updating, slow progress
This commit is contained in:
Morten Hjorth-Jensen
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<meta name="description" content="Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression">
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<title>Week 35: Linear Regression and Review of Statistical Analysis and Probability Theory</title>
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<title>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</title>
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<a class="navbar-brand" href="week35-bs.html">Week 35: Linear Regression and Review of Statistical Analysis and Probability Theory</a>
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<a class="navbar-brand" href="week35-bs.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a>
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</div>
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@@ -160,42 +238,59 @@ MathJax.Hub.Config({
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<li class="dropdown">
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._week35-bs001.html#___sec0" style="font-size: 80%;">Plans for week 35, August 24-28</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs002.html#___sec1" style="font-size: 80%;">Thursday August 27</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week35-bs003.html#___sec2" style="font-size: 80%;">Why Linear Regression (aka Ordinary Least Squares and family)</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week35-bs004.html#___sec3" style="font-size: 80%;">Regression analysis, overarching aims</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs005.html#___sec4" style="font-size: 80%;">Regression analysis, overarching aims II</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs006.html#___sec5" style="font-size: 80%;">Examples</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week35-bs007.html#___sec6" style="font-size: 80%;">General linear models</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs008.html#___sec7" style="font-size: 80%;">Rewriting the fitting procedure as a linear algebra problem</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week35-bs009.html#___sec8" style="font-size: 80%;">Rewriting the fitting procedure as a linear algebra problem, more details</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week35-bs010.html#___sec9" style="font-size: 80%;">Generalizing the fitting procedure as a linear algebra problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs011.html#___sec10" style="font-size: 80%;">Generalizing the fitting procedure as a linear algebra problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs012.html#___sec11" style="font-size: 80%;">Optimizing our parameters</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs013.html#___sec12" style="font-size: 80%;">Our model for the nuclear binding energies</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week35-bs014.html#___sec13" style="font-size: 80%;">Optimizing our parameters, more details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs015.html#___sec14" style="font-size: 80%;">Interpretations and optimizing our parameters</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs016.html#___sec15" style="font-size: 80%;">Interpretations and optimizing our parameters</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs017.html#___sec16" style="font-size: 80%;">Some useful matrix and vector expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs018.html#___sec17" style="font-size: 80%;">Interpretations and optimizing our parameters</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs019.html#___sec18" style="font-size: 80%;">Own code for Ordinary Least Squares</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week35-bs020.html#___sec19" style="font-size: 80%;">Adding error analysis and training set up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs021.html#___sec20" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs022.html#___sec21" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week35-bs023.html#___sec22" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs024.html#___sec23" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week35-bs025.html#___sec24" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week35-bs026.html#___sec25" style="font-size: 80%;">The \( \chi^2 \) function</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week35-bs027.html#___sec26" style="font-size: 80%;">Fitting an Equation of State for Dense Nuclear Matter</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week35-bs028.html#___sec27" style="font-size: 80%;">The code</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs029.html#___sec28" style="font-size: 80%;">Splitting our Data in Training and Test data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs030.html#___sec29" style="font-size: 80%;">The Boston housing data example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs031.html#___sec30" style="font-size: 80%;">Housing data, the code</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs032.html#___sec31" style="font-size: 80%;">Reducing the number of degrees of freedom, overarching view</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs033.html#___sec32" style="font-size: 80%;">Preprocessing our data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs034.html#___sec33" style="font-size: 80%;">More preprocessing</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs035.html#___sec34" style="font-size: 80%;">Simple preprocessing examples, Franke function and regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs036.html#___sec35" style="font-size: 80%;">Friday August 28</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs001.html#plans-for-week-35-august-24-28" style="font-size: 80%;">Plans for week 35, August 24-28</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs002.html#thursday-august-27" style="font-size: 80%;">Thursday August 27</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%;">Why Linear Regression (aka Ordinary Least Squares and family), repeat from last week</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs004.html#regression-analysis-overarching-aims" style="font-size: 80%;">Regression analysis, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs005.html#regression-analysis-overarching-aims-ii" style="font-size: 80%;">Regression analysis, overarching aims II</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs006.html#examples" style="font-size: 80%;">Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs007.html#general-linear-models" style="font-size: 80%;">General linear models</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs008.html#rewriting-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;">Rewriting the fitting procedure as a linear algebra problem</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%;">Rewriting the fitting procedure as a linear algebra problem, more details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;">Generalizing the fitting procedure as a linear algebra problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs011.html#generalizing-the-fitting-procedure-as-a-linear-algebra-problem" style="font-size: 80%;">Generalizing the fitting procedure as a linear algebra problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs012.html#optimizing-our-parameters" style="font-size: 80%;">Optimizing our parameters</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs013.html#our-model-for-the-nuclear-binding-energies" style="font-size: 80%;">Our model for the nuclear binding energies</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs014.html#optimizing-our-parameters-more-details" style="font-size: 80%;">Optimizing our parameters, more details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs018.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;">Interpretations and optimizing our parameters</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs018.