<!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" />
<meta name="generator" content="pandoc" />
<meta name="author" content="Lei Sun" />
<meta name="date" content="2017-05-02" />
<title>Implementation by Rmosek: Correlated Null</title>
<script src="site_libs/jquery-1.11.3/jquery.min.js"></script>
<meta name="viewport" content="width=device-width, initial-scale=1" />
<link href="site_libs/bootstrap-3.3.5/css/cosmo.min.css" rel="stylesheet" />
<script src="site_libs/bootstrap-3.3.5/js/bootstrap.min.js"></script>
<script src="site_libs/bootstrap-3.3.5/shim/html5shiv.min.js"></script>
<script src="site_libs/bootstrap-3.3.5/shim/respond.min.js"></script>
<script src="site_libs/jqueryui-1.11.4/jquery-ui.min.js"></script>
<link href="site_libs/tocify-1.9.1/jquery.tocify.css" rel="stylesheet" />
<script src="site_libs/tocify-1.9.1/jquery.tocify.js"></script>
<script src="site_libs/navigation-1.1/tabsets.js"></script>
<link href="site_libs/highlightjs-1.1/textmate.css" rel="stylesheet" />
<script src="site_libs/highlightjs-1.1/highlight.js"></script>
<link href="site_libs/font-awesome-4.5.0/css/font-awesome.min.css" rel="stylesheet" />
<style type="text/css">code{white-space: pre;}</style>
<style type="text/css">
pre:not([class]) {
background-color: white;
}
</style>
<script type="text/javascript">
if (window.hljs && document.readyState && document.readyState === "complete") {
window.setTimeout(function() {
hljs.initHighlighting();
}, 0);
}
</script>
<style type="text/css">
h1 {
font-size: 34px;
}
h1.title {
font-size: 38px;
}
h2 {
font-size: 30px;
}
h3 {
font-size: 24px;
}
h4 {
font-size: 18px;
}
h5 {
font-size: 16px;
}
h6 {
font-size: 12px;
}
.table th:not([align]) {
text-align: left;
}
</style>
</head>
<body>
<style type = "text/css">
.main-container {
max-width: 940px;
margin-left: auto;
margin-right: auto;
}
code {
color: inherit;
background-color: rgba(0, 0, 0, 0.04);
}
img {
max-width:100%;
height: auto;
}
.tabbed-pane {
padding-top: 12px;
}
button.code-folding-btn:focus {
outline: none;
}
</style>
<style type="text/css">
/* padding for bootstrap navbar */
body {
padding-top: 51px;
padding-bottom: 40px;
}
/* offset scroll position for anchor links (for fixed navbar) */
.section h1 {
padding-top: 56px;
margin-top: -56px;
}
.section h2 {
padding-top: 56px;
margin-top: -56px;
}
.section h3 {
padding-top: 56px;
margin-top: -56px;
}
.section h4 {
padding-top: 56px;
margin-top: -56px;
}
.section h5 {
padding-top: 56px;
margin-top: -56px;
}
.section h6 {
padding-top: 56px;
margin-top: -56px;
}
</style>
<script>
// manage active state of menu based on current page
$(document).ready(function () {
// active menu anchor
href = window.location.pathname
href = href.substr(href.lastIndexOf('/') + 1)
if (href === "")
href = "index.html";
var menuAnchor = $('a[href="' + href + '"]');
// mark it active
menuAnchor.parent().addClass('active');
// if it's got a parent navbar menu mark it active as well
menuAnchor.closest('li.dropdown').addClass('active');
});
</script>
<div class="container-fluid main-container">
<!-- tabsets -->
<script>
$(document).ready(function () {
window.buildTabsets("TOC");
});
</script>
<!-- code folding -->
<script>
$(document).ready(function () {
// move toc-ignore selectors from section div to header
$('div.section.toc-ignore')
.removeClass('toc-ignore')
.children('h1,h2,h3,h4,h5').addClass('toc-ignore');
// establish options
var options = {
selectors: "h1,h2,h3",
theme: "bootstrap3",
context: '.toc-content',
hashGenerator: function (text) {
return text.replace(/[.\\/?&!#<>]/g, '').replace(/\s/g, '_').toLowerCase();
},
ignoreSelector: ".toc-ignore",
scrollTo: 0
};
options.showAndHide = true;
options.smoothScroll = true;
// tocify
var toc = $("#TOC").tocify(options).data("toc-tocify");
});
</script>
<style type="text/css">
#TOC {
margin: 25px 0px 20px 0px;
}
@media (max-width: 768px) {
#TOC {
position: relative;
width: 100%;
}
}
.toc-content {
padding-left: 30px;
padding-right: 40px;
}
div.main-container {
max-width: 1200px;
}
div.tocify {
width: 20%;
max-width: 260px;
max-height: 85%;
}
@media (min-width: 768px) and (max-width: 991px) {
div.tocify {
width: 25%;
}
}
@media (max-width: 767px) {
div.tocify {
width: 100%;
max-width: none;
}
}
.tocify ul, .tocify li {
line-height: 20px;
}
.tocify-subheader .tocify-item {
font-size: 0.90em;
padding-left: 25px;
text-indent: 0;
}
.tocify .list-group-item {
border-radius: 0px;
}
</style>
<!-- setup 3col/9col grid for toc_float and main content -->
<div class="row-fluid">
