update book with material week 39
This commit is contained in:
Morten Hjorth-Jensen
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@@ -1,4 +1,4 @@
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# Sphinx build info version 1
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# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
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config: e92a03a57b79a66b55d813e5d2c5e8ea
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config: 73ce6691cda151d4aabc9466268ebbb7
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tags: 645f666f9bcd5a90fca523b33c5a78b7
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Load Diff
@@ -6,11 +6,11 @@ html[data-theme="light"] .highlight span.linenos.special { color: #000000; backg
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html[data-theme="light"] .highlight .hll { background-color: #fae4c2 }
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html[data-theme="light"] .highlight { background: #fefefe; color: #080808 }
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html[data-theme="light"] .highlight .err { color: #a12236 } /* Error */
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@@ -18,135 +18,135 @@ html[data-theme="light"] .highlight .cp { color: #515151 } /* Comment.Preproc */
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||||
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||||
<li class="toctree-l1"><a class="reference internal" href="exercisesweek39.html">Exercises week 39</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week39.html">Week 39: Resampling methods and logistic regression</a></li>
|
||||
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||||
<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Statistical analysis, bias-variance tradeoff and resampling methods</a></li>
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|
||||
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<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Statistical analysis, bias-variance tradeoff and resampling methods</a></li>
|
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<li class="toctree-l1"><a class="reference internal" href="exercisesweek39.html">Exercises week 39</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week39.html">Week 39: Resampling methods and logistic regression</a></li>
|
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|
||||
<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Statistical analysis, bias-variance tradeoff and resampling methods</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="exercisesweek39.html">Exercises week 39</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week39.html">Week 39: Resampling methods and logistic regression</a></li>
|
||||
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|
||||
<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Statistical analysis, bias-variance tradeoff and resampling methods</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="exercisesweek39.html">Exercises week 39</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week39.html">Week 39: Resampling methods and logistic regression</a></li>
|
||||
</ul>
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<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
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<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Statistical analysis, bias-variance tradeoff and resampling methods</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="exercisesweek39.html">Exercises week 39</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week39.html">Week 39: Resampling methods and logistic regression</a></li>
|
||||
</ul>
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<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Statistical analysis, bias-variance tradeoff and resampling methods</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="exercisesweek39.html">Exercises week 39</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week39.html">Week 39: Resampling methods and logistic regression</a></li>
|
||||
</ul>
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||||
<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
|
||||
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|
||||
@@ -479,11 +480,11 @@ document.write(`
|
||||
<p><strong>b)</strong> Compute the mean square error for the line model and for the second degree polynomial model.</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="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>
|
||||
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
|
||||
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.preprocessing</span><span class="w"> </span><span class="kn">import</span> <span class="n">PolynomialFeatures</span> <span class="c1"># use the fit_transform method of the created object!</span>
|
||||
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.linear_model</span><span class="w"> </span><span class="kn">import</span> <span class="n">LinearRegression</span>
|
||||
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.metrics</span><span class="w"> </span><span class="kn">import</span> <span class="n">mean_squared_error</span>
|
||||
<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>
|
||||
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
|
||||
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">PolynomialFeatures</span> <span class="c1"># use the fit_transform method of the created object!</span>
|
||||
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <span class="n">LinearRegression</span>
|
||||
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">mean_squared_error</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -520,7 +521,7 @@ document.write(`
|
||||
<p>Hopefully your model fit the data quite well, but to know how well the model actually generalizes to unseen data, which is most often what we care about, we need to split our data into training and testing data.</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="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>
