From 41f98033a3f2cbed3ae9c29d538b2a4c6df028db Mon Sep 17 00:00:00 2001
From: Morten Hjorth-Jensen <morten.hjorth-jensen@fys.uio.no>
Date: Mon, 2 Sep 2024 16:29:05 +0200
Subject: [PATCH] update book

---
 .../_build/.doctrees/environment.pickle       | Bin 293557 -> 293635 bytes
 .../_build/.doctrees/exercisesweek36.doctree  | Bin 32755 -> 31914 bytes
 .../html/_sources/exercisesweek36.ipynb       |  80 +++++++-----------
 .../_build/html/exercisesweek36.html          |   7 +-
 doc/LectureNotes/_build/html/searchindex.js   |   2 +-
 .../jupyter_execute/exercisesweek36.ipynb     |  80 +++++++-----------
 doc/LectureNotes/exercisesweek36.ipynb        |  80 +++++++-----------
 doc/src/week36/exercisesweek36.do.txt         |  13 +--
 8 files changed, 91 insertions(+), 171 deletions(-)

diff --git a/doc/LectureNotes/_build/.doctrees/environment.pickle b/doc/LectureNotes/_build/.doctrees/environment.pickle
index ebcc943ea8f3c576870da2b7c67741afcb9ab70f..6855f87e00880500c4ff0af2158481f0fd78cf7d 100644
GIT binary patch
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diff --git a/doc/LectureNotes/_build/html/_sources/exercisesweek36.ipynb b/doc/LectureNotes/_build/html/_sources/exercisesweek36.ipynb
index 44ada7ffb..9bcf939ab 100644
--- a/doc/LectureNotes/_build/html/_sources/exercisesweek36.ipynb
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@@ -2,7 +2,7 @@
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-   "id": "0d8dd9a1",
+   "id": "ba6ac392",
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@@ -14,7 +14,7 @@
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+   "id": "b6e88f71",
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@@ -27,7 +27,7 @@
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@@ -44,7 +44,7 @@
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+   "id": "06e77343",
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@@ -62,7 +62,7 @@
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@@ -74,7 +74,7 @@
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@@ -84,7 +84,7 @@
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+   "id": "c3916302",
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@@ -97,7 +97,7 @@
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-   "id": "e0e80d60",
+   "id": "52a3d66c",
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@@ -107,7 +107,7 @@
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-   "id": "01b82b98",
+   "id": "e537f20e",
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@@ -119,7 +119,7 @@
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-   "id": "fe87982f",
+   "id": "71e5f3a3",
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@@ -134,7 +134,7 @@
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@@ -147,7 +147,7 @@
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@@ -159,7 +159,7 @@
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@@ -171,7 +171,7 @@
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-   "id": "ba8f3cdb",
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@@ -183,41 +183,19 @@
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   {
    "cell_type": "markdown",
-   "id": "118cc5e4",
+   "id": "15007b26",
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-    "with $\\boldsymbol{I}$ being a $p\\times p$ identity matrix with the constraint that"
-   ]
-  },
-  {
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-   "id": "8e829cb2",
-   "metadata": {
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-   "source": [
-    "$$\n",
-    "\\sum_{i=0}^{p-1} \\beta_i^2 \\leq t,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "91ce6d32",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "with $t$ a finite positive number. In the optimization, we will not require that the latter is satisfied.\n",
+    "with $\\boldsymbol{I}$ being a $p\\times p$ identity matrix.\n",
     "\n",
     "The ordinary least squares result is"
    ]
   },
   {
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-   "id": "1f24acd9",
+   "id": "58f20595",
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diff --git a/doc/LectureNotes/_build/html/exercisesweek36.html b/doc/LectureNotes/_build/html/exercisesweek36.html
index edb662e21..f46b4de7b 100644
--- a/doc/LectureNotes/_build/html/exercisesweek36.html
+++ b/doc/LectureNotes/_build/html/exercisesweek36.html
@@ -490,12 +490,7 @@ a finite number larger than zero. We will not implement that here.</p>
 \[
 \hat{\boldsymbol{\beta}}_{\mathrm{Ridge}} = \left(\boldsymbol{X}^T\boldsymbol{X}+\lambda\boldsymbol{I}\right)^{-1}\boldsymbol{X}^T\boldsymbol{y},
 \]</div>
-<p>with <span class="math notranslate nohighlight">\(\boldsymbol{I}\)</span> being a <span class="math notranslate nohighlight">\(p\times p\)</span> identity matrix with the constraint that</p>
-<div class="math notranslate nohighlight">
-\[
-\sum_{i=0}^{p-1} \beta_i^2 \leq t,
-\]</div>
-<p>with <span class="math notranslate nohighlight">\(t\)</span> a finite positive number. In the optimization, we will not require that the latter is satisfied.</p>
