From 8abfd003ccc20d604595c403f563344c2adcad03 Mon Sep 17 00:00:00 2001
From: Morten Hjorth-Jensen <morten.hjorth-jensen@fys.uio.no>
Date: Mon, 20 Oct 2025 13:17:16 +0200
Subject: [PATCH] corrected typos

---
 .../_build/.doctrees/environment.pickle       | Bin 511606 -> 511877 bytes
 .../_build/.doctrees/exercisesweek43.doctree  | Bin 49275 -> 49366 bytes
 .../html/_sources/exercisesweek43.ipynb       |  46 +++++++--
 .../_build/html/exercisesweek43.html          |  90 +++++++++---------
 doc/LectureNotes/_build/html/searchindex.js   |   2 +-
 .../jupyter_execute/exercisesweek43.ipynb     |  46 +++++++--
 6 files changed, 122 insertions(+), 62 deletions(-)

diff --git a/doc/LectureNotes/_build/.doctrees/environment.pickle b/doc/LectureNotes/_build/.doctrees/environment.pickle
index 1e49cad6e2ef933efa53d77e0f6aca1a60ad69b0..f135f60f4be09d3c89a865363c992314bb50eecc 100644
GIT binary patch
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diff --git a/doc/LectureNotes/_build/.doctrees/exercisesweek43.doctree b/doc/LectureNotes/_build/.doctrees/exercisesweek43.doctree
index 675ddfade47eafda3c5de3ca8aa8e03b58bb7bb3..793ebcfad4c242cdd3010123e5668246d3e2a272 100644
GIT binary patch
delta 1389
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diff --git a/doc/LectureNotes/_build/html/_sources/exercisesweek43.ipynb b/doc/LectureNotes/_build/html/_sources/exercisesweek43.ipynb
index 737d0d60c..f80e8787a 100644
--- a/doc/LectureNotes/_build/html/_sources/exercisesweek43.ipynb
+++ b/doc/LectureNotes/_build/html/_sources/exercisesweek43.ipynb
@@ -32,15 +32,15 @@
     "editable": true
    },
    "source": [
-    "# Overarching aims of the exercises weeks 43 and 44\n",
+    "# Overarching aims of the exercises for week 43\n",
     "\n",
     "The aim of the exercises this week is to gain some confidence with\n",
     "ways to visualize the results of a classification problem.  We will\n",
     "target three ways of setting up the analysis. The first and simplest\n",
     "one is the\n",
-    "1. so-called confusion matrix, and the next is the\n",
+    "1. so-called confusion matrix. The next one is the so-called\n",
     "\n",
-    "2. ROC curve and finally the\n",
+    "2. ROC curve. Finally we have the\n",
     "\n",
     "3. Cumulative gain curve.\n",
     "\n",
@@ -446,7 +446,10 @@
    "id": "be9ff0b9",
    "metadata": {
     "collapsed": false,
-    "editable": true
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
    },
    "outputs": [],
    "source": [
@@ -518,7 +521,10 @@
    "id": "d20bb8be",
    "metadata": {
     "collapsed": false,
-    "editable": true
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
    },
    "outputs": [],
    "source": [
@@ -547,7 +553,10 @@
    "id": "d271f0ba",
    "metadata": {
     "collapsed": false,
-    "editable": true
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
    },
    "outputs": [],
    "source": [
@@ -589,7 +598,10 @@
    "id": "3b045d56",
    "metadata": {
     "collapsed": false,
-    "editable": true
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
    },
    "outputs": [],
    "source": [
@@ -611,7 +623,25 @@
    ]
   }
  ],
- "metadata": {},
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.15"
+  }
+ },
  "nbformat": 4,
  "nbformat_minor": 5
 }
diff --git a/doc/LectureNotes/_build/html/exercisesweek43.html b/doc/LectureNotes/_build/html/exercisesweek43.html
index 8d4bd1b6b..9dbce18b1 100644
--- a/doc/LectureNotes/_build/html/exercisesweek43.html
+++ b/doc/LectureNotes/_build/html/exercisesweek43.html
@@ -414,7 +414,7 @@ document.write(`
             <nav aria-label="Page">
                 <ul class="visible nav section-nav flex-column">
 <li class="toc-h1 nav-item toc-entry"><a class="reference internal nav-link" href="#">Exercises week 43</a></li>
-<li class="toc-h1 nav-item toc-entry"><a class="reference internal nav-link" href="#overarching-aims-of-the-exercises-weeks-43-and-44">Overarching aims of the exercises weeks 43 and 44</a><ul class="visible nav section-nav flex-column">
+<li class="toc-h1 nav-item toc-entry"><a class="reference internal nav-link" href="#overarching-aims-of-the-exercises-for-week-43">Overarching aims of the exercises for week 43</a><ul class="visible nav section-nav flex-column">
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#confusion-matrix">Confusion Matrix</a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#roc-curve">ROC Curve</a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#cumulative-gain">Cumulative Gain</a></li>
@@ -446,15 +446,15 @@ doconce format html exercisesweek43.do.txt  -->
 <p><strong>October 20-24, 2025</strong></p>
 <p>Date: <strong>Deadline Friday October 24 at midnight</strong></p>
 </section>
-<section class="tex2jax_ignore mathjax_ignore" id="overarching-aims-of-the-exercises-weeks-43-and-44">
-<h1>Overarching aims of the exercises weeks 43 and 44<a class="headerlink" href="#overarching-aims-of-the-exercises-weeks-43-and-44" title="Link to this heading">#</a></h1>
+<section class="tex2jax_ignore mathjax_ignore" id="overarching-aims-of-the-exercises-for-week-43">
+<h1>Overarching aims of the exercises for week 43<a class="headerlink" href="#overarching-aims-of-the-exercises-for-week-43" title="Link to this heading">#</a></h1>
 <p>The aim of the exercises this week is to gain some confidence with
 ways to visualize the results of a classification problem.  We will
 target three ways of setting up the analysis. The first and simplest
 one is the</p>
 <ol class="arabic simple">
-<li><p>so-called confusion matrix, and the next is the</p></li>
-<li><p>ROC curve and finally the</p></li>
+<li><p>so-called confusion matrix. The next one is the so-called</p></li>
+<li><p>ROC curve. Finally we have the</p></li>
 <li><p>Cumulative gain curve.</p></li>
 </ol>
 <p>We will use Logistic Regression as method for the classification in
@@ -615,41 +615,41 @@ At the end it sets up the confusion matrix and the ROC and cumulative gain curve
 Feel free to use these functionalities (we don’t expect you to write your own code for say the confusion matrix).</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>%matplotlib inline
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="o">%</span><span class="k">matplotlib</span> inline
 
-import matplotlib.pyplot as plt
-import numpy as np
-from sklearn.model_selection import  train_test_split 
-# from sklearn.datasets import fill in the data set
-from sklearn.linear_model import LogisticRegression
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span>  <span class="n">train_test_split</span> 
+<span class="c1"># from sklearn.datasets import fill in the data set</span>
+<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <span class="n">LogisticRegression</span>
 
-# Load the data, fill inn
-mydata.data = ?
+<span class="c1"># Load the data, fill inn</span>
+<span class="n">mydata</span><span class="o">.</span><span class="n">data</span> <span class="o">=</span> <span class="o">?</span>
 
-X_train, X_test, y_train, y_test = train_test_split(mydata.data,cancer.target,random_state=0)
-print(X_train.shape)
-print(X_test.shape)
-# Logistic Regression
-# define which type of problem, binary or multiclass
-logreg = LogisticRegression(solver=&#39;lbfgs&#39;)
-logreg.fit(X_train, y_train)
+<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span> <span class="o">=</span> <span class="n">train_test_split</span><span class="p">(</span><span class="n">mydata</span><span class="o">.</span><span class="n">data</span><span class="p">,</span><span class="n">cancer</span><span class="o">.</span><span class="n">target</span><span class="p">,</span><span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">X_train</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">X_test</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
+<span class="c1"># Logistic Regression</span>
+<span class="c1"># define which type of problem, binary or multiclass</span>
+<span class="n">logreg</span> <span class="o">=</span> <span class="n">LogisticRegression</span><span class="p">(</span><span class="n">solver</span><span class="o">=</span><span class="s1">&#39;lbfgs&#39;</span><span class="p">)</span>
+<span class="n">logreg</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>
 
-from sklearn.preprocessing import LabelEncoder
-from sklearn.model_selection import cross_validate
-#Cross validation
-accuracy = cross_validate(logreg,X_test,y_test,cv=10)[&#39;test_score&#39;]
-print(accuracy)
-print(&quot;Test set accuracy with Logistic Regression: {:.2f}&quot;.format(logreg.score(X_test,y_test)))
+<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">LabelEncoder</span>
+<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">cross_validate</span>
+<span class="c1">#Cross validation</span>
+<span class="n">accuracy</span> <span class="o">=</span> <span class="n">cross_validate</span><span class="p">(</span><span class="n">logreg</span><span class="p">,</span><span class="n">X_test</span><span class="p">,</span><span class="n">y_test</span><span class="p">,</span><span class="n">cv</span><span class="o">=</span><span class="mi">10</span><span class="p">)[</span><span class="s1">&#39;test_score&#39;</span><span class="p">]</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">accuracy</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Test set accuracy with Logistic Regression: </span><span class="si">{:.2f}</span><span class="s2">&quot;</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">logreg</span><span class="o">.</span><span class="n">score</span><span class="p">(</span><span class="n">X_test</span><span class="p">,</span><span class="n">y_test</span><span class="p">)))</span>
 
-import scikitplot as skplt
-y_pred = logreg.predict(X_test)
-skplt.metrics.plot_confusion_matrix(y_test, y_pred, normalize=True)
-plt.show()
-y_probas = logreg.predict_proba(X_test)
-skplt.metrics.plot_roc(y_test, y_probas)
-plt.show()
-skplt.metrics.plot_cumulative_gain(y_test, y_probas)
-plt.show()
+<span class="kn">import</span> <span class="nn">scikitplot</span> <span class="k">as</span> <span class="nn">skplt</span>
+<span class="n">y_pred</span> <span class="o">=</span> <span class="n">logreg</span><span class="o">.</span><span class="n">predict</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
+<span class="n">skplt</span><span class="o">.</span><span class="n">metrics</span><span class="o">.</span><span class="n">plot_confusion_matrix</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_pred</span><span class="p">,</span> <span class="n">normalize</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+<span class="n">y_probas</span> <span class="o">=</span> <span class="n">logreg</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">X_test</span><span class="p">)</span>
+<span class="n">skplt</span><span class="o">.</span><span class="n">metrics</span><span class="o">.</span><span class="n">plot_roc</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_probas</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+<span class="n">skplt</span><span class="o">.</span><span class="n">metrics</span><span class="o">.</span><span class="n">plot_cumulative_gain</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">y_probas</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
 </pre></div>
 </div>
 </div>
@@ -664,9 +664,9 @@ plt.show()
 the MNIST data set and just specialize to two numbers. To do so you can use the following code lines</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>from sklearn.datasets import load_digits
-digits = load_digits(n_class=2) # Load only two classes, e.g., 0 and 1
-X, y = digits.data, digits.target
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">load_digits</span>
+<span class="n">digits</span> <span class="o">=</span> <span class="n">load_digits</span><span class="p">(</span><span class="n">n_class</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span> <span class="c1"># Load only two classes, e.g., 0 and 1</span>
+<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">digits</span><span class="o">.</span><span class="n">data</span><span class="p">,</span> <span class="n">digits</span><span class="o">.</span><span class="n">target</span>
 </pre></div>
 </div>
 </div>
@@ -678,8 +678,8 @@ n_classes=2. You can also control the number of samples, features,
 informative features, redundant features, and more.</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>from sklearn.datasets import make_classification
-X, y = make_classification(n_samples=1000, n_features=20, n_informative=10, n_redundant=5, n_classes=2, random_state=42)
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">make_classification</span>
+<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">make_classification</span><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="mi">1000</span><span class="p">,</span> <span class="n">n_features</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">n_informative</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">n_redundant</span><span class="o">=</span><span class="mi">5</span><span class="p">,</span> <span class="n">n_classes</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>
 </pre></div>
 </div>
 </div>
@@ -696,10 +696,10 @@ the exercises from weeks 41 and 42. This is a three-class data set and
 you can set it up using <strong>scikit-learn</strong>,</p>
 <div class="cell docutils container">
 <div class="cell_input docutils container">
-<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>from sklearn.datasets import load_iris
-iris = load_iris()
-X = iris.data  # Features
-y = iris.target # Target labels
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">load_iris</span>
+<span class="n">iris</span> <span class="o">=</span> <span class="n">load_iris</span><span class="p">()</span>
+<span class="n">X</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">data</span>  <span class="c1"># Features</span>
+<span class="n">y</span> <span class="o">=</span> <span class="n">iris</span><span class="o">.</span><span class="n">target</span> <span class="c1"># Target labels</span>
 </pre></div>
 </div>
 </div>
@@ -775,7 +775,7 @@ gain curve for this (or other) multiclass data set.</p>
   <nav class="bd-toc-nav page-toc">
     <ul class="visible nav section-nav flex-column">
 <li class="toc-h1 nav-item toc-entry"><a class="reference internal nav-link" href="#">Exercises week 43</a></li>
-<li class="toc-h1 nav-item toc-entry"><a class="reference internal nav-link" href="#overarching-aims-of-the-exercises-weeks-43-and-44">Overarching aims of the exercises weeks 43 and 44</a><ul class="visible nav section-nav flex-column">
+<li class="toc-h1 nav-item toc-entry"><a class="reference internal nav-link" href="#overarching-aims-of-the-exercises-for-week-43">Overarching aims of the exercises for week 43</a><ul class="visible nav section-nav flex-column">
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#confusion-matrix">Confusion Matrix</a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#roc-curve">ROC Curve</a></li>
 <li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#cumulative-gain">Cumulative Gain</a></li>
diff --git a/doc/LectureNotes/_build/html/searchindex.js b/doc/LectureNotes/_build/html/searchindex.js
index 3b84933cb..20a909c83 100644
--- a/doc/LectureNotes/_build/html/searchindex.js
+++ b/doc/LectureNotes/_build/html/searchindex.js
@@ -1 +1 @@
-Search.setIndex({"alltitles": {"1a)": [[18, "a"]], "3a)": [[18, "id1"]], "3b)": [[18, "b"]], "4a)": [[18, "id2"]], "4b)": [[18, "id3"]], "A Classification Tree": [[9, "a-classification-tree"]], "A Frequentist approach to data analysis": [[0, "a-frequentist-approach-to-data-analysis"], [32, "a-frequentist-approach-to-data-analysis"]], "A better approach": [[8, "a-better-approach"]], "A first summary": [[32, "a-first-summary"]], "A more compact expression": [[37, "a-more-compact-expression"], [38, "a-more-compact-expression"]], "A new Cost Function": [[36, "a-new-cost-function"]], "A possible implementation of a neural network": [[41, "a-possible-implementation-of-a-neural-network"]], "A quick Reminder on Lagrangian Multipliers": [[8, "a-quick-reminder-on-lagrangian-multipliers"]], "A simple example": [[4, "a-simple-example"]], "A soft classifier": [[8, "a-soft-classifier"]], "A top-down perspective on Neural networks": [[1, "a-top-down-perspective-on-neural-networks"], [40, "a-top-down-perspective-on-neural-networks"]], "A way to Read the Bias-Variance Tradeoff": [[36, "a-way-to-read-the-bias-variance-tradeoff"], [37, "a-way-to-read-the-bias-variance-tradeoff"]], "ADAM algorithm, taken from Goodfellow et al": [[35, "adam-algorithm-taken-from-goodfellow-et-al"]], "ADAM optimizer": [[13, "adam-optimizer"], [35, "id2"]], "Accuracy": [[35, "accuracy"]], "Activation functions": [[12, "activation-functions"], [38, "activation-functions"], [40, "activation-functions"], [40, "id3"], [41, "activation-functions"], [41, "id1"]], "Activation functions, Logistic and Hyperbolic ones": [[38, "activation-functions-logistic-and-hyperbolic-ones"], [40, "activation-functions-logistic-and-hyperbolic-ones"]], "Activation functions, examples": [[41, "activation-functions-examples"]], "AdaGrad Properties": [[35, "adagrad-properties"]], "AdaGrad Update Rule Derivation": [[35, "adagrad-update-rule-derivation"]], "AdaGrad algorithm, taken from Goodfellow et al": [[35, "adagrad-algorithm-taken-from-goodfellow-et-al"]], "Adam Optimizer": [[35, "adam-optimizer"]], "Adam vs. AdaGrad and RMSProp": [[35, "adam-vs-adagrad-and-rmsprop"]], "Adam: Bias Correction": [[35, "adam-bias-correction"]], "Adam: Exponential Moving Averages (Moments)": [[35, "adam-exponential-moving-averages-moments"]], "Adam: Update Rule Derivation": [[35, "adam-update-rule-derivation"]], "Adaptive boosting: AdaBoost, Basic Algorithm": [[10, "adaptive-boosting-adaboost-basic-algorithm"]], "Adaptivity Across Dimensions": [[35, "adaptivity-across-dimensions"]], "Adding Neural Networks": [[38, "adding-neural-networks"]], "Adding a hidden layer": [[39, "adding-a-hidden-layer"], [40, "adding-a-hidden-layer"]], "Adding error analysis and training set up": [[32, "adding-error-analysis-and-training-set-up"], [33, "adding-error-analysis-and-training-set-up"]], "Adjust hyperparameters": [[1, "adjust-hyperparameters"], [40, "adjust-hyperparameters"]], "Algorithms and codes for Adagrad, RMSprop and Adam": [[35, "algorithms-and-codes-for-adagrad-rmsprop-and-adam"]], "Algorithms for Setting up Decision Trees": [[9, "algorithms-for-setting-up-decision-trees"]], "An Overview of Ensemble Methods": [[10, "an-overview-of-ensemble-methods"]], "An extrapolation example": [[4, "an-extrapolation-example"]], "An optimization/minimization problem": [[32, "an-optimization-minimization-problem"]], "Analyzing the last results": [[39, "analyzing-the-last-results"], [40, "analyzing-the-last-results"]], "And a similar example using Tensorflow with Keras": [[41, "and-a-similar-example-using-tensorflow-with-keras"]], "And finally  \\boldsymbol{X}\\boldsymbol{X}^T": [[33, "and-finally-boldsymbol-x-boldsymbol-x-t"]], "And finally ADAM": [[35, "and-finally-adam"]], "And what about using neural networks?": [[32, "and-what-about-using-neural-networks"]], "Another Example from Scikit-Learn\u2019s Repository": [[36, "another-example-from-scikit-learn-s-repository"], [37, "another-example-from-scikit-learn-s-repository"]], "Another Example, now