|
||||
<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>
|
||||
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|
||||
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|
||||
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|
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||||
<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Statistical analysis, bias-variance tradeoff and resampling methods</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="exercisesweek39.html">Exercises week 39</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week39.html">Week 39: Resampling methods and logistic regression</a></li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
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||||
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||||
@@ -515,7 +516,7 @@ 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>
|
||||
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|
||||
<div class="cell_input docutils container">
|
||||
<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>
|
||||
<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>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -544,7 +545,7 @@ 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="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>
|
||||
<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>
|
||||
<span class="k">return</span> <span class="o">...</span>
|
||||
|
||||
<span class="c1">#beta = OLS_parameters(X, y)</span>
|
||||
@@ -569,7 +570,7 @@ 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="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>
|
||||
<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>
|
||||
<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>
|
||||
@@ -593,7 +594,7 @@ 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="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>
|
||||
<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>
|
||||
|
||||
<span class="c1">#X_train, X_test, y_train, y_test = ...</span>
|
||||
</pre></div>
|
||||
|
||||
@@ -28,7 +28,7 @@
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||||
<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Statistical analysis, bias-variance tradeoff and resampling methods</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="exercisesweek39.html">Exercises week 39</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week39.html">Week 39: Resampling methods and logistic regression</a></li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
|
||||
<ul class="nav bd-sidenav">
|
||||
@@ -467,10 +468,10 @@ defining a new cost function to be optimized, that is</p>
|
||||
<h2>Exercise 3 - Scaling data<a class="headerlink" href="#exercise-3-scaling-data" title="Link to this heading">#</a></h2>
|
||||
<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="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>
|
||||
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</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="kn">from</span><span class="w"> </span><span class="nn">sklearn.preprocessing</span><span class="w"> </span><span class="kn">import</span> <span class="n">StandardScaler</span>
|
||||
<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>
|
||||
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</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="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">StandardScaler</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -487,7 +488,7 @@ defining a new cost function to be optimized, that is</p>
|
||||
<p><strong>a)</strong> Adapt your function from last week to only include the intercept column if the boolean argument <code class="docutils literal notranslate"><span class="pre">intercept</span></code> is set to true.</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="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">intercept</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
||||
<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> <span class="n">intercept</span><span class="o">=</span><span class="kc">False</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>
|
||||
@@ -500,7 +501,7 @@ defining a new cost function to be optimized, that is</p>
|
||||
</div>
|
||||
<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="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">intercept</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
|
||||
<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> <span class="n">intercept</span><span class="o">=</span><span class="kc">False</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="p">))</span>
|
||||
<span class="n">X</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">x</span><span class="p">[:]</span>
|
||||
@@ -546,7 +547,7 @@ defining a new cost function to be optimized, that is</p>
|
||||
<p><strong>a)</strong> Implement a function for computing the optimal Ridge parameters using the expression from <strong>2a)</strong>.</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="w"> </span><span class="nf">Ridge_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="nf">Ridge_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="c1"># Assumes X is scaled and has no intercept column</span>
|
||||
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">X</span><span class="p">)</span> <span class="o">@</span> <span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">y</span>
|
||||
|
||||
|
||||
@@ -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=03e43079" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" />
|
||||
<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" />
|
||||
@@ -234,6 +234,7 @@
|
||||
<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Statistical analysis, bias-variance tradeoff and resampling methods</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="exercisesweek39.html">Exercises week 39</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week39.html">Week 39: Resampling methods and logistic regression</a></li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
