update on log reg with examples
This commit is contained in:
mhjensen
@@ -49,7 +49,8 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec4'),
|
||||
('Maximum likelihood', 2, None, '___sec5'),
|
||||
('Minimizing the cross entropy', 2, None, '___sec6')]}
|
||||
('Minimizing the cross entropy', 2, None, '___sec6'),
|
||||
('A _scikit-learn_ example', 2, None, '___sec7')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -94,6 +95,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs005.html#___sec4" style="font-size: 80%;">The cross-entropy as a cost function for logistic regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs006.html#___sec5" style="font-size: 80%;">Maximum likelihood</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs008.html#___sec6" style="font-size: 80%;">Minimizing the cross entropy</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs009.html#___sec7" style="font-size: 80%;">A <b>scikit-learn</b> example</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -128,7 +130,7 @@ MathJax.Hub.Config({
|
||||
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
|
||||
<br>
|
||||
<p>
|
||||
<center><h4>Sep 17, 2018</h4></center> <!-- date -->
|
||||
<center><h4>Sep 20, 2018</h4></center> <!-- date -->
|
||||
<br>
|
||||
<p>
|
||||
<p>
|
||||
@@ -143,6 +145,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._LogReg-bs006.html">7</a></li>
|
||||
<li><a href="._LogReg-bs007.html">8</a></li>
|
||||
<li><a href="._LogReg-bs008.html">9</a></li>
|
||||
<li><a href="._LogReg-bs009.html">10</a></li>
|
||||
<li><a href="._LogReg-bs001.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -49,7 +49,8 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec4'),
|
||||
('Maximum likelihood', 2, None, '___sec5'),
|
||||
('Minimizing the cross entropy', 2, None, '___sec6')]}
|
||||
('Minimizing the cross entropy', 2, None, '___sec6'),
|
||||
('A _scikit-learn_ example', 2, None, '___sec7')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -94,6 +95,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs005.html#___sec4" style="font-size: 80%;">The cross-entropy as a cost function for logistic regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs006.html#___sec5" style="font-size: 80%;">Maximum likelihood</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs008.html#___sec6" style="font-size: 80%;">Minimizing the cross entropy</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs009.html#___sec7" style="font-size: 80%;">A <b>scikit-learn</b> example</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -149,6 +151,7 @@ models</b>, as we will see later.
|
||||
<li><a href="._LogReg-bs006.html">7</a></li>
|
||||
<li><a href="._LogReg-bs007.html">8</a></li>
|
||||
<li><a href="._LogReg-bs008.html">9</a></li>
|
||||
<li><a href="._LogReg-bs009.html">10</a></li>
|
||||
<li><a href="._LogReg-bs002.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -49,7 +49,8 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec4'),
|
||||
('Maximum likelihood', 2, None, '___sec5'),
|
||||
('Minimizing the cross entropy', 2, None, '___sec6')]}
|
||||
('Minimizing the cross entropy', 2, None, '___sec6'),
|
||||
('A _scikit-learn_ example', 2, None, '___sec7')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -94,6 +95,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs005.html#___sec4" style="font-size: 80%;">The cross-entropy as a cost function for logistic regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs006.html#___sec5" style="font-size: 80%;">Maximum likelihood</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs008.html#___sec6" style="font-size: 80%;">Minimizing the cross entropy</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs009.html#___sec7" style="font-size: 80%;">A <b>scikit-learn</b> example</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -137,6 +139,7 @@ belong.