with a polynomial fit": [[34, "another-example-now-with-a-polynomial-fit"]], "Another example, the moons again": [[9, "another-example-the-moons-again"]], "Applied Data Analysis and Machine Learning": [[24, null]], "Artificial neurons": [[38, "artificial-neurons"], [39, "artificial-neurons"]], "Assumptions made": [[36, "assumptions-made"]], "Autocorrelation function": [[29, "autocorrelation-function"]], "Automatic differentiation": [[13, "automatic-differentiation"], [39, "automatic-differentiation"]], "Automatic differentiation through examples": [[39, "automatic-differentiation-through-examples"]], "Back propagation": [[41, "back-propagation"]], "Back propagation and automatic differentiation": [[41, "back-propagation-and-automatic-differentiation"]], "Back to Ridge and LASSO Regression": [[33, "back-to-ridge-and-lasso-regression"], [34, "back-to-ridge-and-lasso-regression"]], "Back to the Cancer Data": [[11, "back-to-the-cancer-data"]], "Background literature": [[26, "background-literature"], [27, "background-literature"]], "Bagging": [[10, "bagging"]], "Bagging Examples": [[10, "bagging-examples"]], "Basic Matrix Features": [[25, "basic-matrix-features"]], "Basic ideas of the Principal Component Analysis (PCA)": [[11, null]], "Basic math of the SVD": [[5, "basic-math-of-the-svd"], [33, "basic-math-of-the-svd"], [34, "basic-math-of-the-svd"]], "Basics": [[7, "basics"], [37, "basics"], [38, "basics"]], "Basics of a tree": [[9, "basics-of-a-tree"]], "Basics of an NN": [[39, "basics-of-an-nn"]], "Batch Normalization": [[1, "batch-normalization"], [40, "batch-normalization"]], "Batches and mini-batches": [[35, "batches-and-mini-batches"]], "Bayes\u2019 Theorem and Ridge and Lasso Regression": [[5, "bayes-theorem-and-ridge-and-lasso-regression"]], "Boosting, a Bird\u2019s Eye View": [[10, "boosting-a-bird-s-eye-view"]], "Bootstrap": [[6, "bootstrap"]], "Bringing it together": [[39, "bringing-it-together"], [40, "bringing-it-together"]], "Bringing it together, first back propagation equation": [[12, "bringing-it-together-first-back-propagation-equation"]], "Building a Feed Forward Neural Network": [[1, null]], "Building a neural network code": [[40, "building-a-neural-network-code"]], "Building a tree, regression": [[9, "building-a-tree-regression"]], "Building neural networks in Tensorflow and Keras": [[1, "building-neural-networks-in-tensorflow-and-keras"], [40, "building-neural-networks-in-tensorflow-and-keras"], [41, "building-neural-networks-in-tensorflow-and-keras"]], "Building our own  neural network code": [[41, "building-our-own-neural-network-code"]], "But none of these can compete with Newton\u2019s method": [[35, "but-none-of-these-can-compete-with-newton-s-method"]], "CNNs in more detail, building convolutional neural networks in Tensorflow and Keras": [[3, "cnns-in-more-detail-building-convolutional-neural-networks-in-tensorflow-and-keras"]], "Cancer Data again now with Decision Trees and other Methods": [[9, "cancer-data-again-now-with-decision-trees-and-other-methods"]], "Chain rule": [[39, "chain-rule"]], "Chain rule, forward and reverse modes": [[39, "chain-rule-forward-and-reverse-modes"]], "Challenge: Choosing a Fixed Learning Rate": [[35, "challenge-choosing-a-fixed-learning-rate"]], "Choose cost function and optimizer": [[1, "choose-cost-function-and-optimizer"], [40, "choose-cost-function-and-optimizer"]], "Class of functions we can approximate": [[39, "class-of-functions-we-can-approximate"]], "Classical PCA Theorem": [[11, "classical-pca-theorem"]], "Classification and Regression, writing our own neural network code": [[27, "classification-and-regression-writing-our-own-neural-network-code"]], "Classification problems": [[37, "classification-problems"], [38, "classification-problems"]], "Clustering and Unsupervised Learning": [[14, null]], "Code Example for Cross-validation and k-fold Cross-validation": [[36, "code-example-for-cross-validation-and-k-fold-cross-validation"], [37, "code-example-for-cross-validation-and-k-fold-cross-validation"]], "Code example": [[39, "code-example"], [40, "code-example"]], "Code example for the Bootstrap method": [[36, "code-example-for-the-bootstrap-method"]], "Code for SVD and Inversion of Matrices": [[5, "code-for-svd-and-inversion-of-matrices"]], "Code with a Number of Minibatches which varies": [[35, "code-with-a-number-of-minibatches-which-varies"]], "Codes and Approaches": [[14, "codes-and-approaches"]], "Codes for the SVD": [[5, "codes-for-the-svd"], [33, "codes-for-the-svd"], [34, "codes-for-the-svd"]], "Coding Setup and Linear Regression": [[15, "coding-setup-and-linear-regression"]], "Collect and pre-process data": [[1, "collect-and-pre-process-data"], [40, "collect-and-pre-process-data"], [40, "id2"], [41, "collect-and-pre-process-data"]], "Communication channels": [[32, "communication-channels"]], "Compact expressions": [[39, "compact-expressions"], [40, "compact-expressions"]], "Compare  Bagging on Trees with Random Forests": [[10, "compare-bagging-on-trees-with-random-forests"]], "Comparing with a numerical scheme": [[2, "comparing-with-a-numerical-scheme"], [41, "comparing-with-a-numerical-scheme"]], "Comparison with OLS": [[34, "comparison-with-ols"]], "Completing the list": [[39, "completing-the-list"], [40, "completing-the-list"]], "Computation of gradients": [[35, "computation-of-gradients"]], "Computing the Gini index": [[9, "computing-the-gini-index"]], "Conditions on convex functions": [[34, "conditions-on-convex-functions"]], "Confidence Intervals": [[36, "confidence-intervals"]], "Confusion Matrix": [[23, "confusion-matrix"]], "Conjugate gradient method": [[13, "conjugate-gradient-method"]], "Convergence rates": [[35, "convergence-rates"]], "Convex function": [[34, "convex-function"]], "Convex functions": [[13, "convex-functions"], [34, "convex-functions"]], "Convolution Examples: Polynomial multiplication": [[3, "convolution-examples-polynomial-multiplication"]], "Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)": [[3, "convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms"]], "Convolutional Neural Network": [[12, "convolutional-neural-network"], [38, "convolutional-neural-network"], [39, "convolutional-neural-network"]], "Convolutional Neural Networks": [[3, null]], "Correlation Function and Design/Feature Matrix": [[33, "correlation-function-and-design-feature-matrix"]], "Correlation Matrix": [[11, "correlation-matrix"], [33, "correlation-matrix"]], "Correlation Matrix with Pandas": [[33, "correlation-matrix-with-pandas"]], "Cost functions": [[40, "cost-functions"], [41, "cost-functions"]], "Counting the number of floating point operations": [[39, "counting-the-number-of-floating-point-operations"]], "Course Format": [[32, "course-format"]], "Course setting": [[28, null]], "Covariance Matrix Examples": [[33, "covariance-matrix-examples"]], "Covariance and Correlation Matrix": [[33, "covariance-and-correlation-matrix"]], "Cross-validation": [[6, "cross-validation"]], "Cross-validation in brief": [[36, "cross-validation-in-brief"], [37, "cross-validation-in-brief"]], "Cumulative Gain": [[23, "cumulative-gain"]], "Deadlines for projects (tentative)": [[32, "deadlines-for-projects-tentative"]], "Decision trees, overarching aims": [[9, null]], "Deep Neural Networks": [[35, "deep-neural-networks"]], "Deep learning methods": [[32, "deep-learning-methods"]], "Define model and architecture": [[1, "define-model-and-architecture"], [40, "define-model-and-architecture"]], "Defining intermediate operations": [[39, "defining-intermediate-operations"]], "Defining the cost function": [[1, "defining-the-cost-function"], [40, "defining-the-cost-function"]], "Defining the problem": [[41, "defining-the-problem"]], "Definitions": [[19, "definitions"], [39, "definitions"], [40, "definitions"]], "Deliverables": [[15, "deliverables"], [16, "deliverables"], [19, "deliverables"], [20, "deliverables"], [26, "deliverables"], [27, "deliverables"]], "Derivation of the AdaGrad Algorithm": [[35, "derivation-of-the-adagrad-algorithm"]], "Derivative of the cost function": [[39, "derivative-of-the-cost-function"], [40, "derivative-of-the-cost-function"]], "Derivatives and the chain rule": [[12, "derivatives-and-the-chain-rule"], [39, "derivatives-and-the-chain-rule"], [40, "derivatives-and-the-chain-rule"]], "Derivatives in terms of z_j^L": [[39, "derivatives-in-terms-of-z-j-l"], [40, "derivatives-in-terms-of-z-j-l"]], "Derivatives of the hidden layer": [[39, "derivatives-of-the-hidden-layer"], [40, "derivatives-of-the-hidden-layer"]], "Derivatives, example 1": [[33, "derivatives-example-1"]], "Deriving OLS from a probability distribution": [[5, "deriving-ols-from-a-probability-distribution"], [36, "deriving-ols-from-a-probability-distribution"]], "Deriving and Implementing Ordinary Least Squares": [[16, "deriving-and-implementing-ordinary-least-squares"]], "Deriving and Implementing Ridge Regression": [[17, "deriving-and-implementing-ridge-regression"]], "Deriving the  Lasso Regression Equations": [[33, "deriving-the-lasso-regression-equations"], [34, "deriving-the-lasso-regression-equations"], [34, "id6"]], "Deriving the  Ridge Regression Equations": [[33, "deriving-the-ridge-regression-equations"], [34, "deriving-the-ridge-regression-equations"], [34, "id3"]], "Deriving the back propagation code for a multilayer perceptron model": [[12, "deriving-the-back-propagation-code-for-a-multilayer-perceptron-model"]], "Developing a code for doing neural networks with back propagation": [[1, "developing-a-code-for-doing-neural-networks-with-back-propagation"], [40, "developing-a-code-for-doing-neural-networks-with-back-propagation"]], "Diagonalize the sample covariance matrix to obtain the principal components": [[11, "diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components"]], "Different kernels and Mercer\u2019s theorem": [[8, "different-kernels-and-mercer-s-theorem"]], "Disadvantages": [[9, "disadvantages"]], "Discriminative Modeling": [[32, "discriminative-modeling"]], "Discussing the correlation data": [[38, "discussing-the-correlation-data"]], "Does Logistic Regression do a better Job?": [[38, "does-logistic-regression-do-a-better-job"]], "Domains and probabilities": [[29, "domains-and-probabilities"]], "Dropout": [[1, "dropout"], [40, "dropout"]], "ELU function": [[40, "elu-function"], [41, "elu-function"]], "Economy-size SVD": [[33, "economy-size-svd"], [34, "economy-size-svd"]], "Elements of Probability Theory and Statistical Data Analysis": [[29, null]], "Empirical Evidence: Convergence Time and Memory in Practice": [[35, "empirical-evidence-convergence-time-and-memory-in-practice"]], "Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods": [[10, null]], "Entropy and the ID3 algorithm": [[9, "entropy-and-the-id3-algorithm"]], "Essential elements of ML": [[32, "essential-elements-of-ml"]], "Evaluate model performance on test data": [[1, "evaluate-model-performance-on-test-data"], [40, "evaluate-model-performance-on-test-data"]], "Example 2": [[33, "example-2"]], "Example 3": [[33, "example-3"]], "Example 4": [[33, "example-4"]], "Example Matrix": [[33, "example-matrix"], [34, "example-matrix"]], "Example code for Bias-Variance tradeoff": [[36, "example-code-for-bias-variance-tradeoff"]], "Example code for Logistic Regression": [[37, "example-code-for-logistic-regression"], [38, "example-code-for-logistic-regression"]], "Example of discriminative modeling, taken from Generative Deep Learning by David Foster": [[32, "example-of-discriminative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of generative modeling, taken from Generative Deep Learning by David Foster": [[32, "example-of-generative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of own Standard scaling": [[33, "example-of-own-standard-scaling"]], "Example relevant for the exercises": [[33, "example-relevant-for-the-exercises"]], "Example: Exponential decay": [[2, "example-exponential-decay"], [41, "example-exponential-decay"]], "Example: Population growth": [[2, "example-population-growth"], [41, "example-population-growth"]], "Example: Solving the one dimensional Poisson equation": [[41, "example-solving-the-one-dimensional-poisson-equation"]], "Example: Solving the wave equation with Neural Networks": [[41, "example-solving-the-wave-equation-with-neural-networks"]], "Example: The diffusion equation": [[2, "example-the-diffusion-equation"], [41, "example-the-diffusion-equation"]], "Example: binary classification problem": [[1, "example-binary-classification-problem"], [40, "example-binary-classification-problem"]], "Examples": [[32, "examples"]], "Examples of XOR, OR and AND gates": [[38, "examples-of-xor-or-and-and-gates"]], "Examples of likelihood functions used in logistic regression and neural networks": [[7, "examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks"]], "Examples of likelihood functions used in logistic regression and nueral networks": [[37, "examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks"]], "Exercise 1": [[21, "exercise-1"]], "Exercise 1 - Choice of model and degrees of freedom": [[17, "exercise-1-choice-of-model-and-degrees-of-freedom"]], "Exercise 1 - Finding the derivative of Matrix-Vector expressions": [[16, "exercise-1-finding-the-derivative-of-matrix-vector-expressions"]], "Exercise 1 - Github Setup": [[15, "exercise-1-github-setup"]], "Exercise 1 - Understand the feed forward pass": [[22, "exercise-1-understand-the-feed-forward-pass"]], "Exercise 1, scale your data": [[18, "exercise-1-scale-your-data"]], "Exercise 1: Creating the report document": [[20, "exercise-1-creating-the-report-document"]], "Exercise 1: Expectation values for ordinary least squares expressions": [[19, "exercise-1-expectation-values-for-ordinary-least-squares-expressions"]], "Exercise 1: Including more data": [[39, "exercise-1-including-more-data"]], "Exercise 1: Setting up various Python environments": [[0, "exercise-1-setting-up-various-python-environments"]], "Exercise 2": [[21, "exercise-2"]], "Exercise 2 - Deriving the expression for OLS": [[16, "exercise-2-deriving-the-expression-for-ols"]], "Exercise 2 - Deriving the expression for Ridge Regression": [[17, "exercise-2-deriving-the-expression-for-ridge-regression"]], "Exercise 2 - Gradient with one layer using autograd": [[22, "exercise-2-gradient-with-one-layer-using-autograd"]], "Exercise 2 - Setting up a Github repository": [[15, "exercise-2-setting-up-a-github-repository"]], "Exercise 2, calculate the gradients": [[18, "exercise-2-calculate-the-gradients"]], "Exercise 2: Adding good figures": [[20, "exercise-2-adding-good-figures"]], "Exercise 2: Expectation values for Ridge regression": [[19, "exercise-2-expectation-values-for-ridge-regression"]], "Exercise 2: Extended program": [[39, "exercise-2-extended-program"]], "Exercise 2: making your own data and exploring scikit-learn": [[0, "exercise-2-making-your-own-data-and-exploring-scikit-learn"]], "Exercise 3": [[21, "exercise-3"]], "Exercise 3 - Creating feature matrix and implementing OLS using the analytical expression": [[16, "exercise-3-creating-feature-matrix-and-implementing-ols-using-the-analytical-expression"]], "Exercise 3 - Fitting an OLS model to data": [[15, "exercise-3-fitting-an-ols-model-to-data"]], "Exercise 3 - Gradient with one layer writing backpropagation by hand": [[22, "exercise-3-gradient-with-one-layer-writing-backpropagation-by-hand"]], "Exercise 3 - Scaling data": [[17, "exercise-3-scaling-data"]], "Exercise 3 - Setting up a Python virtual environment": [[15, "exercise-3-setting-up-a-python-virtual-environment"]], "Exercise 3, using the analytical formulae for OLS and Ridge regression to find the optimal paramters \\boldsymbol{\\theta}": [[18, "exercise-3-using-the-analytical-formulae-for-ols-and-ridge-regression-to-find-the-optimal-paramters-boldsymbol-theta"]], "Exercise 3: Deriving the expression for the Bias-Variance Trade-off": [[19, "exercise-3-deriving-the-expression-for-the-bias-variance-trade-off"]], "Exercise 3: Normalizing our data": [[0, "exercise-3-normalizing-our-data"]], "Exercise 3: Writing an abstract and introduction": [[20, "exercise-3-writing-an-abstract-and-introduction"]], "Exercise 4 - Custom activation for each layer": [[21, "exercise-4-custom-activation-for-each-layer"]], "Exercise 4 - Fitting a polynomial": [[16, "exercise-4-fitting-a-polynomial"]], "Exercise 4 - Gradient with two layers writing backpropagation by hand": [[22, "exercise-4-gradient-with-two-layers-writing-backpropagation-by-hand"]], "Exercise 4 - Implementing Ridge Regression": [[17, "exercise-4-implementing-ridge-regression"]], "Exercise 4 - Testing multiple hyperparameters": [[17, "exercise-4-testing-multiple-hyperparameters"]], "Exercise 4 - The train-test split": [[15, "exercise-4-the-train-test-split"]], "Exercise 4, Implementing the simplest form for gradient descent": [[18, "exercise-4-implementing-the-simplest-form-for-gradient-descent"]], "Exercise 4: Adding Ridge Regression": [[0, "exercise-4-adding-ridge-regression"]], "Exercise 4: Computing the Bias and Variance": [[19, "exercise-4-computing-the-bias-and-variance"]], "Exercise 4: Making the code available and presentable": [[20, "exercise-4-making-the-code-available-and-presentable"]], "Exercise 5 - Comparing your code with sklearn": [[16, "exercise-5-comparing-your-code-with-sklearn"]], "Exercise 5 - Gradient with any number of layers writing backpropagation by hand": [[22, "exercise-5-gradient-with-any-number-of-layers-writing-backpropagation-by-hand"]], "Exercise 5 - Processing multiple inputs at once": [[21, "exercise-5-processing-multiple-inputs-at-once"]], "Exercise 5, Ridge regression and a new Synthetic Dataset": [[18, "exercise-5-ridge-regression-and-a-new-synthetic-dataset"]], "Exercise 5: Analytical exercises": [[0, "exercise-5-analytical-exercises"]], "Exercise 5: Interpretation of scaling and metrics": [[19, "exercise-5-interpretation-of-scaling-and-metrics"]], "Exercise 5: Referencing": [[20, "exercise-5-referencing"]], "Exercise 6 - Batched inputs": [[22, "exercise-6-batched-inputs"]], "Exercise 6 - Predicting on real data": [[21, "exercise-6-predicting-on-real-data"]], "Exercise 7 - Training": [[22, "exercise-7-training"]], "Exercise 7 - Training on real data (Optional)": [[21, "exercise-7-training-on-real-data-optional"]], "Exercise 8 (Optional) - Object orientation": [[22, "exercise-8-optional-object-orientation"]], "Exercise a)": [[23, "exercise-a"]], "Exercise b)": [[23, "exercise-b"]], "Exercise c) week 43": [[23, "exercise-c-week-43"]], "Exercise:  Cross-validation as resampling techniques, adding more complexity": [[6, "exercise-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Exercise: Analysis of real data": [[6, "exercise-analysis-of-real-data"]], "Exercise: Bias-variance trade-off and resampling techniques": [[6, "exercise-bias-variance-trade-off-and-resampling-techniques"]], "Exercise: Lasso Regression on the Franke function  with resampling": [[6, "exercise-lasso-regression-on-the-franke-function-with-resampling"]], "Exercise: Ordinary Least Square (OLS) on the Franke function": [[6, "exercise-ordinary-least-square-ols-on-the-franke-function"]], "Exercise: Ridge Regression on the Franke function  with resampling": [[6, "exercise-ridge-regression-on-the-franke-function-with-resampling"]], "Exercises": [[0, "exercises"], [23, "exercises"]], "Exercises and Projects": [[6, "exercises-and-projects"]], "Exercises and lab session week 