|
||||
<ul class="nav bd-sidenav">
|
||||
@@ -584,7 +585,7 @@ Then we compute the target values <span class="math notranslate nohighlight">\(y
|
||||
<p>Below is the code to generate the dataset:</p>
|
||||
<div class="cell docutils container">
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-python 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>
|
||||
<div class="highlight-python 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>
|
||||
|
||||
<span class="c1"># Set random seed for reproducibility</span>
|
||||
<span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||||
|
||||
@@ -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=03e43079" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" />
|
||||
<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" />
|
||||
@@ -234,6 +234,7 @@
|
||||
<li class="toctree-l1 current active"><a class="current reference internal" href="#">Exercises week 38</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Statistical analysis, bias-variance tradeoff and resampling methods</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="exercisesweek39.html">Exercises week 39</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week39.html">Week 39: Resampling methods and logistic regression</a></li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
|
||||
<ul class="nav bd-sidenav">
|
||||
@@ -525,7 +526,7 @@ C(\boldsymbol{X},\boldsymbol{\beta}) =\frac{1}{n}\sum_{i=0}^{n-1}(y_i-\tilde{y}_
|
||||
<p><strong>a)</strong> Using the expression above, compute the mean squared error, bias and variance of the given data. Check that the sum of the bias and variance correctly gives (approximately) the mean squared error.</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="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>
|
||||
<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>
|
||||
|
||||
<span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
|
||||
<span class="n">bootstraps</span> <span class="o">=</span> <span class="mi">1000</span>
|
||||
@@ -546,15 +547,15 @@ C(\boldsymbol{X},\boldsymbol{\beta}) =\frac{1}{n}\sum_{i=0}^{n-1}(y_i-\tilde{y}_
|
||||
<p><strong>d)</strong> Perform a bias-variance analysis of a polynomial OLS model fit to a one-dimensional function by computing and plotting the bias and variances values as a function of the polynomial degree of your model.</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="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>
|
||||
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
|
||||
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.preprocessing</span><span class="w"> </span><span class="kn">import</span> <span class="p">(</span>
|
||||
<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>
|
||||
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
|
||||
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="p">(</span>
|
||||
<span class="n">PolynomialFeatures</span><span class="p">,</span>
|
||||
<span class="p">)</span> <span class="c1"># use the fit_transform method of the created object!</span>
|
||||
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.linear_model</span><span class="w"> </span><span class="kn">import</span> <span class="n">LinearRegression</span>
|
||||
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.metrics</span><span class="w"> </span><span class="kn">import</span> <span class="n">mean_squared_error</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="kn">from</span><span class="w"> </span><span class="nn">sklearn.utils</span><span class="w"> </span><span class="kn">import</span> <span class="n">resample</span>
|
||||
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <span class="n">LinearRegression</span>
|
||||
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">mean_squared_error</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="kn">from</span> <span class="nn">sklearn.utils</span> <span class="kn">import</span> <span class="n">resample</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
@@ -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" />
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||||
<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=03e43079" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" />
|
||||
<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" />
|
||||
@@ -60,7 +60,7 @@
|
||||
<script>DOCUMENTATION_OPTIONS.pagename = 'exercisesweek39';</script>
|
||||
<link rel="index" title="Index" href="genindex.html" />
|
||||
<link rel="search" title="Search" href="search.html" />
|
||||
<link rel="next" title="Project 1 on Machine Learning, deadline October 6 (midnight), 2025" href="project1.html" />
|
||||
<link rel="next" title="Week 39: Resampling methods and logistic regression" href="week39.html" />
|
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<link rel="prev" title="Week 38: Statistical analysis, bias-variance tradeoff and resampling methods" href="week38.html" />
|
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<meta name="viewport" content="width=device-width, initial-scale=1"/>
|
||||
<meta name="docsearch:language" content="en"/>
|
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@@ -232,6 +232,7 @@
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<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Statistical analysis, bias-variance tradeoff and resampling methods</a></li>
|
||||
<li class="toctree-l1 current active"><a class="current reference internal" href="#">Exercises week 39</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week39.html">Week 39: Resampling methods and logistic regression</a></li>
|
||||
</ul>
|
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<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
|
||||
<ul class="nav bd-sidenav">