|
||||
<li><a href="._LogReg-bs006.html">7</a></li>
|
||||
<li><a href="._LogReg-bs007.html">8</a></li>
|
||||
<li><a href="._LogReg-bs008.html">9</a></li>
|
||||
<li><a href="._LogReg-bs009.html">10</a></li>
|
||||
<li><a href="._LogReg-bs003.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -49,7 +49,8 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec4'),
|
||||
('Maximum likelihood', 2, None, '___sec5'),
|
||||
('Minimizing the cross entropy', 2, None, '___sec6')]}
|
||||
('Minimizing the cross entropy', 2, None, '___sec6'),
|
||||
('A _scikit-learn_ example', 2, None, '___sec7')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -94,6 +95,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs005.html#___sec4" style="font-size: 80%;">The cross-entropy as a cost function for logistic regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs006.html#___sec5" style="font-size: 80%;">Maximum likelihood</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs008.html#___sec6" style="font-size: 80%;">Minimizing the cross entropy</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs009.html#___sec7" style="font-size: 80%;">A <b>scikit-learn</b> example</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -137,6 +139,7 @@ where we use the short-hand notation
|
||||
<li><a href="._LogReg-bs006.html">7</a></li>
|
||||
<li><a href="._LogReg-bs007.html">8</a></li>
|
||||
<li><a href="._LogReg-bs008.html">9</a></li>
|
||||
<li><a href="._LogReg-bs009.html">10</a></li>
|
||||
<li><a href="._LogReg-bs004.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -49,7 +49,8 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec4'),
|
||||
('Maximum likelihood', 2, None, '___sec5'),
|
||||
('Minimizing the cross entropy', 2, None, '___sec6')]}
|
||||
('Minimizing the cross entropy', 2, None, '___sec6'),
|
||||
('A _scikit-learn_ example', 2, None, '___sec7')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -94,6 +95,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs005.html#___sec4" style="font-size: 80%;">The cross-entropy as a cost function for logistic regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs006.html#___sec5" style="font-size: 80%;">Maximum likelihood</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs008.html#___sec6" style="font-size: 80%;">Minimizing the cross entropy</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs009.html#___sec7" style="font-size: 80%;">A <b>scikit-learn</b> example</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -147,6 +149,7 @@ Note that \( 1-f(s)= f(-s) \), which will be useful shortly.
|
||||
<li><a href="._LogReg-bs006.html">7</a></li>
|
||||
<li><a href="._LogReg-bs007.html">8</a></li>
|
||||
<li><a href="._LogReg-bs008.html">9</a></li>
|
||||
<li><a href="._LogReg-bs009.html">10</a></li>
|
||||
<li><a href="._LogReg-bs005.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -49,7 +49,8 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec4'),
|
||||
('Maximum likelihood', 2, None, '___sec5'),
|
||||
('Minimizing the cross entropy', 2, None, '___sec6')]}
|
||||
('Minimizing the cross entropy', 2, None, '___sec6'),
|
||||
('A _scikit-learn_ example', 2, None, '___sec7')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -94,6 +95,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="#___sec4" style="font-size: 80%;">The cross-entropy as a cost function for logistic regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs006.html#___sec5" style="font-size: 80%;">Maximum likelihood</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs008.html#___sec6" style="font-size: 80%;">Minimizing the cross entropy</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs009.html#___sec7" style="font-size: 80%;">A <b>scikit-learn</b> example</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -143,6 +145,7 @@ $$
|
||||
<li><a href="._LogReg-bs006.html">7</a></li>
|
||||
<li><a href="._LogReg-bs007.html">8</a></li>
|
||||
<li><a href="._LogReg-bs008.html">9</a></li>
|
||||
<li><a href="._LogReg-bs009.html">10</a></li>
|
||||
<li><a href="._LogReg-bs006.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -49,7 +49,8 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec4'),
|
||||
('Maximum likelihood', 2, None, '___sec5'),
|
||||
('Minimizing the cross entropy', 2, None, '___sec6')]}
|
||||
('Minimizing the cross entropy', 2, None, '___sec6'),
|
||||