43": [[41, "exercises-and-lab-session-week-43"]], "Exercises week 34": [[15, null]], "Exercises week 35": [[16, null]], "Exercises week 36": [[17, null]], "Exercises week 37": [[18, null]], "Exercises week 38": [[19, null]], "Exercises week 39": [[20, null]], "Exercises week 41": [[21, null]], "Exercises week 42": [[22, null]], "Exercises week 43": [[23, null]], "Expectation value and variance": [[36, "expectation-value-and-variance"]], "Expectation value and variance for \\boldsymbol{\\theta}": [[36, "expectation-value-and-variance-for-boldsymbol-theta"]], "Expectation values": [[29, "expectation-values"]], "Explicit derivatives": [[39, "explicit-derivatives"], [40, "explicit-derivatives"]], "Exploding gradients": [[40, "exploding-gradients"]], "Extending to more predictors": [[37, "extending-to-more-predictors"], [38, "extending-to-more-predictors"]], "Extending to more than one variable": [[34, "extending-to-more-than-one-variable"]], "Extremely useful tools, strongly recommended": [[32, "extremely-useful-tools-strongly-recommended"]], "Feed-forward neural networks": [[12, "feed-forward-neural-networks"], [38, "feed-forward-neural-networks"], [39, "feed-forward-neural-networks"]], "Feed-forward pass": [[1, "feed-forward-pass"], [40, "feed-forward-pass"]], "Final back propagating equation": [[12, "final-back-propagating-equation"], [39, "final-back-propagating-equation"], [40, "final-back-propagating-equation"]], "Final derivatives": [[39, "final-derivatives"]], "Final expression": [[39, "final-expression"], [40, "final-expression"]], "Final expressions for the biases of the hidden layer": [[39, "final-expressions-for-the-biases-of-the-hidden-layer"], [40, "final-expressions-for-the-biases-of-the-hidden-layer"]], "Final technicalities I": [[41, "final-technicalities-i"]], "Final technicalities II": [[41, "final-technicalities-ii"]], "Final technicalities III": [[41, "final-technicalities-iii"]], "Final technicalities IV": [[41, "final-technicalities-iv"]], "Finding the Limit": [[36, "finding-the-limit"]], "Fine-tuning neural network hyperparameters": [[1, "fine-tuning-neural-network-hyperparameters"], [40, "fine-tuning-neural-network-hyperparameters"]], "First network example, simple percepetron with one input": [[39, "first-network-example-simple-percepetron-with-one-input"]], "Fitting an Equation of State for Dense Nuclear Matter": [[0, "fitting-an-equation-of-state-for-dense-nuclear-matter"]], "Fixing the singularity": [[33, "fixing-the-singularity"], [34, "fixing-the-singularity"]], "Format for electronic delivery of report and programs": [[26, "format-for-electronic-delivery-of-report-and-programs"], [27, "format-for-electronic-delivery-of-report-and-programs"]], "Forward and reverse modes": [[39, "forward-and-reverse-modes"]], "Frequently used scaling functions": [[33, "frequently-used-scaling-functions"], [35, "frequently-used-scaling-functions"]], "From OLS to Ridge and Lasso": [[34, "from-ols-to-ridge-and-lasso"]], "From one to many layers, the universal approximation theorem": [[12, "from-one-to-many-layers-the-universal-approximation-theorem"]], "Full object-oriented implementation": [[40, "full-object-oriented-implementation"]], "Functionality in Scikit-Learn": [[33, "functionality-in-scikit-learn"], [35, "functionality-in-scikit-learn"]], "Further Dimensionality Remarks": [[3, "further-dimensionality-remarks"]], "Further properties (important for our analyses later)": [[5, "further-properties-important-for-our-analyses-later"], [33, "further-properties-important-for-our-analyses-later"], [34, "further-properties-important-for-our-analyses-later"]], "Gaussian Elimination": [[25, "gaussian-elimination"]], "General Features": [[9, "general-features"]], "General linear models and linear algebra": [[32, "general-linear-models-and-linear-algebra"]], "Generalizing the fitting procedure as a linear algebra problem": [[32, "generalizing-the-fitting-procedure-as-a-linear-algebra-problem"], [32, "id1"]], "Generative Adversarial Networks": [[4, "generative-adversarial-networks"]], "Generative Models": [[4, "generative-models"]], "Generative Versus Discriminative Modeling": [[32, "generative-versus-discriminative-modeling"]], "Geometric Interpretation and link with Singular Value Decomposition": [[11, "geometric-interpretation-and-link-with-singular-value-decomposition"]], "Getting serious, the  back propagation equations for a neural network": [[39, "getting-serious-the-back-propagation-equations-for-a-neural-network"]], "Getting started with project 1": [[20, "getting-started-with-project-1"]], "Gradient Boosting, Classification Example": [[10, "gradient-boosting-classification-example"]], "Gradient Boosting, Examples of Regression": [[10, "gradient-boosting-examples-of-regression"]], "Gradient Clipping": [[1, "gradient-clipping"], [40, "gradient-clipping"]], "Gradient Descent Example": [[34, "id1"], [35, "id1"]], "Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent": [[10, "gradient-boosting-basics-with-steepest-descent-functional-gradient-descent"]], "Gradient descent": [[2, "gradient-descent"], [41, "gradient-descent"]], "Gradient descent and Ridge": [[34, "gradient-descent-and-ridge"], [35, "gradient-descent-and-ridge"]], "Gradient descent and revisiting Ordinary Least Squares from last week": [[35, "gradient-descent-and-revisiting-ordinary-least-squares-from-last-week"]], "Gradient descent example": [[34, "gradient-descent-example"], [35, "gradient-descent-example"]], "Gradient expressions": [[39, "gradient-expressions"], [40, "gradient-expressions"]], "Grading": [[30, "grading"], [30, "id2"], [32, "grading"]], "Hidden layers": [[40, "hidden-layers"]], "Homogeneous data": [[40, "homogeneous-data"]], "How to take derivatives of Matrix-Vector expressions": [[16, "how-to-take-derivatives-of-matrix-vector-expressions"]], "Hyperplanes and all that": [[8, "hyperplanes-and-all-that"]], "Identifying Terms": [[36, "identifying-terms"]], "Illustration of a single perceptron model and a multi-perceptron model": [[38, "illustration-of-a-single-perceptron-model-and-a-multi-perceptron-model"], [39, "illustration-of-a-single-perceptron-model-and-a-multi-perceptron-model"]], "Important Matrix and vector handling packages": [[25, "important-matrix-and-vector-handling-packages"]], "Important observations": [[39, "important-observations"], [40, "important-observations"]], "Important technicalities: More on Rescaling data": [[33, "important-technicalities-more-on-rescaling-data"]], "Improving gradient descent with momentum": [[35, "improving-gradient-descent-with-momentum"]], "Improving performance": [[1, "improving-performance"], [40, "improving-performance"]], "In general not this simple": [[39, "in-general-not-this-simple"]], "In summary": [[30, "in-summary"]], "Including Stochastic Gradient Descent with Autograd": [[13, "including-stochastic-gradient-descent-with-autograd"], [35, "including-stochastic-gradient-descent-with-autograd"]], "Including more classes": [[37, "including-more-classes"], [38, "including-more-classes"]], "Incremental PCA": [[11, "incremental-pca"]], "Independent and Identically Distributed (iid)": [[36, "independent-and-identically-distributed-iid"]], "Inputs to the activation function": [[39, "inputs-to-the-activation-function"], [40, "inputs-to-the-activation-function"]], "Insights from the paper by Glorot and Bengio": [[40, "insights-from-the-paper-by-glorot-and-bengio"]], "Installing R, C++, cython or Julia": [[32, "installing-r-c-cython-or-julia"]], "Installing R, C++, cython, Numba etc": [[32, "installing-r-c-cython-numba-etc"]], "Instructor information": [[30, "instructor-information"]], "Interpretations and optimizing our parameters": [[32, "interpretations-and-optimizing-our-parameters"], [32, "id2"], [32, "id3"], [33, "interpretations-and-optimizing-our-parameters"], [33, "id1"], [33, "id2"]], "Interpreting the Ridge results": [[33, "interpreting-the-ridge-results"], [34, "interpreting-the-ridge-results"], [34, "id4"]], "Introducing JAX": [[13, "introducing-jax"]], "Introducing the Covariance and Correlation functions": [[11, "introducing-the-covariance-and-correlation-functions"], [33, "introducing-the-covariance-and-correlation-functions"]], "Introduction": [[0, "introduction"], [6, "introduction"], [24, "introduction"], [25, "introduction"]], "Introduction to Neural networks": [[38, "introduction-to-neural-networks"], [39, "introduction-to-neural-networks"]], "Introduction to numerical projects": [[26, "introduction-to-numerical-projects"], [27, "introduction-to-numerical-projects"]], "Is the Logistic activation function (Sigmoid)  our choice?": [[40, "is-the-logistic-activation-function-sigmoid-our-choice"]], "Iterative Fitting, Classification and AdaBoost": [[10, "iterative-fitting-classification-and-adaboost"]], "Iterative Fitting, Regression and Squared-error Cost Function": [[10, "iterative-fitting-regression-and-squared-error-cost-function"]], "Kernel PCA": [[11, "kernel-pca"]], "Kernels and non-linearity": [[8, "kernels-and-non-linearity"]], "LU Decomposition, the inverse of a matrix": [[25, "lu-decomposition-the-inverse-of-a-matrix"]], "Lab sessions Tuesday and Wednesday": [[38, "lab-sessions-tuesday-and-wednesday"]], "Lab sessions on Tuesday and Wednesday": [[39, "lab-sessions-on-tuesday-and-wednesday"]], "Lab sessions week 39": [[37, "lab-sessions-week-39"]], "Lasso Regression": [[34, "lasso-regression"]], "Lasso case": [[34, "lasso-case"]], "Layers": [[1, "layers"], [40, "layers"]], "Layers used to build CNNs": [[3, "layers-used-to-build-cnns"]], "Layout of a neural network with three hidden layers": [[39, "layout-of-a-neural-network-with-three-hidden-layers"]], "Layout of a neural network with three hidden layers (last layer = l=L=4, first layer l=0)": [[40, "layout-of-a-neural-network-with-three-hidden-layers-last-layer-l-l-4-first-layer-l-0"]], "Layout of a simple neural network with no hidden layer": [[39, "layout-of-a-simple-neural-network-with-no-hidden-layer"], [40, "layout-of-a-simple-neural-network-with-no-hidden-layer"]], "Layout of a simple neural network with one hidden layer": [[39, "layout-of-a-simple-neural-network-with-one-hidden-layer"], [40, "layout-of-a-simple-neural-network-with-one-hidden-layer"]], "Layout of a simple neural network with two input nodes, one  hidden layer and one output node": [[39, "layout-of-a-simple-neural-network-with-two-input-nodes-one-hidden-layer-and-one-output-node"]], "Layout of a simple neural network with two input nodes, one  hidden layer with two hidden noeds and one output node": [[40, "layout-of-a-simple-neural-network-with-two-input-nodes-one-hidden-layer-with-two-hidden-noeds-and-one-output-node"]], "Layout of input to first hidden layer l=1 from input layer l=0": [[40, "layout-of-input-to-first-hidden-layer-l-1-from-input-layer-l-0"]], "Learning goals": [[15, "learning-goals"], [16, "learning-goals"], [17, "learning-goals"], [18, "learning-goals"], [19, "learning-goals"], [20, "learning-goals"]], "Learning outcomes": [[24, "learning-outcomes"], [32, "learning-outcomes"]], "Learning rate methods": [[40, "learning-rate-methods"], [41, "learning-rate-methods"]], "Lecture Monday  October 20": [[41, "lecture-monday-october-20"]], "Lecture Monday  October 6": [[39, "lecture-monday-october-6"]], "Lecture Monday September 29, 2025": [[38, "lecture-monday-september-29-2025"]], "Lecture October 13, 2025": [[40, "lecture-october-13-2025"]], "Lecture material": [[37, "lecture-material"]], "Lecture material: Writing a code which implements a feed-forward neural network": [[40, "lecture-material-writing-a-code-which-implements-a-feed-forward-neural-network"]], "Lectures and ComputerLab": [[32, "lectures-and-computerlab"]], "Limitations of NNs": [[40, "limitations-of-nns"]], "Limitations of supervised learning with deep networks": [[1, "limitations-of-supervised-learning-with-deep-networks"], [40, "limitations-of-supervised-learning-with-deep-networks"]], "Linear Algebra, Handling of Arrays and more Python Features": [[25, null]], "Linear Regression": [[0, null]], "Linear Regression Problems": [[33, "linear-regression-problems"], [34, "linear-regression-problems"]], "Linear Regression and  the SVD": [[34, "linear-regression-and-the-svd"]], "Linear Regression, basic elements": [[0, "linear-regression-basic-elements"]], "Linear classifier": [[37, "linear-classifier"]], "Linking Bayes\u2019 Theorem with Ridge and Lasso Regression": [[5, "linking-bayes-theorem-with-ridge-and-lasso-regression"]], "Linking the regression analysis with a statistical interpretation": [[5, "linking-the-regression-analysis-with-a-statistical-interpretation"], [36, "linking-the-regression-analysis-with-a-statistical-interpretation"]], "Linking with the SVD": [[5, "linking-with-the-svd"], [33, "linking-with-the-svd"]], "Links to relevant courses at the University of Oslo": [[31, "links-to-relevant-courses-at-the-university-of-oslo"]], "Logistic Regression": [[7, null], [7, "id1"], [37, "logistic-regression"]], "Logistic Regression, from last week": [[38, "logistic-regression-from-last-week"]], "Logistic function as the root of problems": [[40, "logistic-function-as-the-root-of-problems"]], "MNIST and GANs": [[4, "mnist-and-gans"]], "Machine Learning": [[32, "machine-learning"]], "Machine learning": [[24, "machine-learning"]], "Main textbooks": [[32, "main-textbooks"]], "Making a tree": [[9, "making-a-tree"]], "Making your own Bootstrap: Changing the Level of the Decision Tree": [[10, "making-your-own-bootstrap-changing-the-level-of-the-decision-tree"]], "Making your own test-train splitting": [[33, "making-your-own-test-train-splitting"]], "Material for exercises week 35": [[33, "material-for-exercises-week-35"]], "Material for lab sessions  sessions Tuesday and Wednesday": [[34, "material-for-lab-sessions-sessions-tuesday-and-wednesday"]], "Material for lecture Monday September 2": [[34, "material-for-lecture-monday-september-2"]], "Material for lecture Monday September 8": [[35, "material-for-lecture-monday-september-8"]], "Material for the lab sessions": [[35, "material-for-the-lab-sessions"], [36, "material-for-the-lab-sessions"]], "Material for the lab sessions on Tuesday and Wednesday": [[40, "material-for-the-lab-sessions-on-tuesday-and-wednesday"]], "Material for the lecture on Monday October 6, 2025": [[39, "material-for-the-lecture-on-monday-october-6-2025"]], "Mathematical Interpretation of Ordinary Least Squares": [[5, "mathematical-interpretation-of-ordinary-least-squares"], [33, "mathematical-interpretation-of-ordinary-least-squares"], [34, "mathematical-interpretation-of-ordinary-least-squares"]], "Mathematical model": [[38, "mathematical-model"], [38, "id1"], [38, "id2"], [38, "id3"], [38, "id4"]], "Mathematical optimization of convex functions": [[8, "mathematical-optimization-of-convex-functions"]], "Mathematics of CNNs": [[3, "mathematics-of-cnns"]], "Mathematics of deep learning": [[39, "mathematics-of-deep-learning"], [40, "mathematics-of-deep-learning"]], "Mathematics of deep learning and neural networks": [[39, "mathematics-of-deep-learning-and-neural-networks"]], "Mathematics of the SVD and implications": [[5, "mathematics-of-the-svd-and-implications"], [33, "mathematics-of-the-svd-and-implications"], [34, "mathematics-of-the-svd-and-implications"]], "Matrices in Python": [[32, "matrices-in-python"]], "Matrix  multiplication": [[1, "matrix-multiplication"], [40, "matrix-multiplication"]], "Matrix multiplications": [[40, "matrix-multiplications"]], "Matrix-vector notation": [[38, "matrix-vector-notation"]], "Matrix-vector notation  and activation": [[12, "matrix-vector-notation-and-activation"], [38, "matrix-vector-notation-and-activation"]], "Maximum Likelihood Estimation (MLE)": [[36, "maximum-likelihood-estimation-mle"]], "Maximum likelihood": [[37, "maximum-likelihood"], [38, "maximum-likelihood"]], "Meet the  covariance!": [[29, "meet-the-covariance"]], "Meet the Covariance Matrix": [[5, "meet-the-covariance-matrix"], [33, "meet-the-covariance-matrix"]], "Meet the Hessian Matrix": [[33, "meet-the-hessian-matrix"]], "Meet the Pandas": [[32, "meet-the-pandas"]], "Memory Usage and Scalability": [[35, "memory-usage-and-scalability"]], "Memory constraints": [[35, "memory-constraints"]], "Min-Max Scaling": [[33, "min-max-scaling"]], "Minimization process": [[41, "minimization-process"]], "Minimizing the cost function using gradient descent and automatic differentiation": [[41, "minimizing-the-cost-function-using-gradient-descent-and-automatic-differentiation"]], "Minimizing the cross entropy": [[37, "minimizing-the-cross-entropy"], [38, "minimizing-the-cross-entropy"]], "Momentum based GD": [[13, "momentum-based-gd"], [35, "momentum-based-gd"]], "More classes": [[37, "more-classes"], [38, "more-classes"]], "More complicated Example: The Ising model": [[6, "more-complicated-example-the-ising-model"]], "More complicated function": [[39, "more-complicated-function"]], "More considerations": [[39, "more-considerations"], [40, "more-considerations"]], "More details": [[41, "more-details"], [41, "id4"]], "More examples on bootstrap and cross-validation and errors": [[36, "more-examples-on-bootstrap-and-cross-validation-and-errors"], [37, "more-examples-on-bootstrap-and-cross-validation-and-errors"]], "More interpretations": [[33, "more-interpretations"], [34, "more-interpretations"], [34, "id5"]], "More limitations": [[40, "more-limitations"]], "More on Dimensionalities": [[3, "more-on-dimensionalities"]], "More on Rescaling data": [[6, "more-on-rescaling-data"]], "More on Steepest descent": [[34, "more-on-steepest-descent"]], "More on activation functions, output layers": [[40, "more-on-activation-functions-output-layers"], [41, "more-on-activation-functions-output-layers"]], "More on convex functions": [[34, "more-on-convex-functions"]], "More on the general approximation theorem": [[39, "more-on-the-general-approximation-theorem"]], "More preprocessing": [[33, "more-preprocessing"], [35, "more-preprocessing"]], "More technicalities": [[41, "more-technicalities"]], "More top-down perspectives": [[40, "more-top-down-perspectives"]], "Motivation for Adaptive Step Sizes": [[35, "motivation-for-adaptive-step-sizes"]], "Multiclass classification": [[40, "multiclass-classification"], [41, "multiclass-classification"]], "Multilayer perceptrons": [[12, "multilayer-perceptrons"], [38, "multilayer-perceptrons"], [39, "multilayer-perceptrons"]], "Multivariable functions": [[39, "multivariable-functions"]], "Network requirements": [[2, "network-requirements"], [41, "network-requirements"]], "Neural Networks vs CNNs": [[3, "neural-networks-vs-cnns"]], "Neural network types": [[38, "neural-network-types"], [39, "neural-network-types"]], "Neural networks": [[12, null]], "New expression for the derivative": [[39, "new-expression-for-the-derivative"]], "Non-Convex Problems": [[35, "non-convex-problems"]], "Note about SVD Calculations": [[33, "note-about-svd-calculations"], [34, "note-about-svd-calculations"]], "Note on Scikit-Learn": [[34, "note-on-scikit-learn"]], "Numerical experiments and the covariance, central limit theorem": [[29, "numerical-experiments-and-the-covariance-central-limit-theorem"]], "Numpy and arrays": [[25, "numpy-and-arrays"], [32, "numpy-and-arrays"]], "Numpy examples and Important Matrix and vector handling packages": [[32, "numpy-examples-and-important-matrix-and-vector-handling-packages"]], "Optimization and Deep