Morten Hjorth-Jensen
449 lines
27 KiB
HTML
449 lines
27 KiB
HTML
<!--
|
|
HTML file automatically generated from DocOnce source
|
|
(https://github.com/doconce/doconce/)
|
|
doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako
|
|
-->
|
|
<html>
|
|
<head>
|
|
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
|
|
<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
|
|
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
|
|
<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
|
|
<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
|
|
<!-- Bootstrap style: bootstrap -->
|
|
<!-- doconce format html week35.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=week35-bs --no_mako -->
|
|
<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': [('Plans for week 35, August 30 -September 3',
|
|
2,
|
|
None,
|
|
'plans-for-week-35-august-30-september-3'),
|
|
('Thursday September 2', 2, None, 'thursday-september-2'),
|
|
('Why Linear Regression (aka Ordinary Least Squares and family), '
|
|
'repeat from last week',
|
|
2,
|
|
None,
|
|
'why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week'),
|
|
('Regression analysis, overarching aims',
|
|
2,
|
|
None,
|
|
'regression-analysis-overarching-aims'),
|
|
('Regression analysis, overarching aims II',
|
|
2,
|
|
None,
|
|
'regression-analysis-overarching-aims-ii'),
|
|
('Examples', 2, None, 'examples'),
|
|
('General linear models', 2, None, 'general-linear-models'),
|
|
('Rewriting the fitting procedure as a linear algebra problem',
|
|
2,
|
|
None,
|
|
'rewriting-the-fitting-procedure-as-a-linear-algebra-problem'),
|
|
('Rewriting the fitting procedure as a linear algebra problem, '
|
|
'more details',
|
|
2,
|
|
None,
|
|
'rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details'),
|
|
('Generalizing the fitting procedure as a linear algebra problem',
|
|
2,
|
|
None,
|
|
'generalizing-the-fitting-procedure-as-a-linear-algebra-problem'),
|
|
('Generalizing the fitting procedure as a linear algebra problem',
|
|
2,
|
|
None,
|
|
'generalizing-the-fitting-procedure-as-a-linear-algebra-problem'),
|
|
('Optimizing our parameters',
|
|
2,
|
|
None,
|
|
'optimizing-our-parameters'),
|
|
('Our model for the nuclear binding energies',
|
|
2,
|
|
None,
|
|
'our-model-for-the-nuclear-binding-energies'),
|
|
('Optimizing our parameters, more details',
|
|
2,
|
|
None,
|
|
'optimizing-our-parameters-more-details'),
|
|
('Interpretations and optimizing our parameters',
|
|
2,
|
|
None,
|
|
'interpretations-and-optimizing-our-parameters'),
|
|
('Interpretations and optimizing our parameters',
|
|
2,
|
|
None,
|
|
'interpretations-and-optimizing-our-parameters'),
|
|
('Some useful matrix and vector expressions',
|
|
2,
|
|
None,
|
|
'some-useful-matrix-and-vector-expressions'),
|
|
('Meet the Hessian Matrix', 2, None, 'meet-the-hessian-matrix'),
|
|
('Interpretations and optimizing our parameters',
|
|
2,
|
|
None,
|
|
'interpretations-and-optimizing-our-parameters'),
|
|
('Own code for Ordinary Least Squares',
|
|
2,
|
|
None,
|
|
'own-code-for-ordinary-least-squares'),
|
|
('Adding error analysis and training set up',
|
|
2,
|
|
None,
|
|
'adding-error-analysis-and-training-set-up'),
|
|
('Splitting our Data in Training and Test data',
|
|
2,
|
|
None,
|
|
'splitting-our-data-in-training-and-test-data'),
|
|
('Examples', 2, None, 'examples'),
|
|
('Making your own test-train splitting',
|
|
2,
|
|
None,
|
|
'making-your-own-test-train-splitting'),
|
|
('The Boston housing data example',
|
|
2,
|
|
None,
|
|
'the-boston-housing-data-example'),
|
|
('Housing data, the code', 2, None, 'housing-data-the-code'),
|
|
('Reducing the number of degrees of freedom, overarching view',
|
|
2,
|
|
None,
|
|
'reducing-the-number-of-degrees-of-freedom-overarching-view'),
|
|
('Preprocessing our data', 2, None, 'preprocessing-our-data'),
|
|
('Functionality in Scikit-Learn',
|
|
2,
|
|
None,
|
|
'functionality-in-scikit-learn'),
|
|
('More preprocessing', 2, None, 'more-preprocessing'),
|
|
('Frequently used scaling functions',
|
|
2,
|
|
None,
|
|
'frequently-used-scaling-functions'),
|
|
('Example of own Standard scaling',
|
|
2,
|
|
None,
|
|
'example-of-own-standard-scaling'),
|
|
('Min-Max Scaling', 2, None, 'min-max-scaling'),
|
|
('Testing the Means Squared Error as function of Complexity',
|
|
2,
|
|
None,
|
|
'testing-the-means-squared-error-as-function-of-complexity'),
|
|
('More preprocessing examples, Franke function and regression',
|
|
2,
|
|
None,
|
|
'more-preprocessing-examples-franke-function-and-regression'),
|
|
('Mathematical Interpretation of Ordinary Least Squares',
|
|
2,
|
|
None,
|
|
'mathematical-interpretation-of-ordinary-least-squares'),
|
|
('Residual Error', 2, None, 'residual-error'),
|
|
('Simple case', 2, None, 'simple-case'),
|
|
('The singular value decomposition',
|
|
2,
|
|
None,
|
|
'the-singular-value-decomposition'),
|
|
('Linear Regression Problems',
|
|
2,
|
|
None,
|
|
'linear-regression-problems'),
|
|