+<p>with <span class="math notranslate nohighlight">\(\boldsymbol{I}\)</span> being a <span class="math notranslate nohighlight">\(p\times p\)</span> identity matrix.</p>
 <p>The ordinary least squares result is</p>
 <div class="math notranslate nohighlight">
 \[
diff --git a/doc/LectureNotes/_build/html/searchindex.js b/doc/LectureNotes/_build/html/searchindex.js
index e546ed064..dcf59b505 100644
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class=\"section-number\">3. </span>Linear Regression","<span class=\"section-number\">14. </span>Building a Feed Forward Neural Network","<span class=\"section-number\">15. </span>Solving Differential Equations  with Deep Learning","<span class=\"section-number\">16. </span>Convolutional Neural Networks","<span class=\"section-number\">17. </span>Recurrent neural networks: Overarching view","<span class=\"section-number\">4. </span>Ridge and Lasso Regression","<span class=\"section-number\">5. </span>Resampling Methods","<span class=\"section-number\">6. </span>Logistic Regression","<span class=\"section-number\">8. </span>Support Vector Machines, overarching aims","<span class=\"section-number\">9. </span>Decision trees, overarching aims","<span class=\"section-number\">10. </span>Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods","<span class=\"section-number\">11. </span>Basic ideas of the Principal Component Analysis (PCA)","<span class=\"section-number\">13. </span>Neural networks","<span class=\"section-number\">7. </span>Optimization, the central part of any Machine Learning algortithm","<span class=\"section-number\">12. </span>Clustering and Unsupervised Learning","Exercises week 34","Exercises week 35","Exercises week 36","Applied Data Analysis and Machine Learning","<span class=\"section-number\">2. </span>Linear Algebra, Handling of Arrays and more Python Features","Project 1 on Machine Learning, deadline October 9 (midnight), 2023","Project 2 on Machine Learning, deadline November 17 (Midnight)","Project 3 on Machine Learning, deadline December 18 (midnight), 2023","Teaching schedule with links to material","<span class=\"section-number\">1. </span>Elements of Probability Theory and Statistical Data Analysis","Teachers and Grading","Textbooks","Week 34: Introduction to the course, Logistics and Practicalities","Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression","Week 36: Linear Rgeression and Statistical 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class=\"section-number\">3. </span>Linear Regression","<span class=\"section-number\">14. </span>Building a Feed Forward Neural Network","<span class=\"section-number\">15. </span>Solving Differential Equations  with Deep Learning","<span class=\"section-number\">16. </span>Convolutional Neural Networks","<span class=\"section-number\">17. </span>Recurrent neural networks: Overarching view","<span class=\"section-number\">4. </span>Ridge and Lasso Regression","<span class=\"section-number\">5. </span>Resampling Methods","<span class=\"section-number\">6. </span>Logistic Regression","<span class=\"section-number\">8. </span>Support Vector Machines, overarching aims","<span class=\"section-number\">9. </span>Decision trees, overarching aims","<span class=\"section-number\">10. </span>Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods","<span class=\"section-number\">11. </span>Basic ideas of the Principal Component Analysis (PCA)","<span class=\"section-number\">13. </span>Neural networks","<span class=\"section-number\">7. </span>Optimization, the central part of any Machine Learning algortithm","<span class=\"section-number\">12. </span>Clustering and Unsupervised Learning","Exercises week 34","Exercises week 35","Exercises week 36","Applied Data Analysis and Machine Learning","<span class=\"section-number\">2. </span>Linear Algebra, Handling of Arrays and more Python Features","Project 1 on Machine Learning, deadline October 9 (midnight), 2023","Project 2 on Machine Learning, deadline November 17 (Midnight)","Project 3 on Machine Learning, deadline December 18 (midnight), 2023","Teaching schedule with links to material","<span class=\"section-number\">1. </span>Elements of Probability Theory and Statistical Data Analysis","Teachers and Grading","Textbooks","Week 34: Introduction to the course, Logistics and Practicalities","Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression","Week 36: Linear Rgeression and Statistical 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\ No newline at end of file
diff --git a/doc/LectureNotes/_build/jupyter_execute/exercisesweek36.ipynb b/doc/LectureNotes/_build/jupyter_execute/exercisesweek36.ipynb
index fc262fc8b..34370ec57 100644
--- a/doc/LectureNotes/_build/jupyter_execute/exercisesweek36.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/exercisesweek36.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "0d8dd9a1",
+   "id": "ba6ac392",
    "metadata": {
     "editable": true
    },
@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "11ad120e",
+   "id": "b6e88f71",
    "metadata": {
     "editable": true
    },
@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1b63c849",