learning": [[37, "optimization-and-deep-learning"], [38, "optimization-and-deep-learning"]], "Optimization and gradient descent, the central part of any Machine Learning algortithm": [[34, "optimization-and-gradient-descent-the-central-part-of-any-machine-learning-algortithm"]], "Optimization, the central part of any Machine Learning algortithm": [[13, null], [37, "optimization-the-central-part-of-any-machine-learning-algortithm"], [38, "optimization-the-central-part-of-any-machine-learning-algortithm"]], "Optimizing our parameters": [[32, "optimizing-our-parameters"]], "Optimizing our parameters, more details": [[32, "optimizing-our-parameters-more-details"]], "Optimizing the cost function": [[1, "optimizing-the-cost-function"], [40, "optimizing-the-cost-function"]], "Optimizing the parameters": [[39, "optimizing-the-parameters"], [40, "optimizing-the-parameters"]], "Optional (Note that you should include at least two of these in the report):": [[27, "optional-note-that-you-should-include-at-least-two-of-these-in-the-report"]], "Ordinary Differential Equations first": [[41, "ordinary-differential-equations-first"]], "Organizing our data": [[0, "organizing-our-data"], [32, "organizing-our-data"]], "Other Matrix and Vector Operations": [[25, "other-matrix-and-vector-operations"]], "Other Types of Recurrent Neural Networks": [[4, "other-types-of-recurrent-neural-networks"]], "Other courses on Data science and Machine Learning  at UiO": [[32, "other-courses-on-data-science-and-machine-learning-at-uio"]], "Other courses on Data science and Machine Learning  at UiO, contn": [[32, "other-courses-on-data-science-and-machine-learning-at-uio-contn"]], "Other ingredients of a neural network": [[39, "other-ingredients-of-a-neural-network"]], "Other measures in classification studies": [[38, "other-measures-in-classification-studies"]], "Other measures: Precision, Recall, and the F_1 Measure": [[23, "other-measures-precision-recall-and-the-f-1-measure"]], "Other parameters": [[39, "other-parameters"]], "Other popular texts": [[32, "other-popular-texts"]], "Other techniques": [[11, "other-techniques"]], "Other types of networks": [[12, "other-types-of-networks"], [38, "other-types-of-networks"], [39, "other-types-of-networks"]], "Other ways of visualizing the trees": [[9, "other-ways-of-visualizing-the-trees"]], "Our model for the nuclear binding energies": [[32, "our-model-for-the-nuclear-binding-energies"]], "Output layer": [[39, "output-layer"], [40, "output-layer"]], "Overarching aims of the exercises this week": [[21, "overarching-aims-of-the-exercises-this-week"], [22, "overarching-aims-of-the-exercises-this-week"]], "Overarching aims of the exercises weeks 43 and 44": [[23, "overarching-aims-of-the-exercises-weeks-43-and-44"]], "Overarching view of a neural network": [[39, "overarching-view-of-a-neural-network"]], "Overview of first week": [[32, "overview-of-first-week"]], "Overview video on Stochastic Gradient Descent (SGD)": [[35, "overview-video-on-stochastic-gradient-descent-sgd"]], "Own code for Ordinary Least Squares": [[32, "own-code-for-ordinary-least-squares"], [33, "own-code-for-ordinary-least-squares"]], "PCA and scikit-learn": [[11, "pca-and-scikit-learn"]], "Pandas AI": [[32, "pandas-ai"]], "Parameters of neural networks": [[39, "parameters-of-neural-networks"]], "Part a : Ordinary Least Square (OLS) for the Runge function": [[26, "part-a-ordinary-least-square-ols-for-the-runge-function"]], "Part a): Analytical warm-up": [[27, "part-a-analytical-warm-up"]], "Part b): Writing your own Neural Network code": [[27, "part-b-writing-your-own-neural-network-code"]], "Part b: Adding Ridge regression for the Runge function": [[26, "part-b-adding-ridge-regression-for-the-runge-function"]], "Part c): Testing against other software libraries": [[27, "part-c-testing-against-other-software-libraries"]], "Part c: Writing your own gradient descent code": [[26, "part-c-writing-your-own-gradient-descent-code"]], "Part d): Testing different activation functions and depths of the neural network": [[27, "part-d-testing-different-activation-functions-and-depths-of-the-neural-network"]], "Part d: Including momentum and more advanced ways to update the learning the rate": [[26, "part-d-including-momentum-and-more-advanced-ways-to-update-the-learning-the-rate"]], "Part e): Testing different norms": [[27, "part-e-testing-different-norms"]], "Part e: Writing our own code for Lasso regression": [[26, "part-e-writing-our-own-code-for-lasso-regression"]], "Part f): Classification  analysis using neural networks": [[27, "part-f-classification-analysis-using-neural-networks"]], "Part f: Stochastic gradient descent": [[26, "part-f-stochastic-gradient-descent"]], "Part g) Critical evaluation of the various algorithms": [[27, "part-g-critical-evaluation-of-the-various-algorithms"]], "Part g: Bias-variance trade-off and resampling techniques": [[26, "part-g-bias-variance-trade-off-and-resampling-techniques"]], "Part h): Cross-validation as resampling techniques, adding more complexity": [[26, "part-h-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Partial Differential Equations": [[2, "partial-differential-equations"], [41, "partial-differential-equations"]], "Plan for week 39, September 22-26, 2025": [[37, "plan-for-week-39-september-22-26-2025"]], "Plan for week 41, October 6-10": [[39, "plan-for-week-41-october-6-10"]], "Plans for week 35": [[33, "plans-for-week-35"]], "Plans for week 36": [[34, "plans-for-week-36"]], "Plans for week 37, lecture Monday": [[35, "plans-for-week-37-lecture-monday"]], "Plans for week 38, lecture Monday September 15": [[36, "plans-for-week-38-lecture-monday-september-15"]], "Plans for week 43": [[41, "plans-for-week-43"]], "Plotting the Histogram": [[36, "plotting-the-histogram"]], "Plotting the mean value for each group": [[37, "plotting-the-mean-value-for-each-group"]], "Practical tips": [[13, "practical-tips"], [35, "practical-tips"]], "Practicalities": [[30, "practicalities"], [30, "id1"]], "Preamble: Note on writing reports, using reference material, AI and other tools": [[26, "preamble-note-on-writing-reports-using-reference-material-ai-and-other-tools"], [27, "preamble-note-on-writing-reports-using-reference-material-ai-and-other-tools"]], "Predicting New Points With A Trained Recurrent Neural Network": [[4, "predicting-new-points-with-a-trained-recurrent-neural-network"]], "Preprocessing our data": [[33, "preprocessing-our-data"]], "Prerequisites": [[32, "prerequisites"]], "Prerequisites and background": [[24, "prerequisites-and-background"]], "Prerequisites: Collect and pre-process data": [[3, "prerequisites-collect-and-pre-process-data"]], "Probability Distribution Functions": [[29, "probability-distribution-functions"]], "Program example for gradient descent with Ridge Regression": [[34, "program-example-for-gradient-descent-with-ridge-regression"], [35, "program-example-for-gradient-descent-with-ridge-regression"]], "Program for stochastic gradient": [[13, "program-for-stochastic-gradient"]], "Project 1 on Machine Learning, deadline October 6 (midnight), 2025": [[26, null]], "Project 2 on Machine Learning, deadline November 10 (Midnight)": [[27, null]], "Properties of PDFs": [[29, "properties-of-pdfs"]], "Pros and cons": [[35, "pros-and-cons"]], "Pros and cons of trees, pros": [[9, "pros-and-cons-of-trees-pros"]], "Python installers": [[24, "python-installers"], [32, "python-installers"]], "RMS prop": [[13, "rms-prop"]], "RMSProp algorithm, taken from Goodfellow et al": [[35, "rmsprop-algorithm-taken-from-goodfellow-et-al"]], "RMSProp: Adaptive Learning Rates": [[35, "rmsprop-adaptive-learning-rates"]], "RMSprop for adaptive learning rate with Stochastic Gradient Descent": [[35, "rmsprop-for-adaptive-learning-rate-with-stochastic-gradient-descent"]], "ROC Curve": [[23, "roc-curve"]], "Random Numbers": [[29, "random-numbers"]], "Random forests": [[10, "random-forests"]], "Randomized PCA": [[11, "randomized-pca"]], "Reading material": [[32, "reading-material"]], "Reading recommendations": [[40, "reading-recommendations"]], "Reading recommendations:": [[33, "reading-recommendations"]], "Reading suggestions week 34": [[32, "reading-suggestions-week-34"]], "Readings and Videos": [[36, "readings-and-videos"]], "Readings and Videos, logistic regression": [[37, "readings-and-videos-logistic-regression"]], "Readings and Videos, resampling methods": [[37, "readings-and-videos-resampling-methods"]], "Readings and Videos:": [[35, "readings-and-videos"], [39, "readings-and-videos"]], "Readings and videos": [[40, "readings-and-videos"]], "Recurrent neural networks": [[12, "recurrent-neural-networks"], [38, "recurrent-neural-networks"], [39, "recurrent-neural-networks"]], "Recurrent neural networks: Overarching view": [[4, null]], "Reducing the number of degrees of freedom, overarching view": [[0, "reducing-the-number-of-degrees-of-freedom-overarching-view"], [33, "reducing-the-number-of-degrees-of-freedom-overarching-view"]], "Reducing the number of operations": [[39, "reducing-the-number-of-operations"]], "Reformulating the problem": [[2, "reformulating-the-problem"], [41, "reformulating-the-problem"]], "Regression Case": [[10, "regression-case"]], "Regression analysis and resampling methods": [[26, "regression-analysis-and-resampling-methods"]], "Regression analysis, overarching aims": [[32, "regression-analysis-overarching-aims"]], "Regression analysis, overarching aims II": [[32, "regression-analysis-overarching-aims-ii"]], "Regularization": [[1, "regularization"], [40, "regularization"]], "Relevance": [[38, "relevance"], [40, "relevance"]], "Reminder about the gradient machinery from project 1": [[27, "reminder-about-the-gradient-machinery-from-project-1"]], "Reminder from last week": [[33, "reminder-from-last-week"]], "Reminder from last week: First network example, simple percepetron with one input": [[40, "reminder-from-last-week-first-network-example-simple-percepetron-with-one-input"]], "Reminder on Newton-Raphson\u2019s method": [[34, "reminder-on-newton-raphson-s-method"]], "Reminder on Statistics": [[6, "reminder-on-statistics"]], "Reminder on books with hands-on material and codes": [[39, "reminder-on-books-with-hands-on-material-and-codes"], [40, "reminder-on-books-with-hands-on-material-and-codes"]], "Reminder on different scaling methods": [[35, "reminder-on-different-scaling-methods"]], "Reminder on the chain rule and gradients": [[39, "reminder-on-the-chain-rule-and-gradients"]], "Replace or not": [[13, "replace-or-not"], [35, "replace-or-not"]], "Required Analysis:": [[27, "required-analysis"]], "Required Technologies": [[24, "required-technologies"]], "Resampling Methods": [[6, null]], "Resampling and the Bias-Variance Trade-off": [[19, "resampling-and-the-bias-variance-trade-off"]], "Resampling approaches can be computationally expensive": [[36, "resampling-approaches-can-be-computationally-expensive"], [37, "resampling-approaches-can-be-computationally-expensive"]], "Resampling methods": [[6, "id1"], [36, "resampling-methods"], [36, "id2"], [37, "resampling-methods"], [37, "id1"]], "Resampling methods: Bootstrap": [[36, "resampling-methods-bootstrap"], [37, "resampling-methods-bootstrap"]], "Resampling methods: Bootstrap approach": [[36, "resampling-methods-bootstrap-approach"]], "Resampling methods: Bootstrap background": [[36, "resampling-methods-bootstrap-background"]], "Resampling methods: Bootstrap steps": [[36, "resampling-methods-bootstrap-steps"]], "Resampling methods: More Bootstrap background": [[36, "resampling-methods-more-bootstrap-background"]], "Residual Error": [[33, "residual-error"], [34, "residual-error"]], "Resources on differential equations and deep learning": [[2, "resources-on-differential-equations-and-deep-learning"], [41, "resources-on-differential-equations-and-deep-learning"]], "Revisiting Ordinary Least Squares": [[34, "revisiting-ordinary-least-squares"]], "Revisiting our Linear Regression Solvers": [[13, "revisiting-our-linear-regression-solvers"]], "Revisiting our Logistic Regression case": [[37, "revisiting-our-logistic-regression-case"], [38, "revisiting-our-logistic-regression-case"]], "Rewriting the Covariance and/or Correlation Matrix": [[33, "rewriting-the-covariance-and-or-correlation-matrix"]], "Rewriting the \\delta-function": [[36, "rewriting-the-delta-function"]], "Rewriting the fitting procedure as a linear algebra problem": [[32, "rewriting-the-fitting-procedure-as-a-linear-algebra-problem"]], "Rewriting the fitting procedure as a linear algebra problem, more details": [[32, "rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details"]], "Ridge Regression": [[34, "ridge-regression"]], "Ridge and LASSO Regression": [[33, "ridge-and-lasso-regression"], [34, "ridge-and-lasso-regression"], [34, "id2"]], "Ridge and Lasso Regression": [[5, null], [5, "id1"]], "SGD example": [[35, "sgd-example"]], "SGD vs Full-Batch GD: Convergence Speed and Memory Comparison": [[35, "sgd-vs-full-batch-gd-convergence-speed-and-memory-comparison"]], "SVD analysis": [[34, "svd-analysis"]], "Same code but now with momentum gradient descent": [[13, "same-code-but-now-with-momentum-gradient-descent"], [35, "same-code-but-now-with-momentum-gradient-descent"], [35, "id3"], [35, "id4"]], "Schedule first week": [[32, "schedule-first-week"]], "Schematic Regression Procedure": [[9, "schematic-regression-procedure"]], "Second moment of the gradient": [[35, "second-moment-of-the-gradient"]], "September 15-19": [[19, "september-15-19"]], "Setting up a Multi-layer perceptron model for classification": [[40, "setting-up-a-multi-layer-perceptron-model-for-classification"]], "Setting up the Back propagation algorithm": [[12, "setting-up-the-back-propagation-algorithm"]], "Setting up the Back propagation algorithm, part 3": [[39, "setting-up-the-back-propagation-algorithm-part-3"], [40, "setting-up-the-back-propagation-algorithm-part-3"], [41, "setting-up-the-back-propagation-algorithm-part-3"]], "Setting up the Matrix to be inverted": [[33, "setting-up-the-matrix-to-be-inverted"], [34, "setting-up-the-matrix-to-be-inverted"]], "Setting up the back propagation algorithm": [[39, "setting-up-the-back-propagation-algorithm"]], "Setting up the back propagation algorithm and algorithm for a feed forward NN, initalizations": [[40, "setting-up-the-back-propagation-algorithm-and-algorithm-for-a-feed-forward-nn-initalizations"], [41, "setting-up-the-back-propagation-algorithm-and-algorithm-for-a-feed-forward-nn-initalizations"]], "Setting up the back propagation algorithm, part 1": [[40, "setting-up-the-back-propagation-algorithm-part-1"], [41, "setting-up-the-back-propagation-algorithm-part-1"]], "Setting up the back propagation algorithm, part 2": [[39, "setting-up-the-back-propagation-algorithm-part-2"], [40, "setting-up-the-back-propagation-algorithm-part-2"], [41, "setting-up-the-back-propagation-algorithm-part-2"]], "Setting up the code": [[41, "setting-up-the-code"]], "Setting up the equations for a neural network": [[39, "setting-up-the-equations-for-a-neural-network"], [40, "setting-up-the-equations-for-a-neural-network"]], "Setting up the network using Autograd": [[41, "setting-up-the-network-using-autograd"]], "Setting up the network using Autograd; The full program": [[2, "setting-up-the-network-using-autograd-the-full-program"], [41, "setting-up-the-network-using-autograd-the-full-program"]], "Setting up the network using Autograd; The trial solution": [[41, "setting-up-the-network-using-autograd-the-trial-solution"]], "Setting up the problem": [[41, "setting-up-the-problem"]], "Setup of Network": [[41, "setup-of-network"]], "Similar (second order function now) problem but now with AdaGrad": [[13, "similar-second-order-function-now-problem-but-now-with-adagrad"], [35, "similar-second-order-function-now-problem-but-now-with-adagrad"]], "Simple Python Code to read in Data and perform Classification": [[9, "simple-python-code-to-read-in-data-and-perform-classification"]], "Simple case": [[33, "simple-case"], [34, "simple-case"]], "Simple code for solving the above problem": [[34, "simple-code-for-solving-the-above-problem"]], "Simple example": [[37, "simple-example"], [39, "simple-example"]], "Simple example code": [[35, "simple-example-code"]], "Simple example to illustrate Ordinary Least Squares, Ridge and Lasso Regression": [[34, "simple-example-to-illustrate-ordinary-least-squares-ridge-and-lasso-regression"]], "Simple geometric interpretation": [[34, "simple-geometric-interpretation"]], "Simple linear regression model using scikit-learn": [[0, "simple-linear-regression-model-using-scikit-learn"], [32, "simple-linear-regression-model-using-scikit-learn"]], "Simple neural network and the  back propagation equations": [[39, "simple-neural-network-and-the-back-propagation-equations"], [40, "simple-neural-network-and-the-back-propagation-equations"]], "Simple one-dimensional second-order polynomial": [[18, "simple-one-dimensional-second-order-polynomial"]], "Simple program": [[34, "simple-program"], [35, "simple-program"]], "Simpler examples first, and automatic differentiation": [[39, "simpler-examples-first-and-automatic-differentiation"]], "Slightly different approach": [[35, "slightly-different-approach"]], "Smarter way of evaluating the above function": [[39, "smarter-way-of-evaluating-the-above-function"]], "Sneaking in automatic differentiation using Autograd": [[35, "sneaking-in-automatic-differentiation-using-autograd"]], "Software and needed installations": [[26, "software-and-needed-installations"], [32, "software-and-needed-installations"]], "Solving Differential Equations  with Deep Learning": [[2, null]], "Solving differential equations  with Deep Learning": [[41, "solving-differential-equations-with-deep-learning"]], "Solving the equation using Autograd": [[41, "solving-the-equation-using-autograd"]], "Solving the one dimensional Poisson equation": [[2, "solving-the-one-dimensional-poisson-equation"]], "Solving the wave equation - the full program using Autograd": [[41, "solving-the-wave-equation-the-full-program-using-autograd"]], "Solving the wave equation with Neural Networks": [[2, "solving-the-wave-equation-with-neural-networks"]], "Solving using Newton-Raphson\u2019s method": [[37, "solving-using-newton-raphson-s-method"], [38, "solving-using-newton-raphson-s-method"]], "Some famous Matrices": [[25, "some-famous-matrices"]], "Some parallels from real analysis": [[39, "some-parallels-from-real-analysis"]], "Some selected properties": [[37, "some-selected-properties"]], "Some simple problems": [[13, "some-simple-problems"], [34, "some-simple-problems"]], "Some useful matrix and vector expressions": [[33, "some-useful-matrix-and-vector-expressions"]], "Splitting our Data in Training and Test data": [[0, "splitting-our-data-in-training-and-test-data"], [33, "splitting-our-data-in-training-and-test-data"]], "Standard Approach based on the Normal Distribution": [[36, "standard-approach-based-on-the-normal-distribution"]], "Standard steepest descent": [[13, "standard-steepest-descent"]], "Statistical analysis": [[36, "statistical-analysis"], [37, "statistical-analysis"]], "Statistical analysis and optimization of data": [[24, "statistical-analysis-and-optimization-of-data"], [32, "statistical-analysis-and-optimization-of-data"]], "Steepest descent": [[13, "steepest-descent"], [34, "steepest-descent"]], "Stochastic Gradient Descent": [[35, "stochastic-gradient-descent"]], "Stochastic