1803.08823v3">arXiv:1803.08823v3</a> [physics.comp-ph]</span> for this version) </td> </tr> <tr> <td class="tablecell label"> </td> <td class="tablecell arxivdoi"> <a href="https://doi.org/10.48550/arXiv.1803.08823" id="arxiv-doi-link">https://doi.org/10.48550/arXiv.1803.08823</a><div class="button-and-tooltip"> <button class="more-info" aria-describedby="more-info-desc-1"> <svg height="15" role="presentation" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M256 8C119.043 8 8 119.083 8 256c0 136.997 111.043 248 248 248s248-111.003 248-248C504 119.083 392.957 8 256 8zm0 110c23.196 0 42 18.804 42 42s-18.804 42-42 42-42-18.804-42-42 18.804-42 42-42zm56 254c0 6.627-5.373 12-12 12h-88c-6.627 0-12-5.373-12-12v-24c0-6.627 5.373-12 12-12h12v-64h-12c-6.627 0-12-5.373-12-12v-24c0-6.627 5.373-12 12-12h64c6.627 0 12 5.373 12 12v100h12c6.627 0 12 5.373 12 12v24z" class=""></path></svg> <span class="visually-hidden">Focus to learn more</span> </button>  <div role="tooltip" id="more-info-desc-1"> <span class="left-corner"></span> arXiv-issued DOI via DataCite</div> </div> </td> </tr> <tr> <td class="tablecell label">Journal reference:</td> <td class="tablecell jref">Phyics Reports 810 (2019) 1-124</td> </tr> <tr> <td class="tablecell label"> <abbr title="Digital Object Identifier">Related DOI</abbr>: </td> <td class="tablecell doi"><a href="https://doi.org/10.1016/j.physrep.2019.03.001" data-doi="10.1016/j.physrep.2019.03.001" class="link-https link-external" rel="external noopener nofollow">https://doi.org/10.1016/j.physrep.2019.03.001</a>  <div class="button-and-tooltip"> <button class="more-info" aria-describedby="more-info-desc-1"> <svg height="15" role="presentation" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M256 8C119.043 8 8 119.083 8 256c0 136.997 111.043 248 248 248s248-111.003 248-248C504 119.083 392.957 8 256 8zm0 110c23.196 0 42 18.804 42 42s-18.804 42-42 42-42-18.804-42-42 18.804-42 42-42zm56 254c0 6.627-5.373 12-12 12h-88c-6.627 0-12-5.373-12-12v-24c0-6.627 5.373-12 12-12h12v-64h-12c-6.627 0-12-5.373-12-12v-24c0-6.627 5.373-12 12-12h64c6.627 0 12 5.373 12 12v100h12c6.627 0 12 5.373 12 12v24z" class=""></path></svg> <span class="visually-hidden">Focus to learn more</span> </button>  <div role="tooltip" id="more-info-desc-1"> <span class="left-corner"></span> DOI(s) linking to related resources </div> </div> </td> </tr> </table> </div> </div> </div> <div class="submission-history"> <h2>Submission history</h2> From: Marin Bukov Dr. [<a href="/show-email/296257bb/1803.08823" rel="nofollow">view email</a>] <br/> <strong><a href="/abs/1803.08823v1" rel="nofollow">[v1]</a></strong> Fri, 23 Mar 2018 14:53:05 UTC (12,683 KB)<br/> <strong><a href="/abs/1803.08823v2" rel="nofollow">[v2]</a></strong> Fri, 1 Feb 2019 23:39:08 UTC (14,190 KB)<br/> <strong>[v3]</strong> Mon, 27 May 2019 16:51:57 UTC (14,189 KB)<br/> </div> </div>  <div 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[1803.08823] A high-bias, low-variance introduction to Machine Learning for physicists