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@@ -517,11 +518,11 @@ document.write(`
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||||
</div>
|
||||
</a>
|
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<a class="right-next"
|
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href="project1.html"
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<p class="prev-next-subtitle">next</p>
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<p class="prev-next-title">Project 1 on Machine Learning, deadline October 6 (midnight), 2025</p>
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<p class="prev-next-title">Week 39: Resampling methods and logistic regression</p>
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@@ -27,7 +27,7 @@
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<link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-brands-400.woff2" />
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<link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-regular-400.woff2" />
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<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=03e43079" />
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<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" />
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<link rel="stylesheet" type="text/css" href="_static/togglebutton.css?v=13237357" />
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<link rel="stylesheet" type="text/css" href="_static/copybutton.css?v=76b2166b" />
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@@ -231,6 +231,7 @@
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<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Statistical analysis, bias-variance tradeoff and resampling methods</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="exercisesweek39.html">Exercises week 39</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week39.html">Week 39: Resampling methods and logistic regression</a></li>
|
||||
</ul>
|
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<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
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@@ -28,7 +28,7 @@
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<link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-brands-400.woff2" />
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<link rel="preload" as="font" type="font/woff2" crossorigin href="_static/vendor/fontawesome/6.5.2/webfonts/fa-regular-400.woff2" />
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<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=03e43079" />
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<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" />
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<link rel="stylesheet" type="text/css" href="_static/styles/sphinx-book-theme.css?v=eba8b062" />
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<link rel="stylesheet" type="text/css" href="_static/togglebutton.css?v=13237357" />
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@@ -895,7 +896,7 @@ We assume our data can represented by a fourth-order polynomial. For the <span c
|
||||
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|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># matrix inversion to find theta</span>
|
||||
<span class="c1"># First we set up the data</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>
|
||||
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
|
||||
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">100</span><span class="p">)</span>
|
||||
<span class="n">y</span> <span class="o">=</span> <span class="mf">2.0</span><span class="o">+</span><span class="mi">5</span><span class="o">*</span><span class="n">x</span><span class="o">*</span><span class="n">x</span><span class="o">+</span><span class="mf">0.1</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">100</span><span class="p">)</span>
|
||||
<span class="c1"># and then the design matrix X including the intercept</span>
|
||||
@@ -929,7 +930,7 @@ We assume our data can represented by a fourth-order polynomial. For the <span c
|
||||
Since we are not using <strong>Scikit-Learn</strong> here we can define our own <span class="math notranslate nohighlight">\(R2\)</span> function as</p>
|
||||
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|
||||
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|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">R2</span><span class="p">(</span><span class="n">y_data</span><span class="p">,</span> <span class="n">y_model</span><span class="p">):</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">R2</span><span class="p">(</span><span class="n">y_data</span><span class="p">,</span> <span class="n">y_model</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">y_data</span> <span class="o">-</span> <span class="n">y_model</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">y_data</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">y_data</span><span class="p">))</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
||||
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|
||||
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|
||||
@@ -946,7 +947,7 @@ Since we are not using <strong>Scikit-Learn</strong> here we can define our own
|
||||
<p>We can easily add our <strong>MSE</strong> score as</p>
|
||||
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|
||||
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|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">MSE</span><span class="p">(</span><span class="n">y_data</span><span class="p">,</span><span class="n">y_model</span><span class="p">):</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">MSE</span><span class="p">(</span><span class="n">y_data</span><span class="p">,</span><span class="n">y_model</span><span class="p">):</span>
|
||||
<span class="n">n</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">y_model</span><span class="p">)</span>