<div class="col-xs-12 col-sm-4 col-md-3">
<div id="TOC" class="tocify">
</div>
</div>
<div class="toc-content col-xs-12 col-sm-8 col-md-9">
<div class="navbar navbar-default navbar-fixed-top" role="navigation">
<div class="container">
<div class="navbar-header">
<button type="button" class="navbar-toggle collapsed" data-toggle="collapse" data-target="#navbar">
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</button>
<a class="navbar-brand" href="index.html">truncash</a>
</div>
<div id="navbar" class="navbar-collapse collapse">
<ul class="nav navbar-nav">
<li>
<a href="index.html">Home</a>
</li>
<li>
<a href="about.html">About</a>
</li>
<li>
<a href="license.html">License</a>
</li>
</ul>
<ul class="nav navbar-nav navbar-right">
<li>
<a href="https://github.com/LSun/truncash">
<span class="fa fa-github"></span>
</a>
</li>
</ul>
</div><!--/.nav-collapse -->
</div><!--/.container -->
</div><!--/.navbar -->
<div class="fluid-row" id="header">
<h1 class="title toc-ignore">Implementation by <code>Rmosek</code>: Correlated Null</h1>
<h4 class="author"><em>Lei Sun</em></h4>
<h4 class="date"><em>2017-05-02</em></h4>
</div>
<!-- The file analysis/chunks.R contains chunks that define default settings
shared across the workflowr files. -->
<!-- Update knitr chunk options -->
<!-- Insert the date the file was last updated -->
<p><strong>Last updated:</strong> 2017-11-07</p>
<!-- Insert the code version (Git commit SHA1) if Git repository exists and R
package git2r is installed -->
<p><strong>Code version:</strong> 2c05d59</p>
<!-- Add your analysis here -->
<div id="introduction" class="section level2">
<h2>Introduction</h2>
<p>Being in the development stage, <code>cvxr</code> is not very efficient at <a href="gaussian_derivatives.html">the convex optimization</a> in fitting Gaussian derivatives. We are moving to <code>Rmosek</code>.</p>
<pre class="r"><code>source("../code/gdash.R")</code></pre>
<pre><code>Warning: replacing previous import 'Matrix::crossprod' by 'gmp::crossprod'
when loading 'cvxr'</code></pre>
<pre><code>Warning: replacing previous import 'Matrix::tcrossprod' by
'gmp::tcrossprod' when loading 'cvxr'</code></pre>
<pre class="r"><code>z.mat = read.table("../output/z_null_liver_777.txt")
fd.bh = scan("../output/fd.bh.0.05_null_liver_777.txt")
pihat0 = scan("../output/pihat0_z_null_liver_777.txt")</code></pre>
</div>
<div id="bad" class="section level2">
<h2>Bad</h2>
<p>These data sets are unfriendly for both <code>BH</code> and <code>ASH</code>.</p>
<pre><code>Data Set 355 :
Number of BH false discoveries: 639 ;
ASH's pihat0 = 0.04750946 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.0225585778660563 ; 2 : 1.30307541409737 ; 3 : 0.0529119988564207 ; 4 : 0.86434625413445 ; 5 : 0 ; 6 : 0.115991285668782 ; 7 : 0 ; 8 : 0 ; 9 : 0 ; 10 : 0.012768069558034 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for bad-1.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for bad-2.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 23 :
Number of BH false discoveries: 408 ;
ASH's pihat0 = 0.03139009 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.016039132567407 ; 2 : 1.34993003351774 ; 3 : 0.081263929095916 ; 4 : 0.714486051374311 ; 5 : 0.139320458700019 ; 6 : 0 ; 7 : 0.100823265137825 ; 8 : 0 ; 9 : 0.0608462191710317 ; 10 : 0.000964802431909129 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for bad-3.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for bad-4.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 122 :
Number of BH false discoveries: 331 ;
ASH's pihat0 = 0.04301549 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.00711459304239053 ; 2 : 1.1037821799492 ; 3 : 0 ; 4 : 0.528402132228434 ; 5 : 0 ; 6 : 0 ; 7 : 0 ; 8 : 0 ; 9 : 0.000977244957534518 ; 10 : 0 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for bad-5.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for bad-6.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 749 :
Number of BH false discoveries: 114 ;
ASH's pihat0 = 0.02583276 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.0458626422285871 ; 2 : 1.0692347200711 ; 3 : 0.00127673630293041 ; 4 : 0.437875595583542 ; 5 : 0 ; 6 : 0 ; 7 : 0.110561067339144 ; 8 : 0 ; 9 : 0.104817311821469 ; 10 : 0 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for bad-7.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for bad-8.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 724 :
Number of BH false discoveries: 79 ;