('A _scikit-learn_ example', 2, None, '___sec7')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -94,6 +95,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs005.html#___sec4" style="font-size: 80%;">The cross-entropy as a cost function for logistic regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec5" style="font-size: 80%;">Maximum likelihood</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs008.html#___sec6" style="font-size: 80%;">Minimizing the cross entropy</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs009.html#___sec7" style="font-size: 80%;">A <b>scikit-learn</b> example</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -147,6 +149,7 @@ $$
|
||||
<li class="active"><a href="._LogReg-bs006.html">7</a></li>
|
||||
<li><a href="._LogReg-bs007.html">8</a></li>
|
||||
<li><a href="._LogReg-bs008.html">9</a></li>
|
||||
<li><a href="._LogReg-bs009.html">10</a></li>
|
||||
<li><a href="._LogReg-bs007.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -49,7 +49,8 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec4'),
|
||||
('Maximum likelihood', 2, None, '___sec5'),
|
||||
('Minimizing the cross entropy', 2, None, '___sec6')]}
|
||||
('Minimizing the cross entropy', 2, None, '___sec6'),
|
||||
('A _scikit-learn_ example', 2, None, '___sec7')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -94,6 +95,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs005.html#___sec4" style="font-size: 80%;">The cross-entropy as a cost function for logistic regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs006.html#___sec5" style="font-size: 80%;">Maximum likelihood</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs008.html#___sec6" style="font-size: 80%;">Minimizing the cross entropy</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs009.html#___sec7" style="font-size: 80%;">A <b>scikit-learn</b> example</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -138,6 +140,7 @@ in practice we usually supplement the cross-entropy with additional regularizati
|
||||
<li><a href="._LogReg-bs006.html">7</a></li>
|
||||
<li class="active"><a href="._LogReg-bs007.html">8</a></li>
|
||||
<li><a href="._LogReg-bs008.html">9</a></li>
|
||||
<li><a href="._LogReg-bs009.html">10</a></li>
|
||||
<li><a href="._LogReg-bs008.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -49,7 +49,8 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec4'),
|
||||
('Maximum likelihood', 2, None, '___sec5'),
|
||||
('Minimizing the cross entropy', 2, None, '___sec6')]}
|
||||
('Minimizing the cross entropy', 2, None, '___sec6'),
|
||||
('A _scikit-learn_ example', 2, None, '___sec7')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -94,6 +95,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs005.html#___sec4" style="font-size: 80%;">The cross-entropy as a cost function for logistic regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs006.html#___sec5" style="font-size: 80%;">Maximum likelihood</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec6" style="font-size: 80%;">Minimizing the cross entropy</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs009.html#___sec7" style="font-size: 80%;">A <b>scikit-learn</b> example</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -130,6 +132,7 @@ f(z)[1-f(z)] \). This equation defines a transcendental equation for
|
||||
be written in a closed form.
|
||||
Here we need gradient descent methods!
|
||||
|
||||
<p>
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
<ul class="pagination">
|
||||
@@ -143,6 +146,8 @@ Here we need gradient descent methods!
|
||||
<li><a href="._LogReg-bs006.html">7</a></li>
|
||||
<li><a href="._LogReg-bs007.html">8</a></li>
|
||||
<li class="active"><a href="._LogReg-bs008.html">9</a></li>
|
||||
<li><a href="._LogReg-bs009.html">10</a></li>
|
||||
<li><a href="._LogReg-bs009.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
|
||||
@@ -0,0 +1,177 @@
|
||||
<!--
|
||||
Automatically generated HTML file from DocOnce source
|
||||
(https://github.com/hplgit/doconce/)
|
||||
-->
|
||||
<html>
|
||||
<head>
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
|
||||
<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
|
||||
<meta name="description" content="Data Analysis and Machine Learning: Logistic Regression">
|
||||
|
||||
<title>Data Analysis and Machine Learning: Logistic Regression</title>
|
||||
|
||||
<!-- Bootstrap style: bootstrap -->
|
||||
<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
|
||||
<!-- not necessary
|
||||
<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
|