|
||||
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">y_data</span><span class="o">-</span><span class="n">y_model</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="n">n</span>
|
||||
|
||||
@@ -958,7 +959,7 @@ Since we are not using <strong>Scikit-Learn</strong> here we can define our own
|
||||
<p>and finally the relative error as</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="w"> </span><span class="nf">RelativeError</span><span class="p">(</span><span class="n">y_data</span><span class="p">,</span><span class="n">y_model</span><span class="p">):</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">RelativeError</span><span class="p">(</span><span class="n">y_data</span><span class="p">,</span><span class="n">y_model</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="nb">abs</span><span class="p">((</span><span class="n">y_data</span><span class="o">-</span><span class="n">y_model</span><span class="p">)</span><span class="o">/</span><span class="n">y_data</span><span class="p">)</span>
|
||||
<span class="nb">print</span><span class="p">(</span><span class="n">RelativeError</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">ytilde</span><span class="p">))</span>
|
||||
</pre></div>
|
||||
@@ -985,16 +986,16 @@ but now splitting the data into a training set and a test set.</p>
|
||||
<div class="cell_input docutils container">
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="o">%</span><span class="k">matplotlib</span> inline
|
||||
|
||||
<span class="kn">import</span><span class="w"> </span><span class="nn">os</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>
|
||||
<span class="kn">import</span><span class="w"> </span><span class="nn">pandas</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">pd</span>
|
||||
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</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="kn">import</span> <span class="nn">os</span>
|
||||
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
|
||||
<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
|
||||
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</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="k">def</span><span class="w"> </span><span class="nf">R2</span><span class="p">(</span><span class="n">y_data</span><span class="p">,</span> <span class="n">y_model</span><span class="p">):</span>
|
||||
<span class="k">def</span> <span class="nf">R2</span><span class="p">(</span><span class="n">y_data</span><span class="p">,</span> <span class="n">y_model</span><span class="p">):</span>
|
||||
<span class="k">return</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">y_data</span> <span class="o">-</span> <span class="n">y_model</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">y_data</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">y_data</span><span class="p">))</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
|
||||
<span class="k">def</span><span class="w"> </span><span class="nf">MSE</span><span class="p">(</span><span class="n">y_data</span><span class="p">,</span><span class="n">y_model</span><span class="p">):</span>
|
||||
<span class="k">def</span> <span class="nf">MSE</span><span class="p">(</span><span class="n">y_data</span><span class="p">,</span><span class="n">y_model</span><span class="p">):</span>
|
||||
<span class="n">n</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">y_model</span><span class="p">)</span>
|
||||
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">y_data</span><span class="o">-</span><span class="n">y_model</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="n">n</span>
|
||||
|
||||
@@ -1035,7 +1036,7 @@ but now splitting the data into a training set and a test set.</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="c1"># equivalently in numpy</span>
|
||||
<span class="k">def</span><span class="w"> </span><span class="nf">train_test_split_numpy</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">labels</span><span class="p">,</span> <span class="n">train_size</span><span class="p">,</span> <span class="n">test_size</span><span class="p">):</span>
|
||||
<span class="k">def</span> <span class="nf">train_test_split_numpy</span><span class="p">(</span><span class="n">inputs</span><span class="p">,</span> <span class="n">labels</span><span class="p">,</span> <span class="n">train_size</span><span class="p">,</span> <span class="n">test_size</span><span class="p">):</span>
|
||||
<span class="n">n_inputs</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">inputs</span><span class="p">)</span>
|
||||
<span class="n">inputs_shuffled</span> <span class="o">=</span> <span class="n">inputs</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
|
||||
<span class="n">labels_shuffled</span> <span class="o">=</span> <span class="n">labels</span><span class="o">.</span><span class="n">copy</span><span class="p">()</span>
|
||||
@@ -1140,13 +1141,13 @@ simple test design matrix with random numbers. Each column could then
|
||||
represent a specific feature whose mean value is subracted.</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="w"> </span><span class="nn">sklearn.linear_model</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">skl</span>
|
||||
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.metrics</span><span class="w"> </span><span class="kn">import</span> <span class="n">mean_squared_error</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="kn">from</span><span class="w"> </span><span class="nn">sklearn.preprocessing</span><span class="w"> </span><span class="kn">import</span> <span class="n">MinMaxScaler</span><span class="p">,</span> <span class="n">StandardScaler</span><span class="p">,</span> <span class="n">Normalizer</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>
|
||||
<span class="kn">import</span><span class="w"> </span><span class="nn">pandas</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">pd</span>
|
||||