ASH's pihat0 = 0.01606004 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.0352454327180146 ; 2 : 1.085621208483 ; 3 : 0.072031313135509 ; 4 : 0.313477034131008 ; 5 : 0 ; 6 : 0 ; 7 : 0 ; 8 : 0 ; 9 : 0 ; 10 : 0 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for bad-9.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for bad-10.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 56 :
Number of BH false discoveries: 35 ;
ASH's pihat0 = 0.04829662 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.015603437988185 ; 2 : 0.863695602978145 ; 3 : 0.135238823162622 ; 4 : 0.336622180491709 ; 5 : 0.18630322261983 ; 6 : 0.00268136598387189 ; 7 : 0.0339747362866559 ; 8 : 0.0181307043838827 ; 9 : 0 ; 10 : 0.0344310653486728 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for bad-11.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for bad-12.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 840 :
Number of BH false discoveries: 28 ;
ASH's pihat0 = 0.02316832 ;
Normalized coefficients of Gaussian derivatives:
1 : 0 ; 2 : 1.03471486197017 ; 3 : 0 ; 4 : 0.329235042804543 ; 5 : 0 ; 6 : 0 ; 7 : 0 ; 8 : 0 ; 9 : 0.00321461375022215 ; 10 : 0.0593306511691146 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for bad-13.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for bad-14.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 858 :
Number of BH false discoveries: 16 ;
ASH's pihat0 = 0.05110069 ;
Normalized coefficients of Gaussian derivatives:
1 : 0 ; 2 : 1.00711281742885 ; 3 : 0 ; 4 : 0.390477482047559 ; 5 : 0 ; 6 : 0 ; 7 : 0.0551377637495718 ; 8 : 0 ; 9 : 0.0479292544081263 ; 10 : 0.0837572023674743 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for bad-15.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for bad-16.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 771 :
Number of BH false discoveries: 12 ;
ASH's pihat0 = 0.04316169 ;
Normalized coefficients of Gaussian derivatives:
1 : 0 ; 2 : 0.73920141158121 ; 3 : 0.077182005444609 ; 4 : 0.167446690539398 ; 5 : 0.114289140310117 ; 6 : 0 ; 7 : 0.00550636320542386 ; 8 : 0.0464055959765927 ; 9 : 0 ; 10 : 0.0398398101639301 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for bad-17.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for bad-18.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 389 :
Number of BH false discoveries: 11 ;
ASH's pihat0 = 0.03156173 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.0104278129211743 ; 2 : 0.81975416226431 ; 3 : 0.175093847880514 ; 4 : 0.237691296370699 ; 5 : 0.0928656721296627 ; 6 : 0 ; 7 : 0 ; 8 : 0.0957748191090392 ; 9 : 0 ; 10 : 0.14869448917214 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for bad-19.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for bad-20.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 485 :
Number of BH false discoveries: 9 ;
ASH's pihat0 = 0.04794909 ;
Normalized coefficients of Gaussian derivatives:
1 : 0 ; 2 : 0.688297974677999 ; 3 : 0.102717821163846 ; 4 : 0.1348683673964 ; 5 : 0.0774735270815003 ; 6 : 0 ; 7 : 0 ; 8 : 0 ; 9 : 0 ; 10 : 0 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for bad-21.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for bad-22.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 77 :
Number of BH false discoveries: 7 ;
ASH's pihat0 = 0.05151585 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.0316698203536559 ; 2 : 0.900083565443527 ; 3 : 0.369105500650609 ; 4 : 0.348606888712178 ; 5 : 0.225564147471124 ; 6 : 0 ; 7 : 0 ; 8 : 0 ; 9 : 0 ; 10 : 0 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for bad-23.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for bad-24.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 984 :
Number of BH false discoveries: 7 ;
ASH's pihat0 = 0.04567195 ;
Normalized coefficients of Gaussian derivatives:
1 : 0 ; 2 : 0.699043214591173 ; 3 : 0.100302581737407 ; 4 : 0.145190970625763 ; 5 : 0.0474679405200551 ; 6 : 0 ; 7 : 0 ; 8 : 0.134635889035747 ; 9 : 0 ; 10 : 0.110318005619196 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for bad-25.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for bad-26.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 360 :
Number of BH false discoveries: 6 ;
ASH's pihat0 = 0.0308234 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.0370729985554797 ; 2 : 0.965843584122268 ; 3 : 0.113777617637278 ; 4 : 0.182892304104783 ; 5 : 0.0985758556513691 ; 6 : 0 ; 7 : 0 ; 8 : 0.175602983077514 ; 9 : 0 ; 10 : 0.128160801611689 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for bad-27.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for bad-28.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 522 :