||||
-->
|
||||
|
||||
<style type="text/css">
|
||||
|
||||
/* Add scrollbar to dropdown menus in bootstrap navigation bar */
|
||||
.dropdown-menu {
|
||||
height: auto;
|
||||
max-height: 400px;
|
||||
overflow-x: hidden;
|
||||
}
|
||||
|
||||
/* Adds an invisible element before each target to offset for the navigation
|
||||
bar */
|
||||
.anchor::before {
|
||||
content:"";
|
||||
display:block;
|
||||
height:50px; /* fixed header height for style bootstrap */
|
||||
margin:-50px 0 0; /* negative fixed header height */
|
||||
}
|
||||
</style>
|
||||
|
||||
|
||||
</head>
|
||||
|
||||
<!-- tocinfo
|
||||
{'highest level': 2,
|
||||
'sections': [('Logistic Regression', 2, None, '___sec0'),
|
||||
('Basics', 2, None, '___sec1'),
|
||||
('Linear classifier', 2, None, '___sec2'),
|
||||
('Some selected properties', 2, None, '___sec3'),
|
||||
('The cross-entropy as a cost function for logistic regression',
|
||||
2,
|
||||
None,
|
||||
'___sec4'),
|
||||
('Maximum likelihood', 2, None, '___sec5'),
|
||||
('Minimizing the cross entropy', 2, None, '___sec6'),
|
||||
('A _scikit-learn_ example', 2, None, '___sec7')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
|
||||
|
||||
|
||||
<script type="text/x-mathjax-config">
|
||||
MathJax.Hub.Config({
|
||||
TeX: {
|
||||
equationNumbers: { autoNumber: "none" },
|
||||
extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
|
||||
}
|
||||
});
|
||||
</script>
|
||||
<script type="text/javascript" async
|
||||
src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
|
||||
</script>
|
||||
|
||||
|
||||
|
||||
|
||||
<!-- Bootstrap navigation bar -->
|
||||
<div class="navbar navbar-default navbar-fixed-top">
|
||||
<div class="navbar-header">
|
||||
<button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
|
||||
<span class="icon-bar"></span>
|
||||
<span class="icon-bar"></span>
|
||||
<span class="icon-bar"></span>
|
||||
</button>
|
||||
<a class="navbar-brand" href="LogReg-bs.html">Data Analysis and Machine Learning: Logistic Regression</a>
|
||||
</div>
|
||||
|
||||
<div class="navbar-collapse collapse navbar-responsive-collapse">
|
||||
<ul class="nav navbar-nav navbar-right">
|
||||
<li class="dropdown">
|
||||
<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
|
||||
<ul class="dropdown-menu">
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs001.html#___sec0" style="font-size: 80%;">Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs002.html#___sec1" style="font-size: 80%;">Basics</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs003.html#___sec2" style="font-size: 80%;">Linear classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs004.html#___sec3" style="font-size: 80%;">Some selected properties</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs005.html#___sec4" style="font-size: 80%;">The cross-entropy as a cost function for logistic regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs006.html#___sec5" style="font-size: 80%;">Maximum likelihood</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs008.html#___sec6" style="font-size: 80%;">Minimizing the cross entropy</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec7" style="font-size: 80%;">A <b>scikit-learn</b> example</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
</div> <!-- end of navigation bar -->
|
||||
|
||||
<div class="container">
|
||||
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
|
||||
<a name="part0009"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec7" class="anchor">A <b>scikit-learn</b> example </h2>
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn</span> <span style="color: #008000; font-weight: bold">import</span> datasets
|
||||
iris <span style="color: #666666">=</span> datasets<span style="color: #666666">.</span>load_iris()
|
||||
<span style="color: #008000">list</span>(iris<span style="color: #666666">.</span>keys())
|
||||
[<span style="color: #BA2121">'data'</span>, <span style="color: #BA2121">'target_names'</span>, <span style="color: #BA2121">'feature_names'</span>, <span style="color: #BA2121">'target'</span>, <span style="color: #BA2121">'DESCR'</span>]
|
||||
X <span style="color: #666666">=</span> iris[<span style="color: #BA2121">"data"</span>][:, <span style="color: #666666">3</span>:] <span style="color: #408080; font-style: italic"># petal width</span>
|
||||