Gradient Descent (SGD)": [[13, "stochastic-gradient-descent-sgd"], [35, "stochastic-gradient-descent-sgd"]], "Stochastic variables and the main concepts, the discrete case": [[29, "stochastic-variables-and-the-main-concepts-the-discrete-case"]], "Strongly Convex Case": [[35, "strongly-convex-case"]], "Suggested readings and videos": [[38, "suggested-readings-and-videos"]], "Summary of methods to implement and analyze": [[27, "summary-of-methods-to-implement-and-analyze"]], "Summing up": [[36, "summing-up"], [37, "summing-up"]], "Support Vector Machines, overarching aims": [[8, null]], "Synthetic data generation": [[37, "synthetic-data-generation"], [38, "synthetic-data-generation"]], "Systematic reduction": [[3, "systematic-reduction"]], "Teachers": [[32, "teachers"]], "Teachers and Grading": [[30, null]], "Teaching Assistants Fall semester 2023": [[30, "teaching-assistants-fall-semester-2023"]], "Technicalities": [[41, "technicalities"]], "Tensorflow": [[40, "tensorflow"], [41, "tensorflow"]], "Tentative deadllines for projects": [[30, "tentative-deadllines-for-projects"]], "Testing the Means Squared Error as function of Complexity": [[0, "testing-the-means-squared-error-as-function-of-complexity"], [33, "testing-the-means-squared-error-as-function-of-complexity"]], "Testing the XOR gate and other gates": [[40, "testing-the-xor-gate-and-other-gates"], [41, "testing-the-xor-gate-and-other-gates"]], "Textbooks": [[31, null]], "The  back propagation equations for a neural network": [[40, "the-back-propagation-equations-for-a-neural-network"]], "The Algorithm before theorem": [[11, "the-algorithm-before-theorem"]], "The Breast Cancer Data, now with Keras": [[1, "the-breast-cancer-data-now-with-keras"]], "The CART algorithm for Classification": [[9, "the-cart-algorithm-for-classification"]], "The CART algorithm for Regression": [[9, "the-cart-algorithm-for-regression"]], "The CIFAR01 data set": [[3, "the-cifar01-data-set"]], "The Central Limit Theorem": [[36, "the-central-limit-theorem"]], "The Hessian matrix": [[34, "the-hessian-matrix"], [35, "the-hessian-matrix"]], "The Hessian matrix for Ridge Regression": [[34, "the-hessian-matrix-for-ridge-regression"], [35, "the-hessian-matrix-for-ridge-regression"]], "The Jacobian": [[33, "the-jacobian"]], "The MNIST dataset again": [[3, "the-mnist-dataset-again"]], "The Neural Network": [[40, "the-neural-network"], [41, "the-neural-network"]], "The OLS case": [[34, "the-ols-case"]], "The RELU function family": [[1, "the-relu-function-family"], [40, "the-relu-function-family"], [41, "the-relu-function-family"]], "The Ridge case": [[34, "the-ridge-case"]], "The SVD, a Fantastic Algorithm": [[33, "the-svd-a-fantastic-algorithm"], [34, "the-svd-a-fantastic-algorithm"]], "The Softmax function": [[1, "the-softmax-function"], [40, "the-softmax-function"]], "The \\chi^2 function": [[0, "the-chi-2-function"], [32, "the-chi-2-function"], [32, "id4"], [32, "id5"], [32, "id6"], [32, "id7"], [32, "id8"]], "The analytical solution": [[41, "the-analytical-solution"]], "The approximation theorem in words": [[39, "the-approximation-theorem-in-words"]], "The bias-variance tradeoff": [[6, "the-bias-variance-tradeoff"], [36, "the-bias-variance-tradeoff"], [37, "the-bias-variance-tradeoff"]], "The code for solving the ODE": [[2, "the-code-for-solving-the-ode"], [41, "the-code-for-solving-the-ode"]], "The complete code with a simple data set": [[33, "the-complete-code-with-a-simple-data-set"]], "The cost function rewritten": [[37, "the-cost-function-rewritten"], [38, "the-cost-function-rewritten"]], "The cost/loss function": [[33, "the-cost-loss-function"]], "The course has two central parts": [[24, "the-course-has-two-central-parts"]], "The derivative of the Logistic funtion": [[40, "the-derivative-of-the-logistic-funtion"]], "The derivative of the cost/loss function": [[34, "the-derivative-of-the-cost-loss-function"], [35, "the-derivative-of-the-cost-loss-function"]], "The derivatives": [[39, "the-derivatives"], [40, "the-derivatives"]], "The equations": [[34, "the-equations"]], "The equations for ordinary least squares": [[33, "the-equations-for-ordinary-least-squares"]], "The equations to solve": [[37, "the-equations-to-solve"], [38, "the-equations-to-solve"]], "The first Case": [[34, "the-first-case"]], "The function to solve for": [[41, "the-function-to-solve-for"]], "The gradient step": [[35, "the-gradient-step"]], "The ideal": [[34, "the-ideal"]], "The logistic function": [[7, "the-logistic-function"], [37, "the-logistic-function"]], "The mean squared error and its derivative": [[33, "the-mean-squared-error-and-its-derivative"]], "The moons example": [[8, "the-moons-example"]], "The multilayer  perceptron (MLP)": [[12, "the-multilayer-perceptron-mlp"]], "The network with one input layer, specified number of hidden layers, and one output layer": [[2, "the-network-with-one-input-layer-specified-number-of-hidden-layers-and-one-output-layer"], [41, "the-network-with-one-input-layer-specified-number-of-hidden-layers-and-one-output-layer"]], "The optimization problem": [[39, "the-optimization-problem"]], "The ouput layer": [[39, "the-ouput-layer"], [40, "the-ouput-layer"]], "The plethora  of machine learning algorithms/methods": [[32, "the-plethora-of-machine-learning-algorithms-methods"]], "The problem to solve for": [[41, "the-problem-to-solve-for"]], "The program using Autograd": [[41, "the-program-using-autograd"]], "The same example but now with cross-validation": [[36, "the-same-example-but-now-with-cross-validation"], [37, "the-same-example-but-now-with-cross-validation"]], "The sensitiveness of the gradient descent": [[34, "the-sensitiveness-of-the-gradient-descent"]], "The singular value decomposition": [[5, "the-singular-value-decomposition"], [33, "the-singular-value-decomposition"], [34, "the-singular-value-decomposition"]], "The specific equation to solve for": [[41, "the-specific-equation-to-solve-for"]], "The training": [[39, "the-training"], [40, "the-training"]], "The trial solution": [[41, "the-trial-solution"], [41, "id2"], [41, "id3"], [41, "id5"]], "The two-dimensional case": [[8, "the-two-dimensional-case"]], "Theoretical Convergence Speed and convex optimization": [[35, "theoretical-convergence-speed-and-convex-optimization"]], "Time decay rate": [[35, "time-decay-rate"]], "To our real data: nuclear binding energies. Brief reminder on masses and binding energies": [[32, "to-our-real-data-nuclear-binding-energies-brief-reminder-on-masses-and-binding-energies"]], "Topics covered in this course: Statistical analysis and optimization of data": [[32, "topics-covered-in-this-course-statistical-analysis-and-optimization-of-data"]], "Towards the PCA theorem": [[11, "towards-the-pca-theorem"]], "Train and test datasets": [[1, "train-and-test-datasets"], [40, "train-and-test-datasets"]], "Two parameters": [[37, "two-parameters"], [38, "two-parameters"]], "Two-dimensional Objects": [[3, "two-dimensional-objects"]], "Type of problem": [[2, "type-of-problem"], [41, "type-of-problem"]], "Types of Machine Learning": [[32, "types-of-machine-learning"]], "Understanding what happens": [[36, "understanding-what-happens"], [37, "understanding-what-happens"]], "Universal approximation theorem": [[39, "universal-approximation-theorem"]], "Updating the gradients": [[39, "updating-the-gradients"], [40, "updating-the-gradients"], [41, "updating-the-gradients"]], "Usage of the above learning rate schedulers": [[40, "usage-of-the-above-learning-rate-schedulers"], [41, "usage-of-the-above-learning-rate-schedulers"]], "Use the books!": [[19, "use-the-books"]], "Useful Python libraries": [[24, "useful-python-libraries"], [32, "useful-python-libraries"]], "Using Autograd": [[13, "using-autograd"]], "Using Automatic differentiation": [[41, "using-automatic-differentiation"]], "Using Keras": [[40, "using-keras"], [41, "using-keras"]], "Using Pytorch with the full MNIST data set": [[41, "using-pytorch-with-the-full-mnist-data-set"]], "Using Scikit-learn": [[38, "using-scikit-learn"]], "Using forward Euler to solve the ODE": [[2, "using-forward-euler-to-solve-the-ode"], [41, "using-forward-euler-to-solve-the-ode"]], "Using gradient descent methods, limitations": [[13, "using-gradient-descent-methods-limitations"], [34, "using-gradient-descent-methods-limitations"], [35, "using-gradient-descent-methods-limitations"]], "Using the chain rule and summing over all k entries": [[39, "using-the-chain-rule-and-summing-over-all-k-entries"], [40, "using-the-chain-rule-and-summing-over-all-k-entries"]], "Using the correlation matrix": [[38, "using-the-correlation-matrix"]], "Vanishing gradients": [[40, "vanishing-gradients"]], "Various steps in cross-validation": [[36, "various-steps-in-cross-validation"], [37, "various-steps-in-cross-validation"]], "Visualization": [[1, "visualization"], [1, "id1"], [40, "visualization"], [40, "id1"]], "Visualizing the Tree, Classification": [[9, "visualizing-the-tree-classification"]], "Week 34: Introduction to the course, Logistics and Practicalities": [[32, null]], "Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression": [[33, null]], "Week 36: Linear Regression and Gradient descent": [[34, null]], "Week 37: Gradient descent methods": [[35, null]], "Week 38: Statistical analysis, bias-variance tradeoff and resampling methods": [[36, null]], "Week 39: Resampling methods and logistic regression": [[37, null]], "Week 40: Gradient descent methods (continued) and start Neural networks": [[38, null]], "Week 41 Neural networks and constructing a neural network code": [[39, null]], "Week 42 Constructing a Neural Network code with examples": [[40, null]], "Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations": [[41, null]], "Weights and biases": [[40, "weights-and-biases"]], "What Is Generative Modeling?": [[32, "what-is-generative-modeling"]], "What does it mean?": [[33, "what-does-it-mean"], [34, "what-does-it-mean"]], "What is Machine Learning?": [[0, "what-is-machine-learning"]], "What is a good model?": [[0, "what-is-a-good-model"], [32, "what-is-a-good-model"]], "What is a good model? 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</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", "Exercises week 37", "Exercises week 38", "Exercises week 39", "Exercises week 41", "Exercises week 42", "Exercises week 43", "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 6 (midnight), 2025", "Project 2 on Machine Learning, deadline November 10 (Midnight)", "Course setting", "<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 Regression and Gradient descent", "Week 37: Gradient descent methods", "Week 38: Statistical analysis, bias-variance tradeoff and resampling methods", "Week 39: Resampling methods and logistic regression", "Week 40: Gradient descent methods (continued) and start Neural networks", "Week 41 Neural networks and constructing a neural network code", "Week 42 Constructing a Neural Network code with examples", "Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations"], "titleterms": {"": [8, 10, 34, 35, 36, 37, 38], "0": 40, "04": [], "05": [], "06": [], "07": [], "1": [0, 15, 16, 17, 18, 19, 20, 21, 22, 26, 27, 33, 39, 40, 41], 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"a-top-down-perspective-on-neural-networks"]], "A way to Read the Bias-Variance Tradeoff": [[36, "a-way-to-read-the-bias-variance-tradeoff"], [37, "a-way-to-read-the-bias-variance-tradeoff"]], "ADAM algorithm, taken from Goodfellow et al": [[35, "adam-algorithm-taken-from-goodfellow-et-al"]], "ADAM optimizer": [[13, "adam-optimizer"], [35, "id2"]], "Accuracy": [[35, "accuracy"]], "Activation functions": [[12, "activation-functions"], [38, "activation-functions"], [40, "activation-functions"], [40, "id3"], [41, "activation-functions"], [41, "id1"]], "Activation functions, Logistic and Hyperbolic ones": [[38, "activation-functions-logistic-and-hyperbolic-ones"], [40, "activation-functions-logistic-and-hyperbolic-ones"]], "Activation functions, examples": [[41, "activation-functions-examples"]], "AdaGrad Properties": [[35, "adagrad-properties"]], "AdaGrad Update Rule Derivation": [[35, "adagrad-update-rule-derivation"]], "AdaGrad algorithm, taken from Goodfellow et al": [[35, 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and Adam": [[35, "algorithms-and-codes-for-adagrad-rmsprop-and-adam"]], "Algorithms for Setting up Decision Trees": [[9, "algorithms-for-setting-up-decision-trees"]], "An Overview of Ensemble Methods": [[10, "an-overview-of-ensemble-methods"]], "An extrapolation example": [[4, "an-extrapolation-example"]], "An optimization/minimization problem": [[32, "an-optimization-minimization-problem"]], "Analyzing the last results": [[39, "analyzing-the-last-results"], [40, "analyzing-the-last-results"]], "And a similar example using Tensorflow with Keras": [[41, "and-a-similar-example-using-tensorflow-with-keras"]], "And finally  \\boldsymbol{X}\\boldsymbol{X}^T": [[33, "and-finally-boldsymbol-x-boldsymbol-x-t"]], "And finally ADAM": [[35, "and-finally-adam"]], "And what about using neural networks?": [[32, "and-what-about-using-neural-networks"]], "Another Example from Scikit-Learn\u2019s Repository": [[36, "another-example-from-scikit-learn-s-repository"], [37, 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"compact-expressions"], [40, "compact-expressions"]], "Compare  Bagging on Trees with Random Forests": [[10, "compare-bagging-on-trees-with-random-forests"]], "Comparing with a numerical scheme": [[2, "comparing-with-a-numerical-scheme"], [41, "comparing-with-a-numerical-scheme"]], "Comparison with OLS": [[34, "comparison-with-ols"]], "Completing the list": [[39, "completing-the-list"], [40, "completing-the-list"]], "Computation of gradients": [[35, "computation-of-gradients"]], "Computing the Gini index": [[9, "computing-the-gini-index"]], "Conditions on convex functions": [[34, "conditions-on-convex-functions"]], "Confidence Intervals": [[36, "confidence-intervals"]], "Confusion Matrix": [[23, "confusion-matrix"]], "Conjugate gradient method": [[13, "conjugate-gradient-method"]], "Convergence rates": [[35, "convergence-rates"]], "Convex function": [[34, "convex-function"]], "Convex functions": [[13, "convex-functions"], [34, "convex-functions"]], "Convolution Examples: Polynomial multiplication": [[3, "convolution-examples-polynomial-multiplication"]], "Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)": [[3, "convolution-examples-principle-of-superposition-and-periodic-forces-fourier-transforms"]], "Convolutional Neural Network": [[12, "convolutional-neural-network"], [38, "convolutional-neural-network"], [39, "convolutional-neural-network"]], "Convolutional Neural Networks": [[3, null]], "Correlation Function and Design/Feature Matrix": [[33, "correlation-function-and-design-feature-matrix"]], "Correlation Matrix": [[11, "correlation-matrix"], [33, "correlation-matrix"]], "Correlation Matrix with Pandas": [[33, "correlation-matrix-with-pandas"]], "Cost functions": [[40, "cost-functions"], [41, "cost-functions"]], "Counting the number of floating point operations": [[39, "counting-the-number-of-floating-point-operations"]], "Course Format": [[32, "course-format"]], "Course setting": [[28, null]], "Covariance Matrix Examples": [[33, "covariance-matrix-examples"]], "Covariance and Correlation Matrix": [[33, "covariance-and-correlation-matrix"]], "Cross-validation": [[6, "cross-validation"]], "Cross-validation in brief": [[36, "cross-validation-in-brief"], [37, "cross-validation-in-brief"]], "Cumulative Gain": [[23, "cumulative-gain"]], "Deadlines for projects (tentative)": [[32, "deadlines-for-projects-tentative"]], "Decision trees, overarching aims": [[9, null]], "Deep Neural Networks": [[35, "deep-neural-networks"]], "Deep learning methods": [[32, "deep-learning-methods"]], "Define model and architecture": [[1, "define-model-and-architecture"], [40, "define-model-and-architecture"]], "Defining intermediate operations": [[39, "defining-intermediate-operations"]], "Defining the cost function": [[1, "defining-the-cost-function"], [40, "defining-the-cost-function"]], "Defining the problem": [[41, "defining-the-problem"]], "Definitions": [[19, "definitions"], [39, "definitions"], [40, "definitions"]], "Deliverables": [[15, "deliverables"], [16, "deliverables"], [19, "deliverables"], [20, "deliverables"], [26, "deliverables"], [27, "deliverables"]], "Derivation of the AdaGrad Algorithm": [[35, "derivation-of-the-adagrad-algorithm"]], "Derivative of the cost function": [[39, "derivative-of-the-cost-function"], [40, "derivative-of-the-cost-function"]], "Derivatives and the chain rule": [[12, "derivatives-and-the-chain-rule"], [39, "derivatives-and-the-chain-rule"], [40, "derivatives-and-the-chain-rule"]], "Derivatives in terms of z_j^L": [[39, "derivatives-in-terms-of-z-j-l"], [40, "derivatives-in-terms-of-z-j-l"]], "Derivatives of the hidden layer": [[39, "derivatives-of-the-hidden-layer"], [40, "derivatives-of-the-hidden-layer"]], "Derivatives, example 1": [[33, "derivatives-example-1"]], "Deriving OLS from a probability distribution": [[5, "deriving-ols-from-a-probability-distribution"], [36, "deriving-ols-from-a-probability-distribution"]], "Deriving and Implementing Ordinary Least Squares": [[16, "deriving-and-implementing-ordinary-least-squares"]], "Deriving and Implementing Ridge Regression": [[17, "deriving-and-implementing-ridge-regression"]], "Deriving the  Lasso Regression Equations": [[33, "deriving-the-lasso-regression-equations"], [34, "deriving-the-lasso-regression-equations"], [34, "id6"]], "Deriving the  Ridge Regression Equations": [[33, "deriving-the-ridge-regression-equations"], [34, "deriving-the-ridge-regression-equations"], [34, "id3"]], "Deriving the back propagation code for a multilayer perceptron model": [[12, "deriving-the-back-propagation-code-for-a-multilayer-perceptron-model"]], "Developing a code for doing neural networks with back propagation": [[1, "developing-a-code-for-doing-neural-networks-with-back-propagation"], [40, "developing-a-code-for-doing-neural-networks-with-back-propagation"]], "Diagonalize the sample covariance matrix to obtain the principal components": [[11, 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"example-of-generative-modeling-taken-from-generative-deep-learning-by-david-foster"]], "Example of own Standard scaling": [[33, "example-of-own-standard-scaling"]], "Example relevant for the exercises": [[33, "example-relevant-for-the-exercises"]], "Example: Exponential decay": [[2, "example-exponential-decay"], [41, "example-exponential-decay"]], "Example: Population growth": [[2, "example-population-growth"], [41, "example-population-growth"]], "Example: Solving the one dimensional Poisson equation": [[41, "example-solving-the-one-dimensional-poisson-equation"]], "Example: Solving the wave equation with Neural Networks": [[41, "example-solving-the-wave-equation-with-neural-networks"]], "Example: The diffusion equation": [[2, "example-the-diffusion-equation"], [41, "example-the-diffusion-equation"]], "Example: binary classification problem": [[1, "example-binary-classification-problem"], [40, "example-binary-classification-problem"]], "Examples": [[32, "examples"]], "Examples of XOR, OR and AND gates": [[38, "examples-of-xor-or-and-and-gates"]], "Examples of likelihood functions used in logistic regression and neural networks": [[7, "examples-of-likelihood-functions-used-in-logistic-regression-and-neural-networks"]], "Examples