updating week 46
This commit is contained in:
mhjensen
@@ -7,9 +7,9 @@ Automatically generated HTML file from DocOnce source
|
||||
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
|
||||
<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
|
||||
<meta name="description" content="Week 46: Support Vector Machines">
|
||||
<meta name="description" content="Week 46: Gradient Boosting Summary and Support Vector Machines">
|
||||
|
||||
<title>Week 46: Support Vector Machines</title>
|
||||
<title>Week 46: Gradient Boosting Summary and Support Vector Machines</title>
|
||||
|
||||
<!-- Bootstrap style: bootstrap -->
|
||||
<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
|
||||
@@ -41,39 +41,40 @@ Automatically generated HTML file from DocOnce source
|
||||
|
||||
<!-- tocinfo
|
||||
{'highest level': 2,
|
||||
'sections': [('Support Vector Machines, overarching aims', 2, None, '___sec0'),
|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec3'),
|
||||
('The two-dimensional case', 2, None, '___sec4'),
|
||||
('Getting into the details', 2, None, '___sec5'),
|
||||
('First attempt at a minimization approach', 2, None, '___sec6'),
|
||||
('Solving the equations', 2, None, '___sec7'),
|
||||
('Code Example', 2, None, '___sec8'),
|
||||
('Problems with the Simpler Approach', 2, None, '___sec9'),
|
||||
('A better approach', 2, None, '___sec10'),
|
||||
'sections': [('Overview of week 46', 2, None, '___sec0'),
|
||||
('Support Vector Machines, overarching aims', 2, None, '___sec1'),
|
||||
('Hyperplanes and all that', 2, None, '___sec2'),
|
||||
('What is a hyperplane?', 2, None, '___sec3'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec4'),
|
||||
('The two-dimensional case', 2, None, '___sec5'),
|
||||
('Getting into the details', 2, None, '___sec6'),
|
||||
('First attempt at a minimization approach', 2, None, '___sec7'),
|
||||
('Solving the equations', 2, None, '___sec8'),
|
||||
('Code Example', 2, None, '___sec9'),
|
||||
('Problems with the Simpler Approach', 2, None, '___sec10'),
|
||||
('A better approach', 2, None, '___sec11'),
|
||||
('A quick Reminder on Lagrangian Multipliers',
|
||||
2,
|
||||
None,
|
||||
'___sec11'),
|
||||
('Adding the Multiplier', 2, None, '___sec12'),
|
||||
('Setting up the Problem', 2, None, '___sec13'),
|
||||
('The problem to solve', 2, None, '___sec14'),
|
||||
('The last steps', 2, None, '___sec15'),
|
||||
('A soft classifier', 2, None, '___sec16'),
|
||||
('Soft optmization problem', 2, None, '___sec17'),
|
||||
('Kernels and non-linearity', 2, None, '___sec18'),
|
||||
('The equations', 2, None, '___sec19'),
|
||||
('The problem to solve', 2, None, '___sec20'),
|
||||
("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
||||
('The moons example', 2, None, '___sec22'),
|
||||
'___sec12'),
|
||||
('Adding the Multiplier', 2, None, '___sec13'),
|
||||
('Setting up the Problem', 2, None, '___sec14'),
|
||||
('The problem to solve', 2, None, '___sec15'),
|
||||
('The last steps', 2, None, '___sec16'),
|
||||
('A soft classifier', 2, None, '___sec17'),
|
||||
('Soft optmization problem', 2, None, '___sec18'),
|
||||
('Kernels and non-linearity', 2, None, '___sec19'),
|
||||
('The equations', 2, None, '___sec20'),
|
||||
('The problem to solve', 2, None, '___sec21'),
|
||||
("Different kernels and Mercer's theorem", 2, None, '___sec22'),
|
||||
('The moons example', 2, None, '___sec23'),
|
||||
('Mathematical optimization of convex functions',
|
||||
2,
|
||||
None,
|
||||
'___sec23'),
|
||||
('How do we solve these problems?', 2, None, '___sec24'),
|
||||
('A simple example', 2, None, '___sec25'),
|
||||
('Back to the more realistic cases', 2, None, '___sec26')]}
|
||||
'___sec24'),
|
||||
('How do we solve these problems?', 2, None, '___sec25'),
|
||||
('A simple example', 2, None, '___sec26'),
|
||||
('Back to the more realistic cases', 2, None, '___sec27')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -103,7 +104,7 @@ MathJax.Hub.Config({
|
||||
<span class="icon-bar"></span>
|
||||
<span class="icon-bar"></span>
|
||||
</button>
|
||||