y <span style="color: #666666">=</span> (iris[<span style="color: #BA2121">"target"</span>] <span style="color: #666666">==</span> <span style="color: #666666">2</span>)<span style="color: #666666">.</span>astype(np<span style="color: #666666">.</span>int) <span style="color: #408080; font-style: italic"># 1 if Iris-Virginica, else 0</span>
|
||||
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> LogisticRegression
|
||||
log_reg <span style="color: #666666">=</span> LogisticRegression()
|
||||
log_reg<span style="color: #666666">.</span>fit(X, y)
|
||||
|
||||
X_new <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(<span style="color: #666666">0</span>, <span style="color: #666666">3</span>, <span style="color: #666666">1000</span>)<span style="color: #666666">.</span>reshape(<span style="color: #666666">-1</span>, <span style="color: #666666">1</span>)
|
||||
y_proba <span style="color: #666666">=</span> log_reg<span style="color: #666666">.</span>predict_proba(X_new)
|
||||
plt<span style="color: #666666">.</span>plot(X_new, y_proba[:, <span style="color: #666666">1</span>], <span style="color: #BA2121">"g-"</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">"Iris-Virginica"</span>)
|
||||
plt<span style="color: #666666">.</span>plot(X_new, y_proba[:, <span style="color: #666666">0</span>], <span style="color: #BA2121">"b--"</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">"Not Iris-Virginica"</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
<ul class="pagination">
|
||||
<li><a href="._LogReg-bs008.html">«</a></li>
|
||||
<li><a href="._LogReg-bs000.html">1</a></li>
|
||||
<li><a href="._LogReg-bs001.html">2</a></li>
|
||||
<li><a href="._LogReg-bs002.html">3</a></li>
|
||||
<li><a href="._LogReg-bs003.html">4</a></li>
|
||||
<li><a href="._LogReg-bs004.html">5</a></li>
|
||||
<li><a href="._LogReg-bs005.html">6</a></li>
|
||||
<li><a href="._LogReg-bs006.html">7</a></li>
|
||||
<li><a href="._LogReg-bs007.html">8</a></li>
|
||||
<li><a href="._LogReg-bs008.html">9</a></li>
|
||||
<li class="active"><a href="._LogReg-bs009.html">10</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
</div> <!-- end container -->
|
||||
<!-- include javascript, jQuery *first* -->
|
||||
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
|
||||
<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
|
||||
|
||||
<!-- Bootstrap footer
|
||||
<footer>
|
||||
<a href="http://..."><img width="250" align=right src="http://..."></a>
|
||||
</footer>
|
||||
-->
|
||||
|
||||
|
||||
<center style="font-size:80%">
|
||||
<!-- copyright only on the titlepage -->
|
||||
</center>
|
||||
|
||||
|
||||
</body>
|
||||
</html>
|
||||
|
||||
|
||||
@@ -49,7 +49,8 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec4'),
|
||||
('Maximum likelihood', 2, None, '___sec5'),
|
||||
('Minimizing the cross entropy', 2, None, '___sec6')]}
|
||||
('Minimizing the cross entropy', 2, None, '___sec6'),
|
||||
('A _scikit-learn_ example', 2, None, '___sec7')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -94,6 +95,7 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs005.html#___sec4" style="font-size: 80%;">The cross-entropy as a cost function for logistic regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs006.html#___sec5" style="font-size: 80%;">Maximum likelihood</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs008.html#___sec6" style="font-size: 80%;">Minimizing the cross entropy</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._LogReg-bs009.html#___sec7" style="font-size: 80%;">A <b>scikit-learn</b> example</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -128,7 +130,7 @@ MathJax.Hub.Config({
|
||||
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
|
||||
<br>
|
||||
<p>
|
||||
<center><h4>Sep 17, 2018</h4></center> <!-- date -->
|
||||
<center><h4>Sep 20, 2018</h4></center> <!-- date -->
|
||||
<br>
|
||||
<p>
|
||||
<p>
|
||||
@@ -143,6 +145,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._LogReg-bs006.html">7</a></li>
|
||||
<li><a href="._LogReg-bs007.html">8</a></li>
|
||||
<li><a href="._LogReg-bs008.html">9</a></li>
|
||||
<li><a href="._LogReg-bs009.html">10</a></li>
|
||||
<li><a href="._LogReg-bs001.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -148,7 +148,7 @@ MathJax.Hub.Config({
|
||||
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
|
||||
<br>
|
||||
<p> <br>
|
||||
<center><h4>Sep 17, 2018</h4></center> <!-- date -->
|
||||
<center><h4>Sep 20, 2018</h4></center> <!-- date -->
|
||||
<br>
|
||||
<p>
|
||||
|
||||
@@ -356,6 +356,34 @@ Here we need gradient descent methods!
