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README.html
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<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
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border-bottom-color: #bbb;
border-radius: 3px;
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}
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margin: 0 0.35em 0.25em -1.6em;
vertical-align: middle;
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:checked+.radio-label {
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position: relative;
border-color: #4078c0;
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code .kw { color: #000000; }
code .dt { color: #ed6a43; }
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code .co { color: #969896; }
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code .fu { color: #63a35c; }
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code .an { color: #008080; }
code .cv { color: #008080; }
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<style>
body {
box-sizing: border-box;
min-width: 200px;
max-width: 980px;
margin: 0 auto;
padding: 45px;
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<h1 id="testotm">testOTM</h1>
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<p><code>testOTM</code> is an R package that computes multivariate ranks and quantiles defined through the theory of optimal transportation. It also provides several applications of these statistics, most notably a method for two-sample multivariate goodness-of-fit testing.</p>
<h2 id="installation">Installation</h2>
<p>You can install the released version of <code>testOTM</code> from <a href="https://CRAN.R-project.org">CRAN</a> with:</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb1-1" title="1"><span class="kw">install.packages</span>(<span class="st">"testOTM"</span>)</a></code></pre></div>
<p>You can install the development version from <a href="https://github.com/">GitHub</a> with:</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb2-1" title="1"><span class="co"># install.packages("devtools")</span></a>
<a class="sourceLine" id="cb2-2" title="2"><span class="co"># devtools::install_github("Francis-Hsu/testOTM")</span></a></code></pre></div>
<h2 id="example">Example</h2>
<p>This is a basic example which shows you how to use <code>testOTM</code> to visualize the optimal transport map from (U[0, 1]^2) to a (scaled) bivariate Gaussian sample:</p>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb3-1" title="1"><span class="kw">library</span>(testOTM)</a>
<a class="sourceLine" id="cb3-2" title="2"></a>
<a class="sourceLine" id="cb3-3" title="3"><span class="co"># generate bivariate normal data</span></a>
<a class="sourceLine" id="cb3-4" title="4">p =<span class="st"> </span><span class="dv">2</span></a>
<a class="sourceLine" id="cb3-5" title="5">n =<span class="st"> </span><span class="dv">100</span></a>
<a class="sourceLine" id="cb3-6" title="6">Sigma =<span class="st"> </span><span class="kw">matrix</span>(<span class="kw">c</span>(<span class="dv">2</span>, <span class="dv">1</span>, <span class="dv">1</span>, <span class="dv">2</span>), <span class="dv">2</span>, <span class="dv">2</span>)</a>
<a class="sourceLine" id="cb3-7" title="7">eS =<span class="st"> </span><span class="kw">eigen</span>(Sigma, <span class="dt">symmetric =</span> <span class="ot">TRUE</span>)</a>
<a class="sourceLine" id="cb3-8" title="8">X =<span class="st"> </span><span class="kw">t</span>(eS<span class="op">$</span>vectors <span class="op">%*%</span><span class="st"> </span><span class="kw">diag</span>(<span class="kw">sqrt</span>(<span class="kw">pmax</span>(eS<span class="op">$</span>values, <span class="dv">0</span>)), p) <span class="op">%*%</span><span class="st"> </span><span class="kw">matrix</span>(<span class="kw">rnorm</span>(p <span class="op">*</span><span class="st"> </span>n), p))</a>
<a class="sourceLine" id="cb3-9" title="9"></a>
<a class="sourceLine" id="cb3-10" title="10"><span class="co"># compute the optimal transport map from U[0, 1]^2 to the data</span></a>
<a class="sourceLine" id="cb3-11" title="11"><span class="co"># notice that the data will be scale into [0, 1] range</span></a>
<a class="sourceLine" id="cb3-12" title="12">X.OTM =<span class="st"> </span><span class="kw">tos.fit</span>(X)</a>
<a class="sourceLine" id="cb3-13" title="13"></a>
<a class="sourceLine" id="cb3-14" title="14"><span class="co"># plot the restricted Voronoi diagram and the restricted Delaunay triangulation</span></a>
<a class="sourceLine" id="cb3-15" title="15">oldpar =<span class="st"> </span><span class="kw">par</span>(<span class="dt">mfrow =</span> <span class="kw">c</span>(<span class="dv">1</span>, <span class="dv">2</span>))</a>
<a class="sourceLine" id="cb3-16" title="16"><span class="kw">plot</span>(X.OTM, <span class="dt">which =</span> <span class="st">"Both"</span>, <span class="dt">draw.center =</span> F, <span class="dt">draw.map =</span> T)</a></code></pre></div>