Number of BH false discoveries: 4 ;
ASH's pihat0 = 0.02083846 ;
Normalized coefficients of Gaussian derivatives:
1 : 0 ; 2 : 0.836683104968565 ; 3 : 0 ; 4 : 0.0380324164945556 ; 5 : 0 ; 6 : 0 ; 7 : 0 ; 8 : 0.299307885307397 ; 9 : 0 ; 10 : 0.0990067134691387 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for bad-29.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for bad-30.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 22 :
Number of BH false discoveries: 1 ;
ASH's pihat0 = 0.03271534 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.011182140702874 ; 2 : 0.637669154664922 ; 3 : 0.0954740117610049 ; 4 : 0.0145362179577236 ; 5 : 0.0384875211132818 ; 6 : 0 ; 7 : 0 ; 8 : 0 ; 9 : 0 ; 10 : 0.0366040528004269 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for bad-31.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for bad-32.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 269 :
Number of BH false discoveries: 1 ;
ASH's pihat0 = 0.02787007 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.0350127752264117 ; 2 : 0.665763246213506 ; 3 : 0 ; 4 : 0 ; 5 : 0.360745065018111 ; 6 : 0 ; 7 : 0.660778015759139 ; 8 : 0 ; 9 : 0.341451404165077 ; 10 : 0 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for bad-33.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for bad-34.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 403 :
Number of BH false discoveries: 1 ;
ASH's pihat0 = 0.0531628 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.00287620650301181 ; 2 : 0.547191548824974 ; 3 : 0 ; 4 : 0 ; 5 : 0.0381682188675178 ; 6 : 0.000237362926646135 ; 7 : 0.0760788952836512 ; 8 : 0.155507732499129 ; 9 : 0.0557968950438762 ; 10 : 0.00176813778552284 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for bad-35.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for bad-36.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 923 :
Number of BH false discoveries: 1 ;
ASH's pihat0 = 0.03239883 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.0237509340668928 ; 2 : 0.920816163763449 ; 3 : 0.126877447333694 ; 4 : 0.158793996465808 ; 5 : 0.0298935777348498 ; 6 : 0 ; 7 : 0 ; 8 : 0 ; 9 : 0 ; 10 : 0 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for bad-37.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for bad-38.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 3 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 0.0465218 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.0232314826078553 ; 2 : 0.491281828479503 ; 3 : 0.165633823951823 ; 4 : 0 ; 5 : 0 ; 6 : 0 ; 7 : 0 ; 8 : 0 ; 9 : 0 ; 10 : 0 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for bad-39.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for bad-40.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="good" class="section level2">
<h2>Good</h2>
<p>These data sets are friendly for both <code>BH</code> and <code>ASH</code>.</p>
<pre><code>Data Set 4 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0 ; 2 : 0 ; 3 : 0.0220506376197135 ; 4 : 0 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-1.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-2.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 5 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.00299571447314808 ; 2 : 0 ; 3 : 0 ; 4 : 0 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-3.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-4.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 7 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0 ; 2 : 0 ; 3 : 0 ; 4 : 0.0154789111560678 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-5.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-6.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 8 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.0448250444179864 ; 2 : 0 ; 3 : 0 ; 4 : 0.143559202208159 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-7.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-8.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 9 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0 ; 2 : 0.00733790864173648 ; 3 : 0.0163403533804334 ; 4 : 0 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-9.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-10.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 12 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0 ; 2 : 0 ; 3 : 0 ; 4 : 0.0221346391841642 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-11.