('Fixing the singularity', 2, None, 'fixing-the-singularity'),
|
|
('Basic math of the SVD', 2, None, 'basic-math-of-the-svd'),
|
|
('The SVD, a Fantastic Algorithm',
|
|
2,
|
|
None,
|
|
'the-svd-a-fantastic-algorithm'),
|
|
('Economy-size SVD', 2, None, 'economy-size-svd'),
|
|
('Codes for the SVD', 2, None, 'codes-for-the-svd'),
|
|
('Note about SVD Calculations',
|
|
2,
|
|
None,
|
|
'note-about-svd-calculations'),
|
|
('Friday September 3', 2, None, 'friday-september-3'),
|
|
('Mathematics of the SVD and implications',
|
|
2,
|
|
None,
|
|
'mathematics-of-the-svd-and-implications'),
|
|
('Example Matrix', 2, None, 'example-matrix'),
|
|
('Setting up the Matrix to be inverted',
|
|
2,
|
|
None,
|
|
'setting-up-the-matrix-to-be-inverted'),
|
|
('Further properties (important for our analyses later)',
|
|
2,
|
|
None,
|
|
'further-properties-important-for-our-analyses-later'),
|
|
('Meet the Covariance Matrix',
|
|
2,
|
|
None,
|
|
'meet-the-covariance-matrix'),
|
|
('Introducing the Covariance and Correlation functions',
|
|
2,
|
|
None,
|
|
'introducing-the-covariance-and-correlation-functions'),
|
|
('Covariance and Correlation Matrix',
|
|
2,
|
|
None,
|
|
'covariance-and-correlation-matrix'),
|
|
('Correlation Function and Design/Feature Matrix',
|
|
2,
|
|
None,
|
|
'correlation-function-and-design-feature-matrix'),
|
|
('Covariance Matrix Examples',
|
|
2,
|
|
None,
|
|
'covariance-matrix-examples'),
|
|
('Correlation Matrix', 2, None, 'correlation-matrix'),
|
|
('Correlation Matrix with Pandas',
|
|
2,
|
|
None,
|
|
'correlation-matrix-with-pandas'),
|
|
('Correlation Matrix with Pandas and the Franke function',
|
|
2,
|
|
None,
|
|
'correlation-matrix-with-pandas-and-the-franke-function'),
|
|
('Rewriting the Covariance and/or Correlation Matrix',
|
|
2,
|
|
None,
|
|
'rewriting-the-covariance-and-or-correlation-matrix'),
|
|
('Linking with the SVD', 2, None, 'linking-with-the-svd'),
|
|
('What does it mean?', 2, None, 'what-does-it-mean'),
|
|
('And finally $\\boldsymbol{X}\\boldsymbol{X}^T$',
|
|
2,
|
|
None,
|
|
'and-finally-boldsymbol-x-boldsymbol-x-t'),
|
|
('Ridge and LASSO Regression',
|
|
2,
|
|
None,
|
|
'ridge-and-lasso-regression'),
|
|
('Deriving the Ridge Regression Equations',
|
|
2,
|
|
None,
|
|
'deriving-the-ridge-regression-equations'),
|
|
('Interpreting the Ridge results',
|
|
2,
|
|
None,
|
|
'interpreting-the-ridge-results'),
|
|
('More interpretations', 2, None, 'more-interpretations'),
|
|
('Deriving the Lasso Regression Equations',
|
|
2,
|
|
None,
|
|
'deriving-the-lasso-regression-equations'),
|
|
('Exercises for week 36, September 6-10',
|
|
2,
|
|
None,
|
|
'exercises-for-week-36-september-6-10'),
|
|
('Exercise 1: Adding Ridge and Lasso Regression',
|
|
2,
|
|
None,
|
|
'exercise-1-adding-ridge-and-lasso-regression'),
|
|
('Exercise: Linear Regression for a two-dimensional function',
|
|
3,
|
|
None,
|
|
'exercise-linear-regression-for-a-two-dimensional-function')]}
|
|
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="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso 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="._week35-bs001.html#plans-for-week-35-august-30-september-3" style="font-size: 80%;"><b>Plans for week 35, August 30 -September 3</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-september-2" style="font-size: 80%;"><b>Thursday September 2</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs003.html#why-linear-regression-aka-ordinary-least-squares-and-family-repeat-from-last-week" style="font-size: 80%;"><b>Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;"><b>Regression analysis, overarching aims</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;"><b>Regression analysis, overarching aims II</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;"><b>General linear models</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs009.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details" style="font-size: 80%;"><b>Rewriting the fitting procedure as a linear algebra problem, more details</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;"><b>Generalizing the fitting procedure as a linear algebra problem</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;"><b>Optimizing our parameters</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;"><b>Our model for the nuclear binding energies</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;"><b>Optimizing our parameters, more details</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;"><b>Some useful matrix and vector expressions</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs018.html#meet-the-hessian-matrix" style="font-size: 80%;"><b>Meet the Hessian Matrix</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs019.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;"><b>Interpretations and optimizing our parameters</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs020.html#own-code-for-ordinary-least-squares" style="font-size: 80%;"><b>Own code for Ordinary Least Squares</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs021.