of likelihood functions used in logistic regression and nueral networks": [[37, "examples-of-likelihood-functions-used-in-logistic-regression-and-nueral-networks"]], "Exercise 1": [[21, "exercise-1"]], "Exercise 1 - Choice of model and degrees of freedom": [[17, "exercise-1-choice-of-model-and-degrees-of-freedom"]], "Exercise 1 - Finding the derivative of Matrix-Vector expressions": [[16, "exercise-1-finding-the-derivative-of-matrix-vector-expressions"]], "Exercise 1 - Github Setup": [[15, "exercise-1-github-setup"]], "Exercise 1 - Understand the feed forward pass": [[22, "exercise-1-understand-the-feed-forward-pass"]], "Exercise 1, scale your data": [[18, "exercise-1-scale-your-data"]], "Exercise 1: Creating the report document": [[20, "exercise-1-creating-the-report-document"]], "Exercise 1: Expectation values for ordinary least squares expressions": [[19, "exercise-1-expectation-values-for-ordinary-least-squares-expressions"]], "Exercise 1: Including more data": [[39, "exercise-1-including-more-data"]], "Exercise 1: Setting up various Python environments": [[0, "exercise-1-setting-up-various-python-environments"]], "Exercise 2": [[21, "exercise-2"]], "Exercise 2 - Deriving the expression for OLS": [[16, "exercise-2-deriving-the-expression-for-ols"]], "Exercise 2 - Deriving the expression for Ridge Regression": [[17, "exercise-2-deriving-the-expression-for-ridge-regression"]], "Exercise 2 - Gradient with one layer using autograd": [[22, "exercise-2-gradient-with-one-layer-using-autograd"]], "Exercise 2 - Setting up a Github repository": [[15, "exercise-2-setting-up-a-github-repository"]], "Exercise 2, calculate the gradients": [[18, "exercise-2-calculate-the-gradients"]], "Exercise 2: Adding good figures": [[20, "exercise-2-adding-good-figures"]], "Exercise 2: Expectation values for Ridge regression": [[19, "exercise-2-expectation-values-for-ridge-regression"]], "Exercise 2: Extended program": [[39, "exercise-2-extended-program"]], "Exercise 2: making your own data and exploring scikit-learn": [[0, "exercise-2-making-your-own-data-and-exploring-scikit-learn"]], "Exercise 3": [[21, "exercise-3"]], "Exercise 3 - Creating feature matrix and implementing OLS using the analytical expression": [[16, "exercise-3-creating-feature-matrix-and-implementing-ols-using-the-analytical-expression"]], "Exercise 3 - Fitting an OLS model to data": [[15, "exercise-3-fitting-an-ols-model-to-data"]], "Exercise 3 - Gradient with one layer writing backpropagation by hand": [[22, "exercise-3-gradient-with-one-layer-writing-backpropagation-by-hand"]], "Exercise 3 - Scaling data": [[17, "exercise-3-scaling-data"]], "Exercise 3 - Setting up a Python virtual environment": [[15, "exercise-3-setting-up-a-python-virtual-environment"]], "Exercise 3, using the analytical formulae for OLS and Ridge regression to find the optimal paramters \\boldsymbol{\\theta}": [[18, "exercise-3-using-the-analytical-formulae-for-ols-and-ridge-regression-to-find-the-optimal-paramters-boldsymbol-theta"]], "Exercise 3: Deriving the expression for the Bias-Variance Trade-off": [[19, "exercise-3-deriving-the-expression-for-the-bias-variance-trade-off"]], "Exercise 3: Normalizing our data": [[0, "exercise-3-normalizing-our-data"]], "Exercise 3: Writing an abstract and introduction": [[20, "exercise-3-writing-an-abstract-and-introduction"]], "Exercise 4 - Custom activation for each layer": [[21, "exercise-4-custom-activation-for-each-layer"]], "Exercise 4 - Fitting a polynomial": [[16, "exercise-4-fitting-a-polynomial"]], "Exercise 4 - Gradient with two layers writing backpropagation by hand": [[22, "exercise-4-gradient-with-two-layers-writing-backpropagation-by-hand"]], "Exercise 4 - Implementing Ridge Regression": [[17, "exercise-4-implementing-ridge-regression"]], "Exercise 4 - Testing multiple hyperparameters": [[17, "exercise-4-testing-multiple-hyperparameters"]], "Exercise 4 - The train-test split": [[15, "exercise-4-the-train-test-split"]], "Exercise 4, Implementing the simplest form for gradient descent": [[18, "exercise-4-implementing-the-simplest-form-for-gradient-descent"]], "Exercise 4: Adding Ridge Regression": [[0, "exercise-4-adding-ridge-regression"]], "Exercise 4: Computing the Bias and Variance": [[19, "exercise-4-computing-the-bias-and-variance"]], "Exercise 4: Making the code available and presentable": [[20, "exercise-4-making-the-code-available-and-presentable"]], "Exercise 5 - Comparing your code with sklearn": [[16, "exercise-5-comparing-your-code-with-sklearn"]], "Exercise 5 - Gradient with any number of layers writing backpropagation by hand": [[22, "exercise-5-gradient-with-any-number-of-layers-writing-backpropagation-by-hand"]], "Exercise 5 - Processing multiple inputs at once": [[21, "exercise-5-processing-multiple-inputs-at-once"]], "Exercise 5, Ridge regression and a new Synthetic Dataset": [[18, "exercise-5-ridge-regression-and-a-new-synthetic-dataset"]], "Exercise 5: Analytical exercises": [[0, "exercise-5-analytical-exercises"]], "Exercise 5: Interpretation of scaling and metrics": [[19, "exercise-5-interpretation-of-scaling-and-metrics"]], "Exercise 5: Referencing": [[20, "exercise-5-referencing"]], "Exercise 6 - Batched inputs": [[22, "exercise-6-batched-inputs"]], "Exercise 6 - Predicting on real data": [[21, "exercise-6-predicting-on-real-data"]], "Exercise 7 - Training": [[22, "exercise-7-training"]], "Exercise 7 - Training on real data (Optional)": [[21, "exercise-7-training-on-real-data-optional"]], "Exercise 8 (Optional) - Object orientation": [[22, "exercise-8-optional-object-orientation"]], "Exercise a)": [[23, "exercise-a"]], "Exercise b)": [[23, "exercise-b"]], "Exercise c) week 43": [[23, "exercise-c-week-43"]], "Exercise:  Cross-validation as resampling techniques, adding more complexity": [[6, "exercise-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Exercise: Analysis of real data": [[6, "exercise-analysis-of-real-data"]], "Exercise: Bias-variance trade-off and resampling techniques": [[6, "exercise-bias-variance-trade-off-and-resampling-techniques"]], "Exercise: Lasso Regression on the Franke function  with resampling": [[6, "exercise-lasso-regression-on-the-franke-function-with-resampling"]], "Exercise: Ordinary Least Square (OLS) on the Franke function": [[6, "exercise-ordinary-least-square-ols-on-the-franke-function"]], "Exercise: Ridge Regression on the Franke function  with resampling": [[6, "exercise-ridge-regression-on-the-franke-function-with-resampling"]], "Exercises": [[0, "exercises"], [23, "exercises"]], "Exercises and Projects": [[6, "exercises-and-projects"]], "Exercises and lab session week 43": [[41, "exercises-and-lab-session-week-43"]], "Exercises week 34": [[15, null]], "Exercises week 35": [[16, null]], "Exercises week 36": [[17, null]], "Exercises week 37": [[18, null]], "Exercises week 38": [[19, null]], "Exercises week 39": [[20, null]], "Exercises week 41": [[21, null]], "Exercises week 42": [[22, null]], "Exercises week 43": [[23, null]], "Expectation value and variance": [[36, "expectation-value-and-variance"]], "Expectation value and variance for \\boldsymbol{\\theta}": [[36, "expectation-value-and-variance-for-boldsymbol-theta"]], "Expectation values": [[29, "expectation-values"]], "Explicit derivatives": [[39, "explicit-derivatives"], [40, "explicit-derivatives"]], "Exploding gradients": [[40, "exploding-gradients"]], "Extending to more predictors": [[37, "extending-to-more-predictors"], [38, "extending-to-more-predictors"]], "Extending to more than one variable": [[34, "extending-to-more-than-one-variable"]], "Extremely useful tools, strongly recommended": [[32, "extremely-useful-tools-strongly-recommended"]], "Feed-forward neural networks": [[12, "feed-forward-neural-networks"], [38, "feed-forward-neural-networks"], [39, "feed-forward-neural-networks"]], "Feed-forward pass": [[1, "feed-forward-pass"], [40, "feed-forward-pass"]], "Final back propagating equation": [[12, "final-back-propagating-equation"], [39, "final-back-propagating-equation"], [40, "final-back-propagating-equation"]], "Final derivatives": [[39, "final-derivatives"]], "Final expression": [[39, "final-expression"], [40, "final-expression"]], "Final expressions for the biases of the hidden layer": [[39, "final-expressions-for-the-biases-of-the-hidden-layer"], [40, "final-expressions-for-the-biases-of-the-hidden-layer"]], "Final technicalities I": [[41, "final-technicalities-i"]], "Final technicalities II": [[41, "final-technicalities-ii"]], "Final technicalities III": [[41, "final-technicalities-iii"]], "Final technicalities IV": [[41, "final-technicalities-iv"]], "Finding the Limit": [[36, "finding-the-limit"]], "Fine-tuning neural network hyperparameters": [[1, "fine-tuning-neural-network-hyperparameters"], [40, "fine-tuning-neural-network-hyperparameters"]], "First network example, simple percepetron with one input": [[39, "first-network-example-simple-percepetron-with-one-input"]], "Fitting an Equation of State for Dense Nuclear Matter": [[0, "fitting-an-equation-of-state-for-dense-nuclear-matter"]], "Fixing the singularity": [[33, "fixing-the-singularity"], [34, "fixing-the-singularity"]], "Format for electronic delivery of report and programs": [[26, "format-for-electronic-delivery-of-report-and-programs"], [27, "format-for-electronic-delivery-of-report-and-programs"]], "Forward and reverse modes": [[39, "forward-and-reverse-modes"]], "Frequently used scaling functions": [[33, "frequently-used-scaling-functions"], [35, "frequently-used-scaling-functions"]], "From OLS to Ridge and Lasso": [[34, "from-ols-to-ridge-and-lasso"]], "From one to many layers, the universal approximation theorem": [[12, "from-one-to-many-layers-the-universal-approximation-theorem"]], "Full object-oriented implementation": [[40, "full-object-oriented-implementation"]], "Functionality in Scikit-Learn": [[33, "functionality-in-scikit-learn"], [35, "functionality-in-scikit-learn"]], "Further Dimensionality Remarks": [[3, "further-dimensionality-remarks"]], "Further properties (important for our analyses later)": [[5, "further-properties-important-for-our-analyses-later"], [33, "further-properties-important-for-our-analyses-later"], [34, "further-properties-important-for-our-analyses-later"]], "Gaussian Elimination": [[25, "gaussian-elimination"]], "General Features": [[9, "general-features"]], "General linear models and linear algebra": [[32, "general-linear-models-and-linear-algebra"]], "Generalizing the fitting procedure as a linear algebra problem": [[32, "generalizing-the-fitting-procedure-as-a-linear-algebra-problem"], [32, "id1"]], "Generative Adversarial Networks": [[4, "generative-adversarial-networks"]], "Generative Models": [[4, "generative-models"]], "Generative Versus Discriminative Modeling": [[32, "generative-versus-discriminative-modeling"]], "Geometric Interpretation and link with Singular Value Decomposition": [[11, "geometric-interpretation-and-link-with-singular-value-decomposition"]], "Getting serious, the  back propagation equations for a neural network": [[39, "getting-serious-the-back-propagation-equations-for-a-neural-network"]], "Getting started with project 1": [[20, "getting-started-with-project-1"]], "Gradient Boosting, Classification Example": [[10, "gradient-boosting-classification-example"]], "Gradient Boosting, Examples of Regression": [[10, "gradient-boosting-examples-of-regression"]], "Gradient Clipping": [[1, "gradient-clipping"], [40, "gradient-clipping"]], "Gradient Descent Example": [[34, "id1"], [35, "id1"]], "Gradient boosting: Basics with Steepest Descent/Functional Gradient Descent": [[10, "gradient-boosting-basics-with-steepest-descent-functional-gradient-descent"]], "Gradient descent": [[2, "gradient-descent"], [41, "gradient-descent"]], "Gradient descent and Ridge": [[34, "gradient-descent-and-ridge"], [35, "gradient-descent-and-ridge"]], "Gradient descent and revisiting Ordinary Least Squares from last week": [[35, "gradient-descent-and-revisiting-ordinary-least-squares-from-last-week"]], "Gradient descent example": [[34, "gradient-descent-example"], [35, "gradient-descent-example"]], "Gradient expressions": [[39, "gradient-expressions"], [40, "gradient-expressions"]], "Grading": [[30, "grading"], [30, "id2"], [32, "grading"]], "Hidden layers": [[40, "hidden-layers"]], "Homogeneous data": [[40, "homogeneous-data"]], "How to take derivatives of Matrix-Vector expressions": [[16, "how-to-take-derivatives-of-matrix-vector-expressions"]], "Hyperplanes and all that": [[8, "hyperplanes-and-all-that"]], "Identifying Terms": [[36, "identifying-terms"]], "Illustration of a single perceptron model and a multi-perceptron model": [[38, "illustration-of-a-single-perceptron-model-and-a-multi-perceptron-model"], [39, "illustration-of-a-single-perceptron-model-and-a-multi-perceptron-model"]], "Important Matrix and vector handling packages": [[25, "important-matrix-and-vector-handling-packages"]], "Important observations": [[39, "important-observations"], [40, "important-observations"]], "Important technicalities: More on Rescaling data": [[33, "important-technicalities-more-on-rescaling-data"]], "Improving gradient descent with momentum": [[35, "improving-gradient-descent-with-momentum"]], "Improving performance": [[1, "improving-performance"], [40, "improving-performance"]], "In general not this simple": [[39, "in-general-not-this-simple"]], "In summary": [[30, "in-summary"]], "Including Stochastic Gradient Descent with Autograd": [[13, "including-stochastic-gradient-descent-with-autograd"], [35, "including-stochastic-gradient-descent-with-autograd"]], "Including more classes": [[37, "including-more-classes"], [38, "including-more-classes"]], "Incremental PCA": [[11, "incremental-pca"]], "Independent and Identically Distributed (iid)": [[36, "independent-and-identically-distributed-iid"]], "Inputs to the activation function": [[39, "inputs-to-the-activation-function"], [40, "inputs-to-the-activation-function"]], "Insights from the paper by Glorot and Bengio": [[40, "insights-from-the-paper-by-glorot-and-bengio"]], "Installing R, C++, cython or Julia": [[32, "installing-r-c-cython-or-julia"]], "Installing R, C++, cython, Numba etc": [[32, "installing-r-c-cython-numba-etc"]], "Instructor information": [[30, "instructor-information"]], "Interpretations and optimizing our parameters": [[32, "interpretations-and-optimizing-our-parameters"], [32, "id2"], [32, "id3"], [33, "interpretations-and-optimizing-our-parameters"], [33, "id1"], [33, "id2"]], "Interpreting the Ridge results": [[33, "interpreting-the-ridge-results"], [34, "interpreting-the-ridge-results"], [34, "id4"]], "Introducing JAX": [[13, "introducing-jax"]], "Introducing the Covariance and Correlation functions": [[11, "introducing-the-covariance-and-correlation-functions"], [33, "introducing-the-covariance-and-correlation-functions"]], "Introduction": [[0, "introduction"], [6, "introduction"], [24, "introduction"], [25, "introduction"]], "Introduction to Neural networks": [[38, "introduction-to-neural-networks"], [39, "introduction-to-neural-networks"]], "Introduction to numerical projects": [[26, "introduction-to-numerical-projects"], [27, "introduction-to-numerical-projects"]], "Is the Logistic activation function (Sigmoid)  our choice?": [[40, "is-the-logistic-activation-function-sigmoid-our-choice"]], "Iterative Fitting, Classification and AdaBoost": [[10, "iterative-fitting-classification-and-adaboost"]], "Iterative Fitting, Regression and Squared-error Cost Function": [[10, "iterative-fitting-regression-and-squared-error-cost-function"]], "Kernel PCA": [[11, "kernel-pca"]], "Kernels and non-linearity": [[8, "kernels-and-non-linearity"]], "LU Decomposition, the inverse of a matrix": [[25, "lu-decomposition-the-inverse-of-a-matrix"]], "Lab sessions Tuesday and Wednesday": [[38, "lab-sessions-tuesday-and-wednesday"]], "Lab sessions on Tuesday and Wednesday": [[39, "lab-sessions-on-tuesday-and-wednesday"]], "Lab sessions week 39": [[37, "lab-sessions-week-39"]], "Lasso Regression": [[34, "lasso-regression"]], "Lasso case": [[34, "lasso-case"]], "Layers": [[1, "layers"], [40, "layers"]], "Layers used to build CNNs": [[3, "layers-used-to-build-cnns"]], "Layout of a neural network with three hidden layers": [[39, "layout-of-a-neural-network-with-three-hidden-layers"]], "Layout of a neural network with three hidden layers (last layer = l=L=4, first layer l=0)": [[40, "layout-of-a-neural-network-with-three-hidden-layers-last-layer-l-l-4-first-layer-l-0"]], "Layout of a simple neural network with no hidden layer": [[39, "layout-of-a-simple-neural-network-with-no-hidden-layer"], [40, "layout-of-a-simple-neural-network-with-no-hidden-layer"]], "Layout of a simple neural network with one hidden layer": [[39, "layout-of-a-simple-neural-network-with-one-hidden-layer"], [40, "layout-of-a-simple-neural-network-with-one-hidden-layer"]], "Layout of a simple neural network with two input nodes, one  hidden layer and one output node": [[39, "layout-of-a-simple-neural-network-with-two-input-nodes-one-hidden-layer-and-one-output-node"]], "Layout of a simple neural network with two input nodes, one  hidden layer with two hidden noeds and one output node": [[40, "layout-of-a-simple-neural-network-with-two-input-nodes-one-hidden-layer-with-two-hidden-noeds-and-one-output-node"]], "Layout of input to first hidden layer l=1 from input layer l=0": [[40, "layout-of-input-to-first-hidden-layer-l-1-from-input-layer-l-0"]], "Learning goals": [[15, "learning-goals"], [16, "learning-goals"], [17, "learning-goals"], [18, "learning-goals"], [19, "learning-goals"], [20, "learning-goals"]], "Learning outcomes": [[24, "learning-outcomes"], [32, "learning-outcomes"]], "Learning rate methods": [[40, "learning-rate-methods"], [41, "learning-rate-methods"]], "Lecture Monday  October 20": [[41, "lecture-monday-october-20"]], "Lecture Monday  October 6": [[39, "lecture-monday-october-6"]], "Lecture Monday September 29, 2025": [[38, "lecture-monday-september-29-2025"]], "Lecture October 13, 2025": [[40, "lecture-october-13-2025"]], "Lecture material": [[37, "lecture-material"]], "Lecture material: Writing a code which implements a feed-forward neural network": [[40, "lecture-material-writing-a-code-which-implements-a-feed-forward-neural-network"]], "Lectures and ComputerLab": [[32, "lectures-and-computerlab"]], "Limitations of NNs": [[40, "limitations-of-nns"]], "Limitations of supervised learning with deep networks": [[1, "limitations-of-supervised-learning-with-deep-networks"], [40, "limitations-of-supervised-learning-with-deep-networks"]], "Linear Algebra, Handling of Arrays and more Python Features": [[25, null]], "Linear Regression": [[0, null]], "Linear Regression Problems": [[33, "linear-regression-problems"], [34, "linear-regression-problems"]], "Linear Regression and  the SVD": [[34, "linear-regression-and-the-svd"]], "Linear Regression, basic elements": [[0, "linear-regression-basic-elements"]], "Linear classifier": [[37, "linear-classifier"]], "Linking Bayes\u2019 Theorem with Ridge and Lasso Regression": [[5, "linking-bayes-theorem-with-ridge-and-lasso-regression"]], "Linking the regression analysis with a statistical interpretation": [[5, "linking-the-regression-analysis-with-a-statistical-interpretation"], [36, "linking-the-regression-analysis-with-a-statistical-interpretation"]], "Linking with the SVD": [[5, "linking-with-the-svd"], [33, "linking-with-the-svd"]], "Links