<span class="kn">from</span><span class="w"> </span><span class="nn">IPython.display</span><span class="w"> </span><span class="kn">import</span> <span class="n">display</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">sklearn.linear_model</span> <span class="k">as</span> <span class="nn">skl</span>
|
||||
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">mean_squared_error</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="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">MinMaxScaler</span><span class="p">,</span> <span class="n">StandardScaler</span><span class="p">,</span> <span class="n">Normalizer</span>
|
||||
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
|
||||
<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
|
||||
<span class="kn">from</span> <span class="nn">IPython.display</span> <span class="kn">import</span> <span class="n">display</span>
|
||||
<span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">100</span><span class="p">)</span>
|
||||
<span class="c1"># setting up a 10 x 5 matrix</span>
|
||||
<span class="n">rows</span> <span class="o">=</span> <span class="mi">10</span>
|
||||
@@ -1202,12 +1203,12 @@ the aims is to reproduce Figure 2.11 of <a class="reference external" href="http
|
||||
<p>Write a first code which sets up a design matrix <span class="math notranslate nohighlight">\(X\)</span> defined by a fourth-order polynomial. Scale your data and split it in training and test data.</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="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</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>
|
||||
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.linear_model</span><span class="w"> </span><span class="kn">import</span> <span class="n">LinearRegression</span>
|
||||
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.preprocessing</span><span class="w"> </span><span class="kn">import</span> <span class="n">PolynomialFeatures</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="kn">from</span><span class="w"> </span><span class="nn">sklearn.pipeline</span><span class="w"> </span><span class="kn">import</span> <span class="n">make_pipeline</span>
|
||||
<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><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.linear_model</span> <span class="kn">import</span> <span class="n">LinearRegression</span>
|
||||
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">PolynomialFeatures</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="kn">from</span> <span class="nn">sklearn.pipeline</span> <span class="kn">import</span> <span class="n">make_pipeline</span>
|
||||
|
||||
|
||||
<span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">2018</span><span class="p">)</span>
|
||||
@@ -1487,13 +1488,13 @@ discussion of Ridge regression.</p>
|
||||
<p>The code here is a simple demonstration of how to implement Ridge regression with our own code and compare this with scikit-learn.</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="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>
|
||||
<span class="kn">import</span><span class="w"> </span><span class="nn">pandas</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">pd</span>
|
||||
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</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="kn">from</span><span class="w"> </span><span class="nn">sklearn</span><span class="w"> </span><span class="kn">import</span> <span class="n">linear_model</span>
|
||||
<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>
|
||||
<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
|
||||
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</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="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">linear_model</span>
|
||||
|
||||
<span class="k">def</span><span class="w"> </span><span class="nf">MSE</span><span class="p">(</span><span class="n">y_data</span><span class="p">,</span><span class="n">y_model</span><span class="p">):</span>
|
||||
<span class="k">def</span> <span class="nf">MSE</span><span class="p">(</span><span class="n">y_data</span><span class="p">,</span><span class="n">y_model</span><span class="p">):</span>
|
||||
<span class="n">n</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">y_model</span><span class="p">)</span>
|
||||
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">y_data</span><span class="o">-</span><span class="n">y_model</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="n">n</span>
|
||||
|
||||
@@ -1651,9 +1652,9 @@ In general the economy-size SVD leads to less FLOPS and still conserving the des
|
||||
<h2>Codes for the SVD<a class="headerlink" href="#codes-for-the-svd" title="Link to this heading">#</a></h2>
|
||||
<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="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>
|
||||
<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>
|
||||
<span class="c1"># SVD inversion</span>
|
||||
<span class="k">def</span><span class="w"> </span><span class="nf">SVD</span><span class="p">(</span><span class="n">A</span><span class="p">):</span>
|
||||
<span class="k">def</span> <span class="nf">SVD</span><span class="p">(</span><span class="n">A</span><span class="p">):</span>
|
||||
<span class="w"> </span><span class="sd">''' Takes as input a numpy matrix A and returns inv(A) based on singular value decomposition (SVD).</span>
|
||||
<span class="sd"> SVD is numerically more stable than the inversion algorithms provided by</span>
|
||||
<span class="sd"> numpy and scipy.linalg at the cost of being slower.</span>
|
||||
@@ -2026,7 +2027,7 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</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="c1"># Importing various packages</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>
|
||||
<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
|
||||
<span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
|
||||
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="n">n</span><span class="p">)</span>