+   "id": "bdcd6bb3",
    "metadata": {
     "editable": true
    },
@@ -44,7 +44,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e4b83732",
+   "id": "06e77343",
    "metadata": {
     "editable": true
    },
@@ -62,7 +62,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3c7500f",
+   "id": "5025274e",
    "metadata": {
     "editable": true
    },
@@ -74,7 +74,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "321cd815",
+   "id": "900798b7",
    "metadata": {
     "editable": true
    },
@@ -84,7 +84,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6f0ca592",
+   "id": "c3916302",
    "metadata": {
     "editable": true
    },
@@ -97,7 +97,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e0e80d60",
+   "id": "52a3d66c",
    "metadata": {
     "editable": true
    },
@@ -107,7 +107,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "01b82b98",
+   "id": "e537f20e",
    "metadata": {
     "editable": true
    },
@@ -119,7 +119,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fe87982f",
+   "id": "71e5f3a3",
    "metadata": {
     "editable": true
    },
@@ -134,7 +134,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f340d633",
+   "id": "26fe46d4",
    "metadata": {
     "editable": true
    },
@@ -147,7 +147,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5c87f4a6",
+   "id": "13bacbe7",
    "metadata": {
     "editable": true
    },
@@ -159,7 +159,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "01b7082d",
+   "id": "3ca7c852",
    "metadata": {
     "editable": true
    },
@@ -171,7 +171,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ba8f3cdb",
+   "id": "c6c84292",
    "metadata": {
     "editable": true
    },
@@ -183,41 +183,19 @@
   },
   {
    "cell_type": "markdown",
-   "id": "118cc5e4",
+   "id": "15007b26",
    "metadata": {
     "editable": true
    },
    "source": [
-    "with $\\boldsymbol{I}$ being a $p\\times p$ identity matrix with the constraint that"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "8e829cb2",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\sum_{i=0}^{p-1} \\beta_i^2 \\leq t,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "91ce6d32",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "with $t$ a finite positive number. In the optimization, we will not require that the latter is satisfied.\n",
+    "with $\\boldsymbol{I}$ being a $p\\times p$ identity matrix.\n",
     "\n",
     "The ordinary least squares result is"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "1f24acd9",
+   "id": "58f20595",
    "metadata": {
     "editable": true
    },
@@ -229,7 +207,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4f898e5c",
+   "id": "aab6662a",
    "metadata": {
     "editable": true
    },
@@ -241,7 +219,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dbd99565",
+   "id": "50358368",
    "metadata": {
     "editable": true
    },
@@ -253,7 +231,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0f0cb9de",
+   "id": "a87efdb8",
    "metadata": {
     "editable": true
    },
@@ -269,7 +247,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b74418c2",
+   "id": "23d5e69c",
    "metadata": {
     "editable": true
    },
@@ -281,7 +259,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3b0279b2",
+   "id": "f1086e51",
    "metadata": {
     "editable": true
    },
@@ -291,7 +269,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f3fc4320",
+   "id": "8cad7d30",
    "metadata": {
     "editable": true
    },
@@ -303,7 +281,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c98f5acf",
+   "id": "a7e167a0",
    "metadata": {
     "editable": true
    },
@@ -315,7 +293,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "81e8044a",
+   "id": "a7482960",
    "metadata": {
     "editable": true
    },
@@ -339,7 +317,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c96c8fc3",
+   "id": "abcb7cf9",
    "metadata": {
     "editable": true
    },
@@ -351,7 +329,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "90046598",
+   "id": "bb76fdeb",
    "metadata": {
     "editable": true
    },
@@ -361,7 +339,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5ca23883",
+   "id": "034da514",
    "metadata": {
     "editable": true
    },
@@ -373,7 +351,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b4c131be",
+   "id": "8b5613a0",
    "metadata": {
     "editable": true
    },
diff --git a/doc/LectureNotes/exercisesweek36.ipynb b/doc/LectureNotes/exercisesweek36.ipynb
index 44ada7ffb..9bcf939ab 100644
--- a/doc/LectureNotes/exercisesweek36.ipynb
+++ b/doc/LectureNotes/exercisesweek36.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "0d8dd9a1",
+   "id": "ba6ac392",
    "metadata": {
     "editable": true
    },
@@ -14,7 +14,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "11ad120e",
+   "id": "b6e88f71",
    "metadata": {
     "editable": true
    },
@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1b63c849",
+   "id": "bdcd6bb3",
    "metadata": {
     "editable": true
    },
@@ -44,7 +44,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e4b83732",
+   "id": "06e77343",
    "metadata": {