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;">Interpretations and optimizing our parameters</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs017.html#some-useful-matrix-and-vector-expressions" style="font-size: 80%;">Some useful matrix and vector expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs018.html#interpretations-and-optimizing-our-parameters" style="font-size: 80%;">Interpretations and optimizing our parameters</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs019.html#own-code-for-ordinary-least-squares" style="font-size: 80%;">Own code for Ordinary Least Squares</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs020.html#adding-error-analysis-and-training-set-up" style="font-size: 80%;">Adding error analysis and training set up</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs021.html#fitting-an-equation-of-state-for-dense-nuclear-matter" style="font-size: 80%;">Fitting an Equation of State for Dense Nuclear Matter</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs022.html#the-code" style="font-size: 80%;">The code</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs023.html#splitting-our-data-in-training-and-test-data" style="font-size: 80%;">Splitting our Data in Training and Test data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs024.html#the-boston-housing-data-example" style="font-size: 80%;">The Boston housing data example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs025.html#housing-data-the-code" style="font-size: 80%;">Housing data, the code</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs026.html#reducing-the-number-of-degrees-of-freedom-overarching-view" style="font-size: 80%;">Reducing the number of degrees of freedom, overarching view</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs027.html#preprocessing-our-data" style="font-size: 80%;">Preprocessing our data</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs028.html#more-preprocessing" style="font-size: 80%;">More preprocessing</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs029.html#simple-preprocessing-examples-franke-function-and-regression" style="font-size: 80%;">Simple preprocessing examples, Franke function and regression</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs030.html#friday-september-3" style="font-size: 80%;">Friday September 3</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs031.html#the-singular-value-decomposition" style="font-size: 80%;">The singular value decomposition</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs032.html#linear-regression-problems" style="font-size: 80%;">Linear Regression Problems</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs033.html#fixing-the-singularity" style="font-size: 80%;">Fixing the singularity</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs034.html#basic-math-of-the-svd" style="font-size: 80%;">Basic math of the SVD</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs035.html#the-svd-a-fantastic-algorithm" style="font-size: 80%;">The SVD, a Fantastic Algorithm</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs036.html#economy-size-svd" style="font-size: 80%;">Economy-size SVD</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs037.html#codes-for-the-svd" style="font-size: 80%;">Codes for the SVD</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs038.html#mathematical-properties" style="font-size: 80%;">Mathematical Properties</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs039.html#friday-september-12" style="font-size: 80%;">Friday September 12</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs040.html#ridge-and-lasso-regression" style="font-size: 80%;">Ridge and LASSO Regression</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs041.html#more-on-ridge-regression" style="font-size: 80%;">More on Ridge Regression</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs042.html#interpreting-the-ridge-results" style="font-size: 80%;">Interpreting the Ridge results</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs043.html#more-interpretations" style="font-size: 80%;">More interpretations</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week35-bs044.html#a-better-understanding-of-regularization" style="font-size: 80%;">A better understanding of regularization</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week35-bs045.html#decomposing-the-ols-and-ridge-expressions" style="font-size: 80%;">Decomposing the OLS and Ridge expressions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs046.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;">Introducing the Covariance and Correlation functions</a></li>
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<!-- navigation toc: --> <li><a href="._week35-bs047.html#correlation-function-and-design-feature-matrix" style="font-size: 80%;">Correlation Function and Design/Feature Matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs048.html#covariance-matrix-examples" style="font-size: 80%;">Covariance Matrix Examples</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs049.html#correlation-matrix" style="font-size: 80%;">Correlation Matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs050.html#correlation-matrix-with-pandas" style="font-size: 80%;">Correlation Matrix with Pandas</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs051.html#correlation-matrix-with-pandas-and-the-franke-function" style="font-size: 80%;">Correlation Matrix with Pandas and the Franke function</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs052.html#rewriting-the-covariance-and-or-correlation-matrix" style="font-size: 80%;">Rewriting the Covariance and/or Correlation Matrix</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week35-bs053.html#linking-with-svd" style="font-size: 80%;">Linking with SVD</a></li>
|
||||
|
||||
</ul>
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||||
</li>
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@@ -214,7 +309,7 @@ MathJax.Hub.Config({
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<div class="jumbotron">
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<center><h1>Week 35: Linear Regression and Review of Statistical Analysis and Probability Theory</h1></center> <!-- document title -->
|
||||
<center><h1>Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</h1></center> <!-- document title -->
|
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<p>
|
||||
<!-- author(s): Morten Hjorth-Jensen -->
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||||
@@ -230,7 +325,7 @@ MathJax.Hub.Config({
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<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
|
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<br>
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<p>
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||||
<center><h4>Sep 16, 2020</h4></center> <!-- date -->
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||||
<center><h4>Aug 31, 2021</h4></center> <!-- date -->
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||||
<br>
|
||||
<p>
|
||||
|
||||
@@ -254,7 +349,7 @@ MathJax.Hub.Config({
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<li><a href="._week35-bs008.html">9</a></li>
|
||||
<li><a href="._week35-bs009.html">10</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week35-bs036.html">37</a></li>
|
||||
<li><a href="._week35-bs053.html">54</a></li>
|
||||
<li><a href="._week35-bs001.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
@@ -266,13 +361,13 @@ MathJax.Hub.Config({
|
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|
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<!-- Bootstrap footer
|
||||
<footer>
|
||||
<a href="http://..."><img width="250" align=right src="http://..."></a>
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<a href="https://..."><img width="250" align=right src="https://..."></a>
|
||||
</footer>
|
||||
-->
|
||||
|
||||
|
||||
<center style="font-size:80%">
|
||||
<!-- copyright --> © 1999-2020, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
|
||||
<!-- copyright --> © 1999-2021, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
|
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</center>
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