added p1
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Morten Hjorth-Jensen
@@ -330,7 +330,7 @@ const thebe_selector_output = ".output, .cell_output"
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<!-- ipynb file if we had a myst markdown file -->
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<!-- Download raw file -->
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<a class="dropdown-buttons" href="_sources/Project1.ipynb"><button type="button"
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<a class="dropdown-buttons" href="_sources/project1.ipynb"><button type="button"
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class="btn btn-secondary topbarbtn" title="Download source file" data-toggle="tooltip"
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data-placement="left">.ipynb</button></a>
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<!-- Download PDF via print -->
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@@ -541,33 +541,32 @@ doconce format html Project1.do.txt -->
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<p>Date: <strong>September 2</strong></p>
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<div class="section" id="preamble-note-on-writing-reports-using-reference-material-ai-and-other-tools">
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<h2>Preamble: Note on writing reports, using reference material, AI and other tools<a class="headerlink" href="#preamble-note-on-writing-reports-using-reference-material-ai-and-other-tools" title="Permalink to this headline">¶</a></h2>
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<p>We want you to answer the three different projects by handing reports written like a standard scientific/technical report.
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The link at <a class="reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/ProjectWriting/projectwriting.ipynb">https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/ProjectWriting/projectwriting.ipynb</a> gives some guidance. See also the grading suggestion at <a class="reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/EvaluationGrading/EvaluationForm.md">https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/EvaluationGrading/EvaluationForm.md</a>.</p>
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<p>When using codes from different sources that you have not developed yourself,
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you should refer to these in the bibliography of your report, indicating wherefrom you
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<p>We want you to answer the three different projects by handing in
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reports written like a standard scientific/technical report. The link
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at
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<a class="reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/ProjectWriting/projectwriting.ipynb">https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/ProjectWriting/projectwriting.ipynb</a>
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gives some guidance. See also the grading suggestion at
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<a