|
||||
</section>
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec7">A <b>scikit-learn</b> example </h2>
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn</span> <span style="color: #8B008B; font-weight: bold">import</span> datasets
|
||||
iris = datasets.load_iris()
|
||||
<span style="color: #658b00">list</span>(iris.keys())
|
||||
[<span style="color: #CD5555">'data'</span>, <span style="color: #CD5555">'target_names'</span>, <span style="color: #CD5555">'feature_names'</span>, <span style="color: #CD5555">'target'</span>, <span style="color: #CD5555">'DESCR'</span>]
|
||||
X = iris[<span style="color: #CD5555">"data"</span>][:, <span style="color: #B452CD">3</span>:] <span style="color: #228B22"># petal width</span>
|
||||
y = (iris[<span style="color: #CD5555">"target"</span>] == <span style="color: #B452CD">2</span>).astype(np.int) <span style="color: #228B22"># 1 if Iris-Virginica, else 0</span>
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.linear_model</span> <span style="color: #8B008B; font-weight: bold">import</span> LogisticRegression
|
||||
log_reg = LogisticRegression()
|
||||
log_reg.fit(X, y)
|
||||
|
||||
X_new = np.linspace(<span style="color: #B452CD">0</span>, <span style="color: #B452CD">3</span>, <span style="color: #B452CD">1000</span>).reshape(-<span style="color: #B452CD">1</span>, <span style="color: #B452CD">1</span>)
|
||||
y_proba = log_reg.predict_proba(X_new)
|
||||
plt.plot(X_new, y_proba[:, <span style="color: #B452CD">1</span>], <span style="color: #CD5555">"g-"</span>, label=<span style="color: #CD5555">"Iris-Virginica"</span>)
|
||||
plt.plot(X_new, y_proba[:, <span style="color: #B452CD">0</span>], <span style="color: #CD5555">"b--"</span>, label=<span style="color: #CD5555">"Not Iris-Virginica"</span>)
|
||||
plt.show()
|
||||
</pre></div>
|
||||
</section>
|
||||
|
||||
|
||||
|
||||
</div> <!-- class="slides" -->
|
||||
</div> <!-- class="reveal" -->
|
||||
|
||||
@@ -43,7 +43,8 @@ div { text-align: justify; text-justify: inter-word; }
|
||||
None,
|
||||
'___sec4'),
|
||||
('Maximum likelihood', 2, None, '___sec5'),
|
||||
('Minimizing the cross entropy', 2, None, '___sec6')]}
|
||||
('Minimizing the cross entropy', 2, None, '___sec6'),
|
||||
('A _scikit-learn_ example', 2, None, '___sec7')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -85,7 +86,7 @@ MathJax.Hub.Config({
|
||||
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
|
||||
<br>
|
||||
<p>
|
||||
<center><h4>Sep 17, 2018</h4></center> <!-- date -->
|
||||
<center><h4>Sep 20, 2018</h4></center> <!-- date -->
|
||||
<br>
|
||||
<p>
|
||||
<!-- !split -->
|
||||
@@ -266,6 +267,35 @@ f(z)[1-f(z)] \). This equation defines a transcendental equation for
|
||||
be written in a closed form.
|
||||
Here we need gradient descent methods!