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-12.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 13 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0 ; 2 : 0 ; 3 : 0 ; 4 : 0 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-13.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-14.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 14 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0 ; 2 : 0 ; 3 : 0.0319220622489123 ; 4 : 0.0192425975845108 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-15.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-16.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 16 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.0132467627058809 ; 2 : 0 ; 3 : 0.0050633052630629 ; 4 : 0.0460280223671055 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-17.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-18.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 17 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.019759781277875 ; 2 : 0 ; 3 : 0 ; 4 : 0.0663856267063882 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-19.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-20.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 18 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0 ; 2 : 0 ; 3 : 0.0334151016576349 ; 4 : 0.00459370714209619 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-21.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-22.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 25 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0 ; 2 : 0 ; 3 : 0.0110557207434819 ; 4 : 0.165219572806289 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-23.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-24.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 28 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.0200505087249252 ; 2 : 0 ; 3 : 0 ; 4 : 0 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-25.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-26.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 30 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0 ; 2 : 0 ; 3 : 0.0118483507943389 ; 4 : 0 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-27.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-28.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 34 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0 ; 2 : 0 ; 3 : 0.101371139384381 ; 4 : 0 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-29.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-30.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 35 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.0165529780499778 ; 2 : 0 ; 3 : 0 ; 4 : 0.102360725261069 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-31.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-32.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 36 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.00780175544762885 ; 2 : 0 ; 3 : 0 ; 4 : 0.0653975820808355 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-33.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-34.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 38 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0 ; 2 : 0 ; 3 : 0 ; 4 : 0.0643337534695275 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-35.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-36.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 42 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0 ; 2 : 0 ; 3 : 0.0117929353952078 ; 4 : 0.14259210767113 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-37.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-38.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 43 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0 ; 2 : 0 ; 3 : 0.0266591670097924 ; 4 : 0.119934975949713 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-39.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-40.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 45 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.0197168202529947 ; 2 : 0 ; 3 : 0.00535774384797348 ; 4 : 0.0981326520063197 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-41.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-42.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 46 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0 ; 2 : 0 ; 3 : 0.0142593356797949 ; 4 : 0 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-43.