to relevant courses at the University of Oslo": [[31, "links-to-relevant-courses-at-the-university-of-oslo"]], "Logistic Regression": [[7, null], [7, "id1"], [37, "logistic-regression"]], "Logistic Regression, from last week": [[38, "logistic-regression-from-last-week"]], "Logistic function as the root of problems": [[40, "logistic-function-as-the-root-of-problems"]], "MNIST and GANs": [[4, "mnist-and-gans"]], "Machine Learning": [[32, "machine-learning"]], "Machine learning": [[24, "machine-learning"]], "Main textbooks": [[32, "main-textbooks"]], "Making a tree": [[9, "making-a-tree"]], "Making your own Bootstrap: Changing the Level of the Decision Tree": [[10, "making-your-own-bootstrap-changing-the-level-of-the-decision-tree"]], "Making your own test-train splitting": [[33, "making-your-own-test-train-splitting"]], "Material for exercises week 35": [[33, "material-for-exercises-week-35"]], "Material for lab sessions  sessions Tuesday and Wednesday": [[34, "material-for-lab-sessions-sessions-tuesday-and-wednesday"]], "Material for lecture Monday September 2": [[34, "material-for-lecture-monday-september-2"]], "Material for lecture Monday September 8": [[35, "material-for-lecture-monday-september-8"]], "Material for the lab sessions": [[35, "material-for-the-lab-sessions"], [36, "material-for-the-lab-sessions"]], "Material for the lab sessions on Tuesday and Wednesday": [[40, "material-for-the-lab-sessions-on-tuesday-and-wednesday"]], "Material for the lecture on Monday October 6, 2025": [[39, "material-for-the-lecture-on-monday-october-6-2025"]], "Mathematical Interpretation of Ordinary Least Squares": [[5, "mathematical-interpretation-of-ordinary-least-squares"], [33, "mathematical-interpretation-of-ordinary-least-squares"], [34, "mathematical-interpretation-of-ordinary-least-squares"]], "Mathematical model": [[38, "mathematical-model"], [38, "id1"], [38, "id2"], [38, "id3"], [38, "id4"]], "Mathematical optimization of convex functions": [[8, "mathematical-optimization-of-convex-functions"]], "Mathematics of CNNs": [[3, "mathematics-of-cnns"]], "Mathematics of deep learning": [[39, "mathematics-of-deep-learning"], [40, "mathematics-of-deep-learning"]], "Mathematics of deep learning and neural networks": [[39, "mathematics-of-deep-learning-and-neural-networks"]], "Mathematics of the SVD and implications": [[5, "mathematics-of-the-svd-and-implications"], [33, "mathematics-of-the-svd-and-implications"], [34, "mathematics-of-the-svd-and-implications"]], "Matrices in Python": [[32, "matrices-in-python"]], "Matrix  multiplication": [[1, "matrix-multiplication"], [40, "matrix-multiplication"]], "Matrix multiplications": [[40, "matrix-multiplications"]], "Matrix-vector notation": [[38, "matrix-vector-notation"]], "Matrix-vector notation  and activation": [[12, "matrix-vector-notation-and-activation"], [38, "matrix-vector-notation-and-activation"]], "Maximum Likelihood Estimation (MLE)": [[36, "maximum-likelihood-estimation-mle"]], "Maximum likelihood": [[37, "maximum-likelihood"], [38, "maximum-likelihood"]], "Meet the  covariance!": [[29, "meet-the-covariance"]], "Meet the Covariance Matrix": [[5, "meet-the-covariance-matrix"], [33, "meet-the-covariance-matrix"]], "Meet the Hessian Matrix": [[33, "meet-the-hessian-matrix"]], "Meet the Pandas": [[32, "meet-the-pandas"]], "Memory Usage and Scalability": [[35, "memory-usage-and-scalability"]], "Memory constraints": [[35, "memory-constraints"]], "Min-Max Scaling": [[33, "min-max-scaling"]], "Minimization process": [[41, "minimization-process"]], "Minimizing the cost function using gradient descent and automatic differentiation": [[41, "minimizing-the-cost-function-using-gradient-descent-and-automatic-differentiation"]], "Minimizing the cross entropy": [[37, "minimizing-the-cross-entropy"], [38, "minimizing-the-cross-entropy"]], "Momentum based GD": [[13, "momentum-based-gd"], [35, "momentum-based-gd"]], "More classes": [[37, "more-classes"], [38, "more-classes"]], "More complicated Example: The Ising model": [[6, "more-complicated-example-the-ising-model"]], "More complicated function": [[39, "more-complicated-function"]], "More considerations": [[39, "more-considerations"], [40, "more-considerations"]], "More details": [[41, "more-details"], [41, "id4"]], "More examples on bootstrap and cross-validation and errors": [[36, "more-examples-on-bootstrap-and-cross-validation-and-errors"], [37, "more-examples-on-bootstrap-and-cross-validation-and-errors"]], "More interpretations": [[33, "more-interpretations"], [34, "more-interpretations"], [34, "id5"]], "More limitations": [[40, "more-limitations"]], "More on Dimensionalities": [[3, "more-on-dimensionalities"]], "More on Rescaling data": [[6, "more-on-rescaling-data"]], "More on Steepest descent": [[34, "more-on-steepest-descent"]], "More on activation functions, output layers": [[40, "more-on-activation-functions-output-layers"], [41, "more-on-activation-functions-output-layers"]], "More on convex functions": [[34, "more-on-convex-functions"]], "More on the general approximation theorem": [[39, "more-on-the-general-approximation-theorem"]], "More preprocessing": [[33, "more-preprocessing"], [35, "more-preprocessing"]], "More technicalities": [[41, "more-technicalities"]], "More top-down perspectives": [[40, "more-top-down-perspectives"]], "Motivation for Adaptive Step Sizes": [[35, "motivation-for-adaptive-step-sizes"]], "Multiclass classification": [[40, "multiclass-classification"], [41, "multiclass-classification"]], "Multilayer perceptrons": [[12, "multilayer-perceptrons"], [38, "multilayer-perceptrons"], [39, "multilayer-perceptrons"]], "Multivariable functions": [[39, "multivariable-functions"]], "Network requirements": [[2, "network-requirements"], [41, "network-requirements"]], "Neural Networks vs CNNs": [[3, "neural-networks-vs-cnns"]], "Neural network types": [[38, "neural-network-types"], [39, "neural-network-types"]], "Neural networks": [[12, null]], "New expression for the derivative": [[39, "new-expression-for-the-derivative"]], "Non-Convex Problems": [[35, "non-convex-problems"]], "Note about SVD Calculations": [[33, "note-about-svd-calculations"], [34, "note-about-svd-calculations"]], "Note on Scikit-Learn": [[34, "note-on-scikit-learn"]], "Numerical experiments and the covariance, central limit theorem": [[29, "numerical-experiments-and-the-covariance-central-limit-theorem"]], "Numpy and arrays": [[25, "numpy-and-arrays"], [32, "numpy-and-arrays"]], "Numpy examples and Important Matrix and vector handling packages": [[32, "numpy-examples-and-important-matrix-and-vector-handling-packages"]], "Optimization and Deep learning": [[37, "optimization-and-deep-learning"], [38, "optimization-and-deep-learning"]], "Optimization and gradient descent, the central part of any Machine Learning algortithm": [[34, "optimization-and-gradient-descent-the-central-part-of-any-machine-learning-algortithm"]], "Optimization, the central part of any Machine Learning algortithm": [[13, null], [37, "optimization-the-central-part-of-any-machine-learning-algortithm"], [38, "optimization-the-central-part-of-any-machine-learning-algortithm"]], "Optimizing our parameters": [[32, "optimizing-our-parameters"]], "Optimizing our parameters, more details": [[32, "optimizing-our-parameters-more-details"]], "Optimizing the cost function": [[1, "optimizing-the-cost-function"], [40, "optimizing-the-cost-function"]], "Optimizing the parameters": [[39, "optimizing-the-parameters"], [40, "optimizing-the-parameters"]], "Optional (Note that you should include at least two of these in the report):": [[27, "optional-note-that-you-should-include-at-least-two-of-these-in-the-report"]], "Ordinary Differential Equations first": [[41, "ordinary-differential-equations-first"]], "Organizing our data": [[0, "organizing-our-data"], [32, "organizing-our-data"]], "Other Matrix and Vector Operations": [[25, "other-matrix-and-vector-operations"]], "Other Types of Recurrent Neural Networks": [[4, "other-types-of-recurrent-neural-networks"]], "Other courses on Data science and Machine Learning  at UiO": [[32, "other-courses-on-data-science-and-machine-learning-at-uio"]], "Other courses on Data science and Machine Learning  at UiO, contn": [[32, "other-courses-on-data-science-and-machine-learning-at-uio-contn"]], "Other ingredients of a neural network": [[39, "other-ingredients-of-a-neural-network"]], "Other measures in classification studies": [[38, "other-measures-in-classification-studies"]], "Other measures: Precision, Recall, and the F_1 Measure": [[23, "other-measures-precision-recall-and-the-f-1-measure"]], "Other parameters": [[39, "other-parameters"]], "Other popular texts": [[32, "other-popular-texts"]], "Other techniques": [[11, "other-techniques"]], "Other types of networks": [[12, "other-types-of-networks"], [38, "other-types-of-networks"], [39, "other-types-of-networks"]], "Other ways of visualizing the trees": [[9, "other-ways-of-visualizing-the-trees"]], "Our model for the nuclear binding energies": [[32, "our-model-for-the-nuclear-binding-energies"]], "Output layer": [[39, "output-layer"], [40, "output-layer"]], "Overarching aims of the exercises for week 43": [[23, "overarching-aims-of-the-exercises-for-week-43"]], "Overarching aims of the exercises this week": [[21, "overarching-aims-of-the-exercises-this-week"], [22, "overarching-aims-of-the-exercises-this-week"]], "Overarching view of a neural network": [[39, "overarching-view-of-a-neural-network"]], "Overview of first week": [[32, "overview-of-first-week"]], "Overview video on Stochastic Gradient Descent (SGD)": [[35, "overview-video-on-stochastic-gradient-descent-sgd"]], "Own code for Ordinary Least Squares": [[32, "own-code-for-ordinary-least-squares"], [33, "own-code-for-ordinary-least-squares"]], "PCA and scikit-learn": [[11, "pca-and-scikit-learn"]], "Pandas AI": [[32, "pandas-ai"]], "Parameters of neural networks": [[39, "parameters-of-neural-networks"]], "Part a : Ordinary Least Square (OLS) for the Runge function": [[26, "part-a-ordinary-least-square-ols-for-the-runge-function"]], "Part a): Analytical warm-up": [[27, "part-a-analytical-warm-up"]], "Part b): Writing your own Neural Network code": [[27, "part-b-writing-your-own-neural-network-code"]], "Part b: Adding Ridge regression for the Runge function": [[26, "part-b-adding-ridge-regression-for-the-runge-function"]], "Part c): Testing against other software libraries": [[27, "part-c-testing-against-other-software-libraries"]], "Part c: Writing your own gradient descent code": [[26, "part-c-writing-your-own-gradient-descent-code"]], "Part d): Testing different activation functions and depths of the neural network": [[27, "part-d-testing-different-activation-functions-and-depths-of-the-neural-network"]], "Part d: Including momentum and more advanced ways to update the learning the rate": [[26, "part-d-including-momentum-and-more-advanced-ways-to-update-the-learning-the-rate"]], "Part e): Testing different norms": [[27, "part-e-testing-different-norms"]], "Part e: Writing our own code for Lasso regression": [[26, "part-e-writing-our-own-code-for-lasso-regression"]], "Part f): Classification  analysis using neural networks": [[27, "part-f-classification-analysis-using-neural-networks"]], "Part f: Stochastic gradient descent": [[26, "part-f-stochastic-gradient-descent"]], "Part g) Critical evaluation of the various algorithms": [[27, "part-g-critical-evaluation-of-the-various-algorithms"]], "Part g: Bias-variance trade-off and resampling techniques": [[26, "part-g-bias-variance-trade-off-and-resampling-techniques"]], "Part h): Cross-validation as resampling techniques, adding more complexity": [[26, "part-h-cross-validation-as-resampling-techniques-adding-more-complexity"]], "Partial Differential Equations": [[2, "partial-differential-equations"], [41, "partial-differential-equations"]], "Plan for week 39, September 22-26, 2025": [[37, "plan-for-week-39-september-22-26-2025"]], "Plan for week 41, October 6-10": [[39, "plan-for-week-41-october-6-10"]], "Plans for week 35": [[33, "plans-for-week-35"]], "Plans for week 36": [[34, "plans-for-week-36"]], "Plans for week 37, lecture Monday": [[35, "plans-for-week-37-lecture-monday"]], "Plans for week 38, lecture Monday September 15": [[36, "plans-for-week-38-lecture-monday-september-15"]], "Plans for week 43": [[41, "plans-for-week-43"]], "Plotting the Histogram": [[36, "plotting-the-histogram"]], "Plotting the mean value for each group": [[37, "plotting-the-mean-value-for-each-group"]], "Practical tips": [[13, "practical-tips"], [35, "practical-tips"]], "Practicalities": [[30, "practicalities"], [30, "id1"]], "Preamble: Note on writing reports, using reference material, AI and other tools": [[26, "preamble-note-on-writing-reports-using-reference-material-ai-and-other-tools"], [27, "preamble-note-on-writing-reports-using-reference-material-ai-and-other-tools"]], "Predicting New Points With A Trained Recurrent Neural Network": [[4, "predicting-new-points-with-a-trained-recurrent-neural-network"]], "Preprocessing our data": [[33, "preprocessing-our-data"]], "Prerequisites": [[32, "prerequisites"]], "Prerequisites and background": [[24, "prerequisites-and-background"]], "Prerequisites: Collect and pre-process data": [[3, "prerequisites-collect-and-pre-process-data"]], "Probability Distribution Functions": [[29, "probability-distribution-functions"]], "Program example for gradient descent with Ridge Regression": [[34, "program-example-for-gradient-descent-with-ridge-regression"], [35, "program-example-for-gradient-descent-with-ridge-regression"]], "Program for stochastic gradient": [[13, "program-for-stochastic-gradient"]], "Project 1 on Machine Learning, deadline October 6 (midnight), 2025": [[26, null]], "Project 2 on Machine Learning, deadline November 10 (Midnight)": [[27, null]], "Properties of PDFs": [[29, "properties-of-pdfs"]], "Pros and cons": [[35, "pros-and-cons"]], "Pros and cons of trees, pros": [[9, "pros-and-cons-of-trees-pros"]], "Python installers": [[24, "python-installers"], [32, "python-installers"]], "RMS prop": [[13, "rms-prop"]], "RMSProp algorithm, taken from Goodfellow et al": [[35, "rmsprop-algorithm-taken-from-goodfellow-et-al"]], "RMSProp: Adaptive Learning Rates": [[35, "rmsprop-adaptive-learning-rates"]], "RMSprop for adaptive learning rate with Stochastic Gradient Descent": [[35, "rmsprop-for-adaptive-learning-rate-with-stochastic-gradient-descent"]], "ROC Curve": [[23, "roc-curve"]], "Random Numbers": [[29, "random-numbers"]], "Random forests": [[10, "random-forests"]], "Randomized PCA": [[11, "randomized-pca"]], "Reading material": [[32, "reading-material"]], "Reading recommendations": [[40, "reading-recommendations"]], "Reading recommendations:": [[33, "reading-recommendations"]], "Reading suggestions week 34": [[32, "reading-suggestions-week-34"]], "Readings and Videos": [[36, "readings-and-videos"]], "Readings and Videos, logistic regression": [[37, "readings-and-videos-logistic-regression"]], "Readings and Videos, resampling methods": [[37, "readings-and-videos-resampling-methods"]], "Readings and Videos:": [[35, "readings-and-videos"], [39, "readings-and-videos"]], "Readings and videos": [[40, "readings-and-videos"]], "Recurrent neural networks": [[12, "recurrent-neural-networks"], [38, "recurrent-neural-networks"], [39, "recurrent-neural-networks"]], "Recurrent neural networks: Overarching view": [[4, null]], "Reducing the number of degrees of freedom, overarching view": [[0, "reducing-the-number-of-degrees-of-freedom-overarching-view"], [33, "reducing-the-number-of-degrees-of-freedom-overarching-view"]], "Reducing the number of operations": [[39, "reducing-the-number-of-operations"]], "Reformulating the problem": [[2, "reformulating-the-problem"], [41, "reformulating-the-problem"]], "Regression Case": [[10, "regression-case"]], "Regression analysis and resampling methods": [[26, "regression-analysis-and-resampling-methods"]], "Regression analysis, overarching aims": [[32, "regression-analysis-overarching-aims"]], "Regression analysis, overarching aims II": [[32, "regression-analysis-overarching-aims-ii"]], "Regularization": [[1, "regularization"], [40, "regularization"]], "Relevance": [[38, "relevance"], [40, "relevance"]], "Reminder about the gradient machinery from project 1": [[27, "reminder-about-the-gradient-machinery-from-project-1"]], "Reminder from last week": [[33, "reminder-from-last-week"]], "Reminder from last week: First network example, simple percepetron with one input": [[40, "reminder-from-last-week-first-network-example-simple-percepetron-with-one-input"]], "Reminder on Newton-Raphson\u2019s method": [[34, "reminder-on-newton-raphson-s-method"]], "Reminder on Statistics": [[6, "reminder-on-statistics"]], "Reminder on books with hands-on material and codes": [[39, "reminder-on-books-with-hands-on-material-and-codes"], [40, "reminder-on-books-with-hands-on-material-and-codes"]], "Reminder on different scaling methods": [[35, "reminder-on-different-scaling-methods"]], "Reminder on the chain rule and gradients": [[39, "reminder-on-the-chain-rule-and-gradients"]], "Replace or not": [[13, "replace-or-not"], [35, "replace-or-not"]], "Required Analysis:": [[27, "required-analysis"]], "Required Technologies": [[24, "required-technologies"]], "Resampling Methods": [[6, null]], "Resampling and the Bias-Variance Trade-off": [[19, "resampling-and-the-bias-variance-trade-off"]], "Resampling approaches can be computationally expensive": [[36, "resampling-approaches-can-be-computationally-expensive"], [37, "resampling-approaches-can-be-computationally-expensive"]], "Resampling methods": [[6, "id1"], [36, "resampling-methods"], [36, "id2"], [37, "resampling-methods"], [37, "id1"]], "Resampling methods: Bootstrap": [[36, "resampling-methods-bootstrap"], [37, "resampling-methods-bootstrap"]], "Resampling methods: Bootstrap approach": [[36, "resampling-methods-bootstrap-approach"]], "Resampling methods: Bootstrap background": [[36, "resampling-methods-bootstrap-background"]], "Resampling methods: Bootstrap steps": [[36, "resampling-methods-bootstrap-steps"]], "Resampling methods: More Bootstrap background": [[36, "resampling-methods-more-bootstrap-background"]], "Residual Error": [[33, "residual-error"], [34, "residual-error"]], "Resources on differential equations and deep learning": [[2, "resources-on-differential-equations-and-deep-learning"], [41, "resources-on-differential-equations-and-deep-learning"]], "Revisiting Ordinary Least Squares": [[34, "revisiting-ordinary-least-squares"]], "Revisiting our Linear Regression Solvers": [[13, "revisiting-our-linear-regression-solvers"]], "Revisiting our Logistic Regression case": [[37, "revisiting-our-logistic-regression-case"], [38, "revisiting-our-logistic-regression-case"]], "Rewriting the Covariance and/or Correlation Matrix": [[33, "rewriting-the-covariance-and-or-correlation-matrix"]], "Rewriting the \\delta-function": [[36, "rewriting-the-delta-function"]], "Rewriting the fitting procedure as a linear algebra problem": [[32, "rewriting-the-fitting-procedure-as-a-linear-algebra-problem"]], "Rewriting the fitting procedure as a linear algebra problem, more details": [[32, "rewriting-the-fitting-procedure-as-a-linear-algebra-problem-more-details"]], "Ridge Regression": [[34, "ridge-regression"]], "Ridge and LASSO Regression": [[33, "ridge-and-lasso-regression"], [34, "ridge-and-lasso-regression"], [34, "id2"]], "Ridge