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;"><b>Adding error analysis and training set up</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs022.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;"><b>Splitting our Data in Training and Test data</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs023.html#examples" style="font-size: 80%;"><b>Examples</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs024.html#making-your-own-test-train-splitting" style="font-size: 80%;"><b>Making your own test-train splitting</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs025.html#the-boston-housing-data-example" style="font-size: 80%;"><b>The Boston housing data example</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs026.html#housing-data-the-code" style="font-size: 80%;"><b>Housing data, the code</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs027.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs028.html#preprocessing-our-data" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs029.html#functionality-in-scikit-learn" style="font-size: 80%;"><b>Functionality in Scikit-Learn</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="#more-preprocessing" style="font-size: 80%;"><b>More preprocessing</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs031.html#frequently-used-scaling-functions" style="font-size: 80%;"><b>Frequently used scaling functions</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs032.html#example-of-own-standard-scaling" style="font-size: 80%;"><b>Example of own Standard scaling</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs033.html#min-max-scaling" style="font-size: 80%;"><b>Min-Max Scaling</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs034.html#testing-the-means-squared-error-as-function-of-complexity" style="font-size: 80%;"><b>Testing the Means Squared Error as function of Complexity</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs035.html#more-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;"><b>More preprocessing examples, Franke function and regression</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs036.html#mathematical-interpretation-of-ordinary-least-squares" style="font-size: 80%;"><b>Mathematical Interpretation of Ordinary Least Squares</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs037.html#residual-error" style="font-size: 80%;"><b>Residual Error</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs038.html#simple-case" style="font-size: 80%;"><b>Simple case</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs039.html#the-singular-value-decomposition" style="font-size: 80%;"><b>The singular value decomposition</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs040.html#linear-regression-problems" style="font-size: 80%;"><b>Linear Regression Problems</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs041.html#fixing-the-singularity" style="font-size: 80%;"><b>Fixing the singularity</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs042.html#basic-math-of-the-svd" style="font-size: 80%;"><b>Basic math of the SVD</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs043.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;"><b>The SVD, a Fantastic Algorithm</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs044.html#economy-size-svd" style="font-size: 80%;"><b>Economy-size SVD</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs045.html#codes-for-the-svd" style="font-size: 80%;"><b>Codes for the SVD</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs046.html#note-about-svd-calculations" style="font-size: 80%;"><b>Note about SVD Calculations</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs047.html#friday-september-3" style="font-size: 80%;"><b>Friday September 3</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs048.html#mathematics-of-the-svd-and-implications" style="font-size: 80%;"><b>Mathematics of the SVD and implications</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs049.html#example-matrix" style="font-size: 80%;"><b>Example Matrix</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs050.html#setting-up-the-matrix-to-be-inverted" style="font-size: 80%;"><b>Setting up the Matrix to be inverted</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs051.html#further-properties-important-for-our-analyses-later" style="font-size: 80%;"><b>Further properties (important for our analyses later)</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs052.html#meet-the-covariance-matrix" style="font-size: 80%;"><b>Meet the Covariance Matrix</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs053.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs054.html#covariance-and-correlation-matrix" style="font-size: 80%;"><b>Covariance and Correlation Matrix</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs055.