<p><img 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" /><!-- --></p>
<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb4-1" title="1"><span class="kw">par</span>(oldpar)</a></code></pre></div>
<h2 id="acknowledgment">Acknowledgment</h2>
<p>The author is extremely grateful to Prof. <a href="http://www.stat.columbia.edu/~bodhi/Bodhi/Welcome.html">Bodhisattva Sen</a> and his student Promit Ghosal for their guidance in the development of this package. The author would also like to thank Dr. <a href="https://members.loria.fr/BLevy/">Bruno Lévy</a> for his assistance with the <a href="http://alice.loria.fr/index.php/software/4-library/75-geogram.html">Geogram</a> library, and the <a href="http://www.trame-project.com/">TraME</a> team, whose <a href="https://github.com/TraME-Project/Rgeogram"><code>Rgeogram</code></a> package provides inspirations to the early build of this package.</p>
<h2 id="reference">Reference</h2>
<div id="refs" class="references">
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<div id="ref-B1991">
<p>Brenier, Yann. 1991. “Polar Factorization and Monotone Rearrangement of Vector-Valued Functions.” <em>Communications on Pure and Applied Mathematics</em> 44 (4): 375–417. <a href="https://doi.org/10.1002/cpa.3160440402">https://doi.org/10.1002/cpa.3160440402</a>.</p>
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<p>Cheng, Siu-Wing, Tamal Krishna Dey, and Jonathan Richard Shewchuk. 2013. <em>Delaunay Mesh Generation</em>. Chapman; Hall/CRC.</p>
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<p>Chernozhukov, Victor, Alfred Galichon, Marc Hallin, and Marc Henry. 2017. “Monge–Kantorovich Depth, Quantiles, Ranks and Signs.” <em>The Annals of Statistics</em> 45 (1): 223–56. <a href="https://doi.org/10.1214/16-AOS1450">https://doi.org/10.1214/16-AOS1450</a>.</p>
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<div id="ref-GS2019">
<p>Ghosal, Promit, and Bodhisattva Sen. 2019. “Multivariate Ranks and Quantiles Using Optimal Transportation and Applications to Goodness-of-Fit Testing.” <a href="http://arxiv.org/abs/1905.05340">http://arxiv.org/abs/1905.05340</a>.</p>
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<div id="ref-GLSY2015">
<p>Gu, Xianfeng, Feng Luo, Jian Sun, and Shing-Tung Yau. 2015. “Variational Principles for Minkowski Type Problems, Discrete Optimal Transport, and Discrete Monge-Ampere Equations.” <em>Asian Journal of Mathematics</em> 20 (January). <a href="https://doi.org/10.4310/AJM.2016.v20.n2.a7">https://doi.org/10.4310/AJM.2016.v20.n2.a7</a>.</p>
</div>
<div id="ref-WEB:GEOGRAM">
<p>Inria, project ALICE-GRAPHYS. 2019. “Geogram: A Programming Library of Geometric Algorithms.” <a href="http://alice.loria.fr/software/geogram/doc/html/index.html">http://alice.loria.fr/software/geogram/doc/html/index.html</a>.</p>
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<div id="ref-L2015">
<p>Lévy, Bruno. 2015. “A Numerical Algorithm for L2 Semi-Discrete Optimal Transport in 3D.” <em>ESAIM: M2AN</em> 49 (6): 1693–1715. <a href="https://doi.org/10.1051/m2an/2015055">https://doi.org/10.1051/m2an/2015055</a>.</p>
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<p>Lévy, Bruno. 2015. “Robustness and Efficiency of Geometric Programs The Predicate Construction Kit (PCK).” <em>Computer-Aided Design</em>. <a href="https://hal.inria.fr/hal-01225202">https://hal.inria.fr/hal-01225202</a>.</p>
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<p>Lévy, Bruno, and Erica L. Schwindt. 2018. “Notions of Optimal Transport Theory and How to Implement Them on a Computer.” <em>Computers & Graphics</em> 72: 135–48. <a href="https://doi.org/10.1016/j.cag.2018.01.009">https://doi.org/10.1016/j.cag.2018.01.009</a>.</p>
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<p>Liu, Yang, Wenping Wang, Bruno Lévy, Feng Sun, Dong-Ming Yan, Lin Lu, and Chenglei Yang. 2009. “On Centroidal Voronoi Tessellation–Energy Smoothness and Fast Computation.” <em>ACM Transactions on Graphics</em> 28 (4): Article 101. <a href="https://doi.org/10.1145/1559755.1559758">https://doi.org/10.1145/1559755.1559758</a>.</p>
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<p>McCann, Robert J. 1995. “Existence and Uniqueness of Monotone Measure-Preserving Maps.” <em>Duke Math. J.</em> 80 (2): 309–23. <a href="https://doi.org/10.1215/S0012-7094-95-08013-2">https://doi.org/10.1215/S0012-7094-95-08013-2</a>.</p>
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<p>Toth, Csaba D., Joseph O’Rourke, and Jacob E. Goodman, eds. 2017. <em>Handbook of Discrete and Computational Geometry</em>. 3rd ed. Chapman; Hall/CRC.</p>
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<div id="ref-Xin2016">
<p>Xin, Shi-Qing, Bruno Lévy, Zhonggui Chen, Lei Chu, Yaohui Yu, Changhe Tu, and Wenping Wang. 2016. “Centroidal Power Diagrams with Capacity Constraints: Computation, Applications, and Extension.” <em>ACM Trans. Graph.</em> 35 (6): 244:1–244:12. <a href="https://doi.org/10.1145/2980179.2982428">https://doi.org/10.1145/2980179.2982428</a>.</p>
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