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec7">A <b>scikit-learn</b> example </h2>
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
|
||||
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn</span> <span style="color: #8B008B; font-weight: bold">import</span> datasets
|
||||
iris = datasets.load_iris()
|
||||
<span style="color: #658b00">list</span>(iris.keys())
|
||||
[<span style="color: #CD5555">'data'</span>, <span style="color: #CD5555">'target_names'</span>, <span style="color: #CD5555">'feature_names'</span>, <span style="color: #CD5555">'target'</span>, <span style="color: #CD5555">'DESCR'</span>]
|
||||
X = iris[<span style="color: #CD5555">"data"</span>][:, <span style="color: #B452CD">3</span>:] <span style="color: #228B22"># petal width</span>
|
||||
y = (iris[<span style="color: #CD5555">"target"</span>] == <span style="color: #B452CD">2</span>).astype(np.int) <span style="color: #228B22"># 1 if Iris-Virginica, else 0</span>
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.linear_model</span> <span style="color: #8B008B; font-weight: bold">import</span> LogisticRegression
|
||||
log_reg = LogisticRegression()
|
||||
log_reg.fit(X, y)
|
||||
|
||||
X_new = np.linspace(<span style="color: #B452CD">0</span>, <span style="color: #B452CD">3</span>, <span style="color: #B452CD">1000</span>).reshape(-<span style="color: #B452CD">1</span>, <span style="color: #B452CD">1</span>)
|
||||
y_proba = log_reg.predict_proba(X_new)
|
||||
plt.plot(X_new, y_proba[:, <span style="color: #B452CD">1</span>], <span style="color: #CD5555">"g-"</span>, label=<span style="color: #CD5555">"Iris-Virginica"</span>)
|
||||
plt.plot(X_new, y_proba[:, <span style="color: #B452CD">0</span>], <span style="color: #CD5555">"b--"</span>, label=<span style="color: #CD5555">"Not Iris-Virginica"</span>)
|
||||
plt.show()
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
|
||||
|
||||
@@ -48,7 +48,8 @@ div { text-align: justify; text-justify: inter-word; }
|
||||
None,
|
||||
'___sec4'),
|
||||
('Maximum likelihood', 2, None, '___sec5'),
|
||||
('Minimizing the cross entropy', 2, None, '___sec6')]}
|
||||
('Minimizing the cross entropy', 2, None, '___sec6'),
|
||||
('A _scikit-learn_ example', 2, None, '___sec7')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -90,7 +91,7 @@ MathJax.Hub.Config({
|
||||
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
|
||||
<br>
|
||||
<p>
|
||||
<center><h4>Sep 17, 2018</h4></center> <!-- date -->
|
||||
<center><h4>Sep 20, 2018</h4></center> <!-- date -->
|
||||
<br>
|
||||
<p>
|
||||
<!-- !split -->
|
||||
@@ -271,6 +272,35 @@ f(z)[1-f(z)] \). This equation defines a transcendental equation for
|
||||
be written in a closed form.
|
||||
Here we need gradient descent methods!
|
||||
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec7">A <b>scikit-learn</b> example </h2>
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn</span> <span style="color: #008000; font-weight: bold">import</span> datasets
|
||||
iris <span style="color: #666666">=</span> datasets<span style="color: #666666">.</span>load_iris()
|
||||
<span style="color: #008000">list</span>(iris<span style="color: #666666">.</span>keys())
|
||||
[<span style="color: #BA2121">'data'</span>, <span style="color: #BA2121">'target_names'</span>, <span style="color: #BA2121">'feature_names'</span>, <span style="color: #BA2121">'target'</span>, <span style="color: #BA2121">'DESCR'</span>]
|
||||
X <span style="color: #666666">=</span> iris[<span style="color: #BA2121">"data"</span>][:, <span style="color: #666666">3</span>:] <span style="color: #408080; font-style: italic"># petal width</span>
|
||||
y <span style="color: #666666">=</span> (iris[<span style="color: #BA2121">"target"</span>] <span style="color: #666666">==</span> <span style="color: #666666">2</span>)<span style="color: #666666">.</span>astype(np<span style="color: #666666">.</span>int) <span style="color: #408080; font-style: italic"># 1 if Iris-Virginica, else 0</span>
|
||||
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> LogisticRegression
|
||||
log_reg <span style="color: #666666">=</span> LogisticRegression()
|
||||
log_reg<span style="color: #666666">.</span>fit(X, y)
|
||||
|
||||
X_new <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(<span style="color: #666666">0</span>, <span style="color: #666666">3</span>, <span style="color: #666666">1000</span>)<span style="color: #666666">.</span>reshape(<span style="color: #666666">-1</span>, <span style="color: #666666">1</span>)
|
||||
y_proba <span style="color: #666666">=</span> log_reg<span style="color: #666666">.</span>predict_proba(X_new)
|
||||
plt<span style="color: #666666">.</span>plot(X_new, y_proba[:, <span style="color: #666666">1</span>], <span style="color: #BA2121">"g-"</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">"Iris-Virginica"</span>)
|
||||
plt<span style="color: #666666">.</span>plot(X_new, y_proba[:, <span style="color: #666666">0</span>], <span style="color: #BA2121">"b--"</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">"Not Iris-Virginica"</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
|
||||
<p>
|
||||
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
|
||||
|
||||
@@ -10,7 +10,7 @@
|
||||
"<!-- Author: --> \n",
|
||||
"**Morten Hjorth-Jensen**, Department of Physics, University of Oslo and Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University\n",
|
||||
"\n",
|
||||
"Date: **Sep 17, 2018**\n",
|
||||
"Date: **Sep 20, 2018**\n",
|
||||
"\n",
|
||||
"Copyright 1999-2018, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license\n",
|
||||
"\n",
|
||||
@@ -285,7 +285,40 @@
|
||||
"f(z)[1-f(z)]$. This equation defines a transcendental equation for\n",
|
||||
"$\\mathbf{w}$, the solution of which, unlike linear regression, cannot\n",
|
||||
"be written in a closed form. \n",
|
||||
"Here we need gradient descent methods!"