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs056.html#covariance-matrix-examples" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs057.html#correlation-matrix" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs058.html#correlation-matrix-with-pandas" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs059.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs060.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs061.html#linking-with-the-svd" style="font-size: 80%;"><b>Linking with the SVD</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs062.html#what-does-it-mean" style="font-size: 80%;"><b>What does it mean?</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs063.html#and-finally-boldsymbol-x-boldsymbol-x-t" style="font-size: 80%;"><b>And finally \( \boldsymbol{X}\boldsymbol{X}^T \)</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs064.html#ridge-and-lasso-regression" style="font-size: 80%;"><b>Ridge and LASSO Regression</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs065.html#deriving-the-ridge-regression-equations" style="font-size: 80%;"><b>Deriving the Ridge Regression Equations</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs066.html#interpreting-the-ridge-results" style="font-size: 80%;"><b>Interpreting the Ridge results</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs067.html#more-interpretations" style="font-size: 80%;"><b>More interpretations</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs068.html#deriving-the-lasso-regression-equations" style="font-size: 80%;"><b>Deriving the Lasso Regression Equations</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs069.html#exercises-for-week-36-september-6-10" style="font-size: 80%;"><b>Exercises for week 36, September 6-10</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-1-adding-ridge-and-lasso-regression" style="font-size: 80%;"><b>Exercise 1: Adding Ridge and Lasso Regression</b></a></li>
|
|
<!-- navigation toc: --> <li><a href="._week35-bs069.html#exercise-linear-regression-for-a-two-dimensional-function" style="font-size: 80%;"> Exercise: Linear Regression for a two-dimensional function</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="part0030"></a>
|
|
<!-- !split -->
|
|
<h2 id="more-preprocessing" class="anchor">More preprocessing </h2>
|
|
|
|
<div class="panel panel-default">
|
|
<div class="panel-body">
|
|
<!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
|
|
<p>The <b>Normalizer</b> scales each data
|
|
point such that the feature vector has a euclidean length of one. In other words, it
|
|
projects a data point on the circle (or sphere in the case of higher dimensions) with a
|
|
radius of 1. This means every data point is scaled by a different number (by the
|
|
inverse of it’s length).
|
|
This normalization is often used when only the direction (or angle) of the data matters,
|
|
not the length of the feature vector.
|
|
</p>
|
|
|
|
<p>The <b>RobustScaler</b> works similarly to the StandardScaler in that it
|
|
ensures statistical properties for each feature that guarantee that
|
|
they are on the same scale. However, the RobustScaler uses the median
|
|
and quartiles, instead of mean and variance. This makes the
|
|
RobustScaler ignore data points that are very different from the rest
|
|
(like measurement errors). These odd data points are also called
|
|
outliers, and might often lead to trouble for other scaling
|
|
techniques.
|
|
</p>
|
|
</div>
|
|
</div>
|
|
|
|
|
|
<p>
|
|
<!-- navigation buttons at the bottom of the page -->
|
|
<ul class="pagination">
|
|
<li><a href="._week35-bs029.html">«</a></li>
|
|
<li><a href="._week35-bs000.html">1</a></li>
|
|
<li><a href="">...</a></li>
|
|
<li><a href="._week35-bs022.html">23</a></li>
|
|
<li><a href="._week35-bs023.html">24</a></li>
|
|
<li><a href="._week35-bs024.html">25</a></li>
|
|
<li><a href="._week35-bs025.html">26</a></li>
|
|
<li><a href="._week35-bs026.html">27</a></li>
|
|
<li><a href="._week35-bs027.html">28</a></li>
|
|
<li><a href="._week35-bs028.html">29</a></li>
|
|
<li><a href="._week35-bs029.html">30</a></li>
|
|
<li class="active"><a href="._week35-bs030.html">31</a></li>
|
|
<li><a href="._week35-bs031.html">32</a></li>
|
|
<li><a href="._week35-bs032.html">33</a></li>
|
|
<li><a href="._week35-bs033.html">34</a></li>
|
|
<li><a href="._week35-bs034.html">35</a></li>
|
|
<li><a href="._week35-bs035.html">36</a></li>
|
|
<li><a href="._week35-bs036.html">37</a></li>
|
|
<li><a href="._week35-bs037.html">38</a></li>
|
|
<li><a href="._week35-bs038.html">39</a></li>
|
|
<li><a href="._week35-bs039.html">40</a></li>
|
|
<li><a href="">...</a></li>
|
|
<li><a href="._week35-bs069.html">70</a></li>
|
|
<li><a href="._week35-bs031.html">»</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="https://..."><img width="250" align=right src="https://..."></a>
|
|
</footer>
|
|
-->
|
|
<center style="font-size:80%">
|
|
<!-- copyright only on the titlepage -->
|
|
</center>
|
|
</body>
|
|
</html>
|
|
|