and Lasso Regression": [[5, null], [5, "id1"]], "SGD example": [[35, "sgd-example"]], "SGD vs Full-Batch GD: Convergence Speed and Memory Comparison": [[35, "sgd-vs-full-batch-gd-convergence-speed-and-memory-comparison"]], "SVD analysis": [[34, "svd-analysis"]], "Same code but now with momentum gradient descent": [[13, "same-code-but-now-with-momentum-gradient-descent"], [35, "same-code-but-now-with-momentum-gradient-descent"], [35, "id3"], [35, "id4"]], "Schedule first week": [[32, "schedule-first-week"]], "Schematic Regression Procedure": [[9, "schematic-regression-procedure"]], "Second moment of the gradient": [[35, "second-moment-of-the-gradient"]], "September 15-19": [[19, "september-15-19"]], "Setting up a Multi-layer perceptron model for classification": [[40, "setting-up-a-multi-layer-perceptron-model-for-classification"]], "Setting up the Back propagation algorithm": [[12, "setting-up-the-back-propagation-algorithm"]], "Setting up the Back propagation algorithm, part 3": [[39, "setting-up-the-back-propagation-algorithm-part-3"], [40, "setting-up-the-back-propagation-algorithm-part-3"], [41, "setting-up-the-back-propagation-algorithm-part-3"]], "Setting up the Matrix to be inverted": [[33, "setting-up-the-matrix-to-be-inverted"], [34, "setting-up-the-matrix-to-be-inverted"]], "Setting up the back propagation algorithm": [[39, "setting-up-the-back-propagation-algorithm"]], "Setting up the back propagation algorithm and algorithm for a feed forward NN, initalizations": [[40, "setting-up-the-back-propagation-algorithm-and-algorithm-for-a-feed-forward-nn-initalizations"], [41, "setting-up-the-back-propagation-algorithm-and-algorithm-for-a-feed-forward-nn-initalizations"]], "Setting up the back propagation algorithm, part 1": [[40, "setting-up-the-back-propagation-algorithm-part-1"], [41, "setting-up-the-back-propagation-algorithm-part-1"]], "Setting up the back propagation algorithm, part 2": [[39, "setting-up-the-back-propagation-algorithm-part-2"], [40, "setting-up-the-back-propagation-algorithm-part-2"], [41, "setting-up-the-back-propagation-algorithm-part-2"]], "Setting up the code": [[41, "setting-up-the-code"]], "Setting up the equations for a neural network": [[39, "setting-up-the-equations-for-a-neural-network"], [40, "setting-up-the-equations-for-a-neural-network"]], "Setting up the network using Autograd": [[41, "setting-up-the-network-using-autograd"]], "Setting up the network using Autograd; The full program": [[2, "setting-up-the-network-using-autograd-the-full-program"], [41, "setting-up-the-network-using-autograd-the-full-program"]], "Setting up the network using Autograd; The trial solution": [[41, "setting-up-the-network-using-autograd-the-trial-solution"]], "Setting up the problem": [[41, "setting-up-the-problem"]], "Setup of Network": [[41, "setup-of-network"]], "Similar (second order function now) problem but now with AdaGrad": [[13, "similar-second-order-function-now-problem-but-now-with-adagrad"], [35, "similar-second-order-function-now-problem-but-now-with-adagrad"]], "Simple Python Code to read in Data and perform Classification": [[9, "simple-python-code-to-read-in-data-and-perform-classification"]], "Simple case": [[33, "simple-case"], [34, "simple-case"]], "Simple code for solving the above problem": [[34, "simple-code-for-solving-the-above-problem"]], "Simple example": [[37, "simple-example"], [39, "simple-example"]], "Simple example code": [[35, "simple-example-code"]], "Simple example to illustrate Ordinary Least Squares, Ridge and Lasso Regression": [[34, "simple-example-to-illustrate-ordinary-least-squares-ridge-and-lasso-regression"]], "Simple geometric interpretation": [[34, "simple-geometric-interpretation"]], "Simple linear regression model using scikit-learn": [[0, "simple-linear-regression-model-using-scikit-learn"], [32, "simple-linear-regression-model-using-scikit-learn"]], "Simple neural network and the  back propagation equations": [[39, "simple-neural-network-and-the-back-propagation-equations"], [40, "simple-neural-network-and-the-back-propagation-equations"]], "Simple one-dimensional second-order polynomial": [[18, "simple-one-dimensional-second-order-polynomial"]], "Simple program": [[34, "simple-program"], [35, "simple-program"]], "Simpler examples first, and automatic differentiation": [[39, "simpler-examples-first-and-automatic-differentiation"]], "Slightly different approach": [[35, "slightly-different-approach"]], "Smarter way of evaluating the above function": [[39, "smarter-way-of-evaluating-the-above-function"]], "Sneaking in automatic differentiation using Autograd": [[35, "sneaking-in-automatic-differentiation-using-autograd"]], "Software and needed installations": [[26, "software-and-needed-installations"], [32, "software-and-needed-installations"]], "Solving Differential Equations  with Deep Learning": [[2, null]], "Solving differential equations  with Deep Learning": [[41, "solving-differential-equations-with-deep-learning"]], "Solving the equation using Autograd": [[41, "solving-the-equation-using-autograd"]], "Solving the one dimensional Poisson equation": [[2, "solving-the-one-dimensional-poisson-equation"]], "Solving the wave equation - the full program using Autograd": [[41, "solving-the-wave-equation-the-full-program-using-autograd"]], "Solving the wave equation with Neural Networks": [[2, "solving-the-wave-equation-with-neural-networks"]], "Solving using Newton-Raphson\u2019s method": [[37, "solving-using-newton-raphson-s-method"], [38, "solving-using-newton-raphson-s-method"]], "Some famous Matrices": [[25, "some-famous-matrices"]], "Some parallels from real analysis": [[39, "some-parallels-from-real-analysis"]], "Some selected properties": [[37, "some-selected-properties"]], "Some simple problems": [[13, "some-simple-problems"], [34, "some-simple-problems"]], "Some useful matrix and vector expressions": [[33, "some-useful-matrix-and-vector-expressions"]], "Splitting our Data in Training and Test data": [[0, "splitting-our-data-in-training-and-test-data"], [33, "splitting-our-data-in-training-and-test-data"]], "Standard Approach based on the Normal Distribution": [[36, "standard-approach-based-on-the-normal-distribution"]], "Standard steepest descent": [[13, "standard-steepest-descent"]], "Statistical analysis": [[36, "statistical-analysis"], [37, "statistical-analysis"]], "Statistical analysis and optimization of data": [[24, "statistical-analysis-and-optimization-of-data"], [32, "statistical-analysis-and-optimization-of-data"]], "Steepest descent": [[13, "steepest-descent"], [34, "steepest-descent"]], "Stochastic Gradient Descent": [[35, "stochastic-gradient-descent"]], "Stochastic Gradient Descent (SGD)": [[13, "stochastic-gradient-descent-sgd"], [35, "stochastic-gradient-descent-sgd"]], "Stochastic variables and the main concepts, the discrete case": [[29, "stochastic-variables-and-the-main-concepts-the-discrete-case"]], "Strongly Convex Case": [[35, "strongly-convex-case"]], "Suggested readings and videos": [[38, "suggested-readings-and-videos"]], "Summary of methods to implement and analyze": [[27, "summary-of-methods-to-implement-and-analyze"]], "Summing up": [[36, "summing-up"], [37, "summing-up"]], "Support Vector Machines, overarching aims": [[8, null]], "Synthetic data generation": [[37, "synthetic-data-generation"], [38, "synthetic-data-generation"]], "Systematic reduction": [[3, "systematic-reduction"]], "Teachers": [[32, "teachers"]], "Teachers and Grading": [[30, null]], "Teaching Assistants Fall semester 2023": [[30, "teaching-assistants-fall-semester-2023"]], "Technicalities": [[41, "technicalities"]], "Tensorflow": [[40, "tensorflow"], [41, "tensorflow"]], "Tentative deadllines for projects": [[30, "tentative-deadllines-for-projects"]], "Testing the Means Squared Error as function of Complexity": [[0, "testing-the-means-squared-error-as-function-of-complexity"], [33, "testing-the-means-squared-error-as-function-of-complexity"]], "Testing the XOR gate and other gates": [[40, "testing-the-xor-gate-and-other-gates"], [41, "testing-the-xor-gate-and-other-gates"]], "Textbooks": [[31, null]], "The  back propagation equations for a neural network": [[40, "the-back-propagation-equations-for-a-neural-network"]], "The Algorithm before theorem": [[11, "the-algorithm-before-theorem"]], "The Breast Cancer Data, now with Keras": [[1, "the-breast-cancer-data-now-with-keras"]], "The CART algorithm for Classification": [[9, "the-cart-algorithm-for-classification"]], "The CART algorithm for Regression": [[9, "the-cart-algorithm-for-regression"]], "The CIFAR01 data set": [[3, "the-cifar01-data-set"]], "The Central Limit Theorem": [[36, "the-central-limit-theorem"]], "The Hessian matrix": [[34, "the-hessian-matrix"], [35, "the-hessian-matrix"]], "The Hessian matrix for Ridge Regression": [[34, "the-hessian-matrix-for-ridge-regression"], [35, "the-hessian-matrix-for-ridge-regression"]], "The Jacobian": [[33, "the-jacobian"]], "The MNIST dataset again": [[3, "the-mnist-dataset-again"]], "The Neural Network": [[40, "the-neural-network"], [41, "the-neural-network"]], "The OLS case": [[34, "the-ols-case"]], "The RELU function family": [[1, "the-relu-function-family"], [40, "the-relu-function-family"], [41, "the-relu-function-family"]], "The Ridge case": [[34, "the-ridge-case"]], "The SVD, a Fantastic Algorithm": [[33, "the-svd-a-fantastic-algorithm"], [34, "the-svd-a-fantastic-algorithm"]], "The Softmax function": [[1, "the-softmax-function"], [40, "the-softmax-function"]], "The \\chi^2 function": [[0, "the-chi-2-function"], [32, "the-chi-2-function"], [32, "id4"], [32, "id5"], [32, "id6"], [32, "id7"], [32, "id8"]], "The analytical solution": [[41, "the-analytical-solution"]], "The approximation theorem in words": [[39, "the-approximation-theorem-in-words"]], "The bias-variance tradeoff": [[6, "the-bias-variance-tradeoff"], [36, "the-bias-variance-tradeoff"], [37, "the-bias-variance-tradeoff"]], "The code for solving the ODE": [[2, "the-code-for-solving-the-ode"], [41, "the-code-for-solving-the-ode"]], "The complete code with a simple data set": [[33, "the-complete-code-with-a-simple-data-set"]], "The cost function rewritten": [[37, "the-cost-function-rewritten"], [38, "the-cost-function-rewritten"]], "The cost/loss function": [[33, "the-cost-loss-function"]], "The course has two central parts": [[24, "the-course-has-two-central-parts"]], "The derivative of the Logistic funtion": [[40, "the-derivative-of-the-logistic-funtion"]], "The derivative of the cost/loss function": [[34, "the-derivative-of-the-cost-loss-function"], [35, "the-derivative-of-the-cost-loss-function"]], "The derivatives": [[39, "the-derivatives"], [40, "the-derivatives"]], "The equations": [[34, "the-equations"]], "The equations for ordinary least squares": [[33, "the-equations-for-ordinary-least-squares"]], "The equations to solve": [[37, "the-equations-to-solve"], [38, "the-equations-to-solve"]], "The first Case": [[34, "the-first-case"]], "The function to solve for": [[41, "the-function-to-solve-for"]], "The gradient step": [[35, "the-gradient-step"]], "The ideal": [[34, "the-ideal"]], "The logistic function": [[7, "the-logistic-function"], [37, "the-logistic-function"]], "The mean squared error and its derivative": [[33, "the-mean-squared-error-and-its-derivative"]], "The moons example": [[8, "the-moons-example"]], "The multilayer  perceptron (MLP)": [[12, "the-multilayer-perceptron-mlp"]], "The network with one input layer, specified number of hidden layers, and one output layer": [[2, "the-network-with-one-input-layer-specified-number-of-hidden-layers-and-one-output-layer"], [41, "the-network-with-one-input-layer-specified-number-of-hidden-layers-and-one-output-layer"]], "The optimization problem": [[39, "the-optimization-problem"]], "The ouput layer": [[39, "the-ouput-layer"], [40, "the-ouput-layer"]], "The plethora  of machine learning algorithms/methods": [[32, "the-plethora-of-machine-learning-algorithms-methods"]], "The problem to solve for": [[41, "the-problem-to-solve-for"]], "The program using Autograd": [[41, "the-program-using-autograd"]], "The same example but now with cross-validation": [[36, "the-same-example-but-now-with-cross-validation"], [37, 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Brief reminder on masses and binding energies": [[32, "to-our-real-data-nuclear-binding-energies-brief-reminder-on-masses-and-binding-energies"]], "Topics covered in this course: Statistical analysis and optimization of data": [[32, "topics-covered-in-this-course-statistical-analysis-and-optimization-of-data"]], "Towards the PCA theorem": [[11, "towards-the-pca-theorem"]], "Train and test datasets": [[1, "train-and-test-datasets"], [40, "train-and-test-datasets"]], "Two parameters": [[37, "two-parameters"], [38, "two-parameters"]], "Two-dimensional Objects": [[3, "two-dimensional-objects"]], "Type of problem": [[2, "type-of-problem"], [41, "type-of-problem"]], "Types of Machine Learning": [[32, "types-of-machine-learning"]], "Understanding what happens": [[36, "understanding-what-happens"], [37, "understanding-what-happens"]], "Universal approximation theorem": [[39, "universal-approximation-theorem"]], "Updating the gradients": [[39, "updating-the-gradients"], [40, "updating-the-gradients"], [41, "updating-the-gradients"]], "Usage of the above learning rate schedulers": [[40, "usage-of-the-above-learning-rate-schedulers"], [41, "usage-of-the-above-learning-rate-schedulers"]], "Use the books!": [[19, "use-the-books"]], "Useful Python libraries": [[24, "useful-python-libraries"], [32, "useful-python-libraries"]], "Using Autograd": [[13, "using-autograd"]], "Using Automatic differentiation": [[41, "using-automatic-differentiation"]], "Using Keras": [[40, "using-keras"], [41, "using-keras"]], "Using Pytorch with the full MNIST data set": [[41, "using-pytorch-with-the-full-mnist-data-set"]], "Using Scikit-learn": [[38, "using-scikit-learn"]], "Using forward Euler to solve the ODE": [[2, "using-forward-euler-to-solve-the-ode"], [41, "using-forward-euler-to-solve-the-ode"]], "Using gradient descent methods, limitations": [[13, "using-gradient-descent-methods-limitations"], [34, "using-gradient-descent-methods-limitations"], [35, "using-gradient-descent-methods-limitations"]], "Using the chain rule and summing over all k entries": [[39, "using-the-chain-rule-and-summing-over-all-k-entries"], [40, "using-the-chain-rule-and-summing-over-all-k-entries"]], "Using the correlation matrix": [[38, "using-the-correlation-matrix"]], "Vanishing gradients": [[40, "vanishing-gradients"]], "Various steps in cross-validation": [[36, "various-steps-in-cross-validation"], [37, "various-steps-in-cross-validation"]], "Visualization": [[1, "visualization"], [1, "id1"], [40, "visualization"], [40, "id1"]], "Visualizing the Tree, Classification": [[9, "visualizing-the-tree-classification"]], "Week 34: Introduction to the course, Logistics and Practicalities": [[32, null]], "Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression": [[33, null]], "Week 36: Linear Regression and Gradient descent": [[34, null]], "Week 37: Gradient descent methods": [[35, null]], "Week 38: Statistical analysis, bias-variance tradeoff and resampling methods": [[36, null]], "Week 39: Resampling methods and logistic regression": [[37, null]], "Week 40: Gradient descent methods (continued) and start Neural networks": [[38, null]], "Week 41 Neural networks and constructing a neural network code": [[39, null]], "Week 42 Constructing a Neural Network code with examples": [[40, null]], "Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations": [[41, null]], "Weights and biases": [[40, "weights-and-biases"]], "What Is Generative Modeling?": [[32, "what-is-generative-modeling"]], "What does it mean?": [[33, "what-does-it-mean"], [34, "what-does-it-mean"]], "What is Machine Learning?": [[0, "what-is-machine-learning"]], "What is a good model?": [[0, "what-is-a-good-model"], [32, "what-is-a-good-model"]], "What is a good model? 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</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", "Exercises week 37", "Exercises week 38", "Exercises week 39", "Exercises week 41", "Exercises week 42", "Exercises week 43", "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 6 (midnight), 2025", "Project 2 on Machine Learning, deadline November 10 (Midnight)", "Course setting", "<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 Regression and Gradient descent", "Week 37: Gradient descent methods", "Week 38: Statistical analysis, bias-variance tradeoff and resampling methods", "Week 39: Resampling methods and logistic regression", "Week 40: Gradient descent methods (continued) and start Neural networks", "Week 41 Neural networks and constructing a neural network code", "Week 42 Constructing a Neural Network code with examples", "Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations"], "titleterms": {"": [8, 10, 34, 35, 36, 37, 38], "0": 40, "04": [], "05": [], "06": [], "07": [], "1": [0, 15, 16, 17, 18, 19, 20, 21, 22, 26, 27, 33, 39, 40, 41], 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diff --git a/doc/LectureNotes/_build/jupyter_execute/exercisesweek43.ipynb b/doc/LectureNotes/_build/jupyter_execute/exercisesweek43.ipynb
index 20e5e5ba1..e02a479e8 100644
--- a/doc/LectureNotes/_build/jupyter_execute/exercisesweek43.ipynb
+++ b/doc/LectureNotes/_build/jupyter_execute/exercisesweek43.ipynb
@@ -32,15 +32,15 @@
     "editable": true
    },
    "source": [
-    "# Overarching aims of the exercises weeks 43 and 44\n",
+    "# Overarching aims of the exercises for week 43\n",
     "\n",
     "The aim of the exercises this week is to gain some confidence with\n",
     "ways to visualize the results of a classification problem.  We will\n",
     "target three ways of setting up the analysis. The first and simplest\n",
     "one is the\n",
-    "1. so-called confusion matrix, and the next is the\n",
+    "1. so-called confusion matrix. The next one is the so-called\n",
     "\n",
-    "2. ROC curve and finally the\n",
+    "2. ROC curve. Finally we have the\n",
     "\n",
     "3. Cumulative gain curve.\n",
     "\n",
@@ -446,7 +446,10 @@
    "id": "be9ff0b9",
    "metadata": {
     "collapsed": false,
-    "editable": true
+    "editable": true,
+    "jupyter": {
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+    }
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    "source": [
@@ -518,7 +521,10 @@
    "id": "d20bb8be",
    "metadata": {
     "collapsed": false,
-    "editable": true
+    "editable": true,
+    "jupyter": {
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+    }
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    "source": [
@@ -547,7 +553,10 @@
    "id": "d271f0ba",
    "metadata": {
     "collapsed": false,
-    "editable": true
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
    },
    "outputs": [],
    "source": [
@@ -589,7 +598,10 @@
    "id": "3b045d56",
    "metadata": {
     "collapsed": false,
-    "editable": true
+    "editable": true,
+    "jupyter": {
+     "outputs_hidden": false
+    }
    },
    "outputs": [],
    "source": [
@@ -611,7 +623,25 @@
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   }
  ],
- "metadata": {},
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.15"
+  }
+ },
  "nbformat": 4,
  "nbformat_minor": 5
 }
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