lars/FYS-STK4155
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

update exercises w38 and w39

Browse Source
This commit is contained in:
KarlHenrik
2025-09-10 12:14:32 +02:00
parent cee5f8e1f0
commit fbdf9c32f8
196 changed files with 23368 additions and 300 deletions
Download Patch File Download Diff File Expand all files Collapse all files
doc/LectureNotes/_build/html/exercisesweek35.html
+5 -5
View File
@@ -28,7 +28,7 @@
<link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-brands-400.woff2" />
<link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-regular-400.woff2" />
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" />
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=03e43079" />
<link rel="stylesheet" type="text/css" href="_static/styles/sphinx-book-theme.css?v=eba8b062" />
<link rel="stylesheet" type="text/css" href="_static/togglebutton.css?v=13237357" />
<link rel="stylesheet" type="text/css" href="_static/copybutton.css?v=76b2166b" />
@@ -514,7 +514,7 @@ f_i =\sum_{j=0}^{n-1}a_{ij}x_j,
<p>We calculate the optimal intercept by including a feature with the constant value of 1 in our model, which is then multplied by some parameter <span class="math notranslate nohighlight">\(\theta_0\)</span> from the OLS method into the optimal intercept value (which will be <span class="math notranslate nohighlight">\(\theta_0\)</span>). In practice, we include the intercept in our model by adding a column of ones to the start of our feature matrix.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
</pre></div>
</div>
</div>
@@ -543,7 +543,7 @@ f_i =\sum_{j=0}^{n-1}a_{ij}x_j,
<p><strong>b)</strong> Use the expression from <strong>3d)</strong> to find the optimal parameters <span class="math notranslate nohighlight">\(\boldsymbol{\hat{\beta}_{OLS}}\)</span> for predicting spending based on these features. Create a function for this operation, as you are going to need to use it a lot.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">OLS_parameters</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">OLS_parameters</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
<span class="k">return</span> <span class="o">...</span>
<span class="c1">#beta = OLS_parameters(X, y)</span>
@@ -568,7 +568,7 @@ f_i =\sum_{j=0}^{n-1}a_{ij}x_j,
<p><strong>a)</strong> Create a feature matrix <span class="math notranslate nohighlight">\(\boldsymbol{X}\)</span> for the features <span class="math notranslate nohighlight">\(x, x^2, x^3, x^4, x^5\)</span>, including an intercept column of ones at the start. Make this into a function, as you will do this a lot over the next weeks.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">polynomial_features</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">p</span><span class="p">):</span>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">polynomial_features</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">p</span><span class="p">):</span>
<span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">n</span><span class="p">,</span> <span class="n">p</span> <span class="o">+</span> <span class="mi">1</span><span class="p">))</span>
<span class="c1">#X[:, 0] = ...</span>
@@ -592,7 +592,7 @@ f_i =\sum_{j=0}^{n-1}a_{ij}x_j,
<p><strong>c)</strong> Like in exercise 4 last week, split your feature matrix and target data into a training split and test split.</p>
<div class="cell docutils container">
<div class="cell_input docutils container">
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></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>
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.model_selection</span><span class="w"> </span><span class="kn">import</span> <span class="n">train_test_split</span>
<span class="c1">#X_train, X_test, y_train, y_test = ...</span>
</pre></div>