     "editable": true
    },
@@ -62,7 +62,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c3c7500f",
+   "id": "5025274e",
    "metadata": {
     "editable": true
    },
@@ -74,7 +74,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "321cd815",
+   "id": "900798b7",
    "metadata": {
     "editable": true
    },
@@ -84,7 +84,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6f0ca592",
+   "id": "c3916302",
    "metadata": {
     "editable": true
    },
@@ -97,7 +97,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e0e80d60",
+   "id": "52a3d66c",
    "metadata": {
     "editable": true
    },
@@ -107,7 +107,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "01b82b98",
+   "id": "e537f20e",
    "metadata": {
     "editable": true
    },
@@ -119,7 +119,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fe87982f",
+   "id": "71e5f3a3",
    "metadata": {
     "editable": true
    },
@@ -134,7 +134,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f340d633",
+   "id": "26fe46d4",
    "metadata": {
     "editable": true
    },
@@ -147,7 +147,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5c87f4a6",
+   "id": "13bacbe7",
    "metadata": {
     "editable": true
    },
@@ -159,7 +159,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "01b7082d",
+   "id": "3ca7c852",
    "metadata": {
     "editable": true
    },
@@ -171,7 +171,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ba8f3cdb",
+   "id": "c6c84292",
    "metadata": {
     "editable": true
    },
@@ -183,41 +183,19 @@
   },
   {
    "cell_type": "markdown",
-   "id": "118cc5e4",
+   "id": "15007b26",
    "metadata": {
     "editable": true
    },
    "source": [
-    "with $\\boldsymbol{I}$ being a $p\\times p$ identity matrix with the constraint that"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "8e829cb2",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "$$\n",
-    "\\sum_{i=0}^{p-1} \\beta_i^2 \\leq t,\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "91ce6d32",
-   "metadata": {
-    "editable": true
-   },
-   "source": [
-    "with $t$ a finite positive number. In the optimization, we will not require that the latter is satisfied.\n",
+    "with $\\boldsymbol{I}$ being a $p\\times p$ identity matrix.\n",
     "\n",
     "The ordinary least squares result is"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "1f24acd9",
+   "id": "58f20595",
    "metadata": {
     "editable": true
    },
@@ -229,7 +207,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4f898e5c",
+   "id": "aab6662a",
    "metadata": {
     "editable": true
    },
@@ -241,7 +219,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dbd99565",
+   "id": "50358368",
    "metadata": {
     "editable": true
    },
@@ -253,7 +231,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0f0cb9de",
+   "id": "a87efdb8",
    "metadata": {
     "editable": true
    },
@@ -269,7 +247,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b74418c2",
+   "id": "23d5e69c",
    "metadata": {
     "editable": true
    },
@@ -281,7 +259,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3b0279b2",
+   "id": "f1086e51",
    "metadata": {
     "editable": true
    },
@@ -291,7 +269,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f3fc4320",
+   "id": "8cad7d30",
    "metadata": {
     "editable": true
    },
@@ -303,7 +281,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c98f5acf",
+   "id": "a7e167a0",
    "metadata": {
     "editable": true
    },
@@ -315,7 +293,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "81e8044a",
+   "id": "a7482960",
    "metadata": {
     "editable": true
    },
@@ -339,7 +317,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c96c8fc3",
+   "id": "abcb7cf9",
    "metadata": {
     "editable": true
    },
@@ -351,7 +329,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "90046598",
+   "id": "bb76fdeb",
    "metadata": {
     "editable": true
    },
@@ -361,7 +339,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5ca23883",
+   "id": "034da514",
    "metadata": {
     "editable": true
    },
@@ -373,7 +351,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b4c131be",
+   "id": "8b5613a0",
    "metadata": {
     "editable": true
    },
diff --git a/doc/src/week36/exercisesweek36.do.txt b/doc/src/week36/exercisesweek36.do.txt
index 02cdefc62..603cea562 100644
--- a/doc/src/week36/exercisesweek36.do.txt
+++ b/doc/src/week36/exercisesweek36.do.txt
@@ -59,24 +59,15 @@ that $\vert\vert \bm{\beta}\vert\vert_2^2\le t$, where $t$ is
 a finite number larger than zero. We will not implement that here.
 
 === a) Expression for Ridge regression ===
+
 Show that the optimal parameters
 !bt
 \[
 \hat{\bm{\beta}}_{\mathrm{Ridge}} = \left(\bm{X}^T\bm{X}+\lambda\bm{I}\right)^{-1}\bm{X}^T\bm{y},
 \]
 !et
+with $\bm{I}$ being a $p\times p$ identity matrix.
 
-with $\bm{I}$ being a $p\times p$ identity matrix,
-
-with the constraint that
-
-!bt
-\[
-\sum_{i=0}^{p-1} \beta_i^2 \leq t,
-\]
-!et
-
-with $t$ a finite positive number. In the optimization, we will not require that the latter is satisfied.
 
 The ordinary least squares result is
 !bt