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-44.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 47 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.0553713103730739 ; 2 : 0 ; 3 : 0 ; 4 : 0.0424140129177028 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-45.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-46.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 49 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0 ; 2 : 0 ; 3 : 0.0399557075219927 ; 4 : 0.0203389185614439 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-47.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-48.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 52 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.0717118497321021 ; 2 : 0 ; 3 : 0 ; 4 : 0 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-49.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-50.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 53 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0 ; 2 : 0 ; 3 : 0.0203994359033729 ; 4 : 0 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-51.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-52.png" width="672" style="display: block; margin: auto;" /></p>
<pre><code>Data Set 54 :
Number of BH false discoveries: 0 ;
ASH's pihat0 = 1 ;
Normalized coefficients of Gaussian derivatives:
1 : 0.0226491329325567 ; 2 : 0 ; 3 : 0 ; 4 : 0.0369913458520336 ;</code></pre>
<p><img src="figure/Rmosek.rmd/gd fitting for good-53.png" width="672" style="display: block; margin: auto;" /><img src="figure/Rmosek.rmd/gd fitting for good-54.png" width="672" style="display: block; margin: auto;" /></p>
</div>
<div id="remarks" class="section level2">
<h2>Remarks</h2>
<p>The implementation by <code>Rmosek</code> is more convenient, cleaner, yet more complicated. Need to understand different issues such as initialization, optimal orders, controlling parameters, dual construction, etc.</p>
</div>
<div id="session-information" class="section level2">
<h2>Session information</h2>
<!-- Insert the session information into the document -->
<pre class="r"><code>sessionInfo()</code></pre>
<pre><code>R version 3.4.2 (2017-09-28)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS Sierra 10.12.6
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRlapack.dylib
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] Rmosek_7.1.3 PolynomF_0.94 cvxr_0.0.0.9400 REBayes_0.85
[5] Matrix_1.2-11 SQUAREM_2017.10-1 EQL_1.0-0 ttutils_1.0-1
loaded via a namespace (and not attached):
[1] Rcpp_0.12.13 lattice_0.20-35 gmp_0.5-13.1 digest_0.6.12
[5] rprojroot_1.2 MASS_7.3-47 grid_3.4.2 backports_1.1.1
[9] git2r_0.19.0 magrittr_1.5 evaluate_0.10.1 stringi_1.1.5
[13] rmarkdown_1.6 tools_3.4.2 stringr_1.2.0 yaml_2.1.14
[17] compiler_3.4.2 htmltools_0.3.6 knitr_1.17 </code></pre>
</div>
<hr>
<p>
This <a href="http://rmarkdown.rstudio.com">R Markdown</a> site was created with <a href="https://github.com/jdblischak/workflowr">workflowr</a>
</p>
<hr>
<!-- To enable disqus, uncomment the section below and provide your disqus_shortname -->
<!-- disqus
<div id="disqus_thread"></div>
<script type="text/javascript">
/* * * CONFIGURATION VARIABLES: EDIT BEFORE PASTING INTO YOUR WEBPAGE * * */
var disqus_shortname = 'rmarkdown'; // required: replace example with your forum shortname
/* * * DON'T EDIT BELOW THIS LINE * * */
(function() {
var dsq = document.createElement('script'); dsq.type = 'text/javascript'; dsq.async = true;
dsq.src = '//' + disqus_shortname + '.disqus.com/embed.js';
(document.getElementsByTagName('head')[0] || document.getElementsByTagName('body')[0]).appendChild(dsq);
})();
</script>
<noscript>Please enable JavaScript to view the <a href="http://disqus.com/?ref_noscript">comments powered by Disqus.</a></noscript>
<a href="http://disqus.com" class="dsq-brlink">comments powered by <span class="logo-disqus">Disqus</span></a>
-->
</div>
</div>
</div>
<script>
// add bootstrap table styles to pandoc tables
function bootstrapStylePandocTables() {
$('tr.header').parent('thead').parent('table').addClass('table table-condensed');
}
$(document).ready(function () {
bootstrapStylePandocTables();
});
</script>
<!-- dynamically load mathjax for compatibility with self-contained -->
<script>
(function () {
var script = document.createElement("script");
script.type = "text/javascript";
script.src = "https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML";
document.getElementsByTagName("head")[0].appendChild(script);
})();
</script>
</body>
</html>