<a class="navbar-brand" href="week46-bs.html">Week 46: Support Vector Machines</a>
|
||||
<a class="navbar-brand" href="week46-bs.html">Week 46: Gradient Boosting Summary and Support Vector Machines</a>
|
||||
</div>
|
||||
|
||||
<div class="navbar-collapse collapse navbar-responsive-collapse">
|
||||
@@ -111,33 +112,34 @@ MathJax.Hub.Config({
|
||||
<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="#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec0" style="font-size: 80%;">Overview of week 46</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Solving the equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Adding the Multiplier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">Setting up the Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">The last steps</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">A soft classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Soft optmization problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">Kernels and non-linearity</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">How do we solve these problems?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">A simple example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs028.html#___sec27" style="font-size: 80%;">Back to the more realistic cases</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -153,35 +155,17 @@ MathJax.Hub.Config({
|
||||
<a name="part0001"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec0" class="anchor">Support Vector Machines, overarching aims </h2>
|
||||
<h2 id="___sec0" class="anchor">Overview of week 46 </h2>
|
||||
|
||||
<ul>
|
||||
<li> <b>Thursday</b>: Summary of Gradient Boosting and further examples of applications.</li>
|
||||
<li> <b>Friday</b>: Support Vector Machines, classification and regression</li>
|
||||
</ul>
|
||||
|
||||
Geron's chapter 5. Chapter 12 (sections 12.1-12.3 are the most relevant ones) of Hastie et al contains also a good discussion.
|
||||
|
||||
<p>
|
||||
A Support Vector Machine (SVM) is a very powerful and versatile
|
||||
Machine Learning method, capable of performing linear or nonlinear
|
||||
classification, regression, and even outlier detection. It is one of
|
||||
the most popular models in Machine Learning, and anyone interested in
|
||||
Machine Learning should have it in their toolbox. SVMs are
|
||||
particularly well suited for classification of complex but small-sized or
|
||||
medium-sized datasets.
|
||||
|
||||
<p>
|
||||
The case with two well-separated classes only can be understood in an
|
||||
intuitive way in terms of lines in a two-dimensional space separating
|
||||
the two classes (see figure below).
|
||||
|
||||
<p>
|
||||
The basic mathematics behind the SVM is however less familiar to most of us.
|
||||
It relies on the definition of hyperplanes and the
|
||||
definition of a <b>margin</b> which separates classes (in case of
|
||||
classification problems) of variables. It is also used for regression
|
||||
problems.
|
||||
|
||||
<p>
|
||||
With SVMs we distinguish between hard margin and soft margins. The
|
||||
latter introduces a so-called softening parameter to be discussed
|
||||
below. We distinguish also between linear and non-linear
|
||||
approaches. The latter are the most frequent ones since it is rather
|
||||
unlikely that we can separate classes easily by say straight lines.
|
||||
<a href="https://www.youtube.com/watch?v=efR1C6CvhmE&ab_channel=StatQuestwithJoshStarmer" target="_self">Overview of Support Vector Machines</a>. see also <a href="https://www.youtube.com/watch?v=N1vOgolbjSc&ab_channel=AliceZhao" target="_self">this video</a>.
|
||||
|
||||
<p>
|
||||
<p>
|
||||
@@ -200,7 +184,7 @@ unlikely that we can separate classes easily by say straight lines.
|
||||
<li><a href="._week46-bs009.html">10</a></li>
|
||||
<li><a href="._week46-bs010.html">11</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week46-bs027.html">28</a></li>
|
||||
<li><a href="._week46-bs028.html">29</a></li>
|
||||
<li><a href="._week46-bs002.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
Reference in New Issue
Block a user