|
||||
"Here we need gradient descent methods!\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"## A **scikit-learn** example"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"%matplotlib inline\n",
|
||||
"\n",
|
||||
"import numpy as np\n",
|
||||
"import matplotlib.pyplot as plt\n",
|
||||
"from sklearn import datasets\n",
|
||||
"iris = datasets.load_iris()\n",
|
||||
"list(iris.keys())\n",
|
||||
"['data', 'target_names', 'feature_names', 'target', 'DESCR']\n",
|
||||
"X = iris[\"data\"][:, 3:] # petal width\n",
|
||||
"y = (iris[\"target\"] == 2).astype(np.int) # 1 if Iris-Virginica, else 0\n",
|
||||
"\n",
|
||||
"from sklearn.linear_model import LogisticRegression\n",
|
||||
"log_reg = LogisticRegression()\n",
|
||||
"log_reg.fit(X, y)\n",
|
||||
"\n",
|
||||
"X_new = np.linspace(0, 3, 1000).reshape(-1, 1)\n",
|
||||
"y_proba = log_reg.predict_proba(X_new)\n",
|
||||
"plt.plot(X_new, y_proba[:, 1], \"g-\", label=\"Iris-Virginica\")\n",
|
||||
"plt.plot(X_new, y_proba[:, 0], \"b--\", label=\"Not Iris-Virginica\")\n",
|
||||
"plt.show()"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
||||
Binary file not shown.
Binary file not shown.
Binary file not shown.
Binary file not shown.
@@ -151,3 +151,29 @@ f(z)[1-f(z)]$. This equation defines a transcendental equation for
|
||||
$\mathbf{w}$, the solution of which, unlike linear regression, cannot
|
||||
be written in a closed form.
|
||||
Here we need gradient descent methods!
|
||||
|
||||
|
||||
!split
|
||||
===== A _scikit-learn_ example =====
|
||||
|
||||
!bc pycod
|
||||
import numpy as np
|
||||
import matplotlib.pyplot as plt
|
||||
from sklearn import datasets
|
||||
iris = datasets.load_iris()
|
||||
list(iris.keys())
|
||||
['data', 'target_names', 'feature_names', 'target', 'DESCR']
|
||||
X = iris["data"][:, 3:] # petal width
|
||||
y = (iris["target"] == 2).astype(np.int) # 1 if Iris-Virginica, else 0
|
||||
|
||||
from sklearn.linear_model import LogisticRegression
|
||||
log_reg = LogisticRegression()
|
||||
log_reg.fit(X, y)
|
||||
|
||||
X_new = np.linspace(0, 3, 1000).reshape(-1, 1)
|
||||
y_proba = log_reg.predict_proba(X_new)
|
||||
plt.plot(X_new, y_proba[:, 1], "g-", label="Iris-Virginica")
|
||||
plt.plot(X_new, y_proba[:, 0], "b--", label="Not Iris-Virginica")
|
||||
plt.show()
|
||||
|
||||
!ec
|
||||
|
||||
Reference in New Issue
Block a user