|
||||
<span class="nb">print</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">x</span><span class="p">))</span>
|
||||
@@ -2049,7 +2050,7 @@ code which sets up the correlations matrix for the previous example in
|
||||
a more brute force way. Here we scale the mean values for each column of the design matrix, calculate the relevant mean values and variances and then finally set up the <span class="math notranslate nohighlight">\(2\times 2\)</span> correlation matrix (since we have only two vectors).</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="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>
|
||||
<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>
|
||||
<span class="n">n</span> <span class="o">=</span> <span class="mi">100</span>
|
||||
<span class="c1"># define two vectors </span>
|
||||
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">random</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="n">n</span><span class="p">)</span>
|
||||
@@ -2084,8 +2085,8 @@ this matrix we easily see that it is a positive definite matrix.</p>
|
||||
<p>We whow here how we can set up the correlation matrix using <strong>pandas</strong>, as done in this simple code</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="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>
|
||||
<span class="kn">import</span><span class="w"> </span><span class="nn">pandas</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">pd</span>
|
||||
<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>
|
||||
<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
|
||||
<span class="n">n</span> <span class="o">=</span> <span class="mi">10</span>
|
||||
<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="n">n</span><span class="p">)</span>
|
||||
<span class="n">x</span> <span class="o">=</span> <span class="n">x</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
|
||||
@@ -2523,20 +2524,20 @@ and <span class="math notranslate nohighlight">\(\tilde{X}_{ij} = X_{ij} - \frac
|
||||
Note also that we do not split the data into training and test.</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="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>
|
||||
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</span>
|
||||
<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>
|
||||
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
|
||||
|
||||
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.linear_model</span><span class="w"> </span><span class="kn">import</span> <span class="n">LinearRegression</span>
|
||||
<span class="kn">from</span> <span class="nn">sklearn.linear_model</span> <span class="kn">import</span> <span class="n">LinearRegression</span>
|
||||
|
||||
|
||||
<span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">2021</span><span class="p">)</span>
|
||||
|
||||
<span class="k">def</span><span class="w"> </span><span class="nf">MSE</span><span class="p">(</span><span class="n">y_data</span><span class="p">,</span><span class="n">y_model</span><span class="p">):</span>
|
||||
<span class="k">def</span> <span class="nf">MSE</span><span class="p">(</span><span class="n">y_data</span><span class="p">,</span><span class="n">y_model</span><span class="p">):</span>
|
||||
<span class="n">n</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">y_model</span><span class="p">)</span>
|
||||
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">y_data</span><span class="o">-</span><span class="n">y_model</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="n">n</span>
|
||||
|
||||
|
||||
<span class="k">def</span><span class="w"> </span><span class="nf">fit_beta</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">def</span> <span class="nf">fit_beta</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="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">pinv</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">X</span><span class="p">)</span> <span class="o">@</span> <span class="n">X</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">y</span>
|
||||
|
||||
|
||||
@@ -2666,13 +2667,13 @@ intercept.</p>
|
||||
<p>Armed with this wisdom, we attempt first to simply set the intercept equal to <strong>False</strong> in our implementation of Ridge regression for our well-known vanilla data set.</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="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>
|
||||
<span class="kn">import</span><span class="w"> </span><span class="nn">pandas</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">pd</span>
|
||||
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</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="kn">from</span><span class="w"> </span><span class="nn">sklearn</span><span class="w"> </span><span class="kn">import</span> <span class="n">linear_model</span>
|
||||
<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>
|
||||
<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
|
||||
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</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="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">linear_model</span>
|
||||
|
||||
<span class="k">def</span><span class="w"> </span><span class="nf">MSE</span><span class="p">(</span><span class="n">y_data</span><span class="p">,</span><span class="n">y_model</span><span class="p">):</span>
|
||||
<span class="k">def</span> <span class="nf">MSE</span><span class="p">(</span><span class="n">y_data</span><span class="p">,</span><span class="n">y_model</span><span class="p">):</span>
|
||||
<span class="n">n</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">y_model</span><span class="p">)</span>
|
||||
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">y_data</span><span class="o">-</span><span class="n">y_model</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="n">n</span>
|
||||
|
||||
@@ -2741,14 +2742,14 @@ What happens if we do not include the intercept in our fit?
|
||||
Let us see how we can change this code by zero centering.</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="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>
|
||||
<span class="kn">import</span><span class="w"> </span><span class="nn">pandas</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">pd</span>
|
||||
<span class="kn">import</span><span class="w"> </span><span class="nn">matplotlib.pyplot</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">plt</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="kn">from</span><span class="w"> </span><span class="nn">sklearn</span><span class="w"> </span><span class="kn">import</span> <span class="n">linear_model</span>
|
||||
<span class="kn">from</span><span class="w"> </span><span class="nn">sklearn.preprocessing</span><span class="w"> </span><span class="kn">import</span> <span class="n">StandardScaler</span>
|
||||
<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>
|
||||
<span class="kn">import</span> <span class="nn">pandas</span> <span class="k">as</span> <span class="nn">pd</span>
|
||||
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</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="kn">from</span> <span class="nn">sklearn</span> <span class="kn">import</span> <span class="n">linear_model</span>
|
||||
<span class="kn">from</span> <span class="nn">sklearn.preprocessing</span> <span class="kn">import</span> <span class="n">StandardScaler</span>
|
||||
|
||||
<span class="k">def</span><span class="w"> </span><span class="nf">MSE</span><span class="p">(</span><span class="n">y_data</span><span class="p">,</span><span class="n">y_model</span><span class="p">):</span>
|
||||
<span class="k">def</span> <span class="nf">MSE</span><span class="p">(</span><span class="n">y_data</span><span class="p">,</span><span class="n">y_model</span><span class="p">):</span>
|
||||
<span class="n">n</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">y_model</span><span class="p">)</span>
|
||||
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">y_data</span><span class="o">-</span><span class="n">y_model</span><span class="p">)</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span><span class="o">/</span><span class="n">n</span>
|
||||
<span class="c1"># A seed just to ensure that the random numbers are the same for every run.</span>
|
||||
|
||||
@@ -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=03e43079" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" />
|
||||
<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" />
|
||||
@@ -234,6 +234,7 @@
|
||||
<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Statistical analysis, bias-variance tradeoff and resampling methods</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="exercisesweek39.html">Exercises week 39</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week39.html">Week 39: Resampling methods and logistic regression</a></li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
|
||||
<ul class="nav bd-sidenav">
|
||||
|
||||
@@ -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=03e43079" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" />
|
||||
<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" />
|
||||
@@ -234,6 +234,7 @@
|
||||
<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Statistical analysis, bias-variance tradeoff and resampling methods</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="exercisesweek39.html">Exercises week 39</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week39.html">Week 39: Resampling methods and logistic regression</a></li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
|
||||
<ul class="nav bd-sidenav">
|
||||
|
||||
@@ -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=03e43079" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/pygments.css?v=fa44fd50" />
|
||||
<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" />
|
||||
@@ -234,6 +234,7 @@
|
||||
<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
|
||||
<li class="toctree-l1 current active"><a class="current reference internal" href="#">Week 38: Statistical analysis, bias-variance tradeoff and resampling methods</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="exercisesweek39.html">Exercises week 39</a></li>
|
||||
<li class="toctree-l1"><a class="reference internal" href="week39.html">Week 39: Resampling methods and logistic regression</a></li>
|
||||
</ul>
|
||||
<p aria-level="2" class="caption" role="heading"><span class="caption-text">Projects</span></p>
|
||||
<ul class="nav bd-sidenav">
|
||||
|
||||
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@@ -51,7 +51,8 @@ parts:
|
||||
- file: week37.ipynb
|
||||
- file: exercisesweek38.ipynb
|
||||
- file: week38.ipynb
|
||||
- file: exercisesweek39.ipynb
|
||||
- file: exercisesweek39.ipynb
|
||||
- file: week39.ipynb
|
||||
- caption: Projects
|
||||
numbered: false
|
||||
chapters:
|
||||
|
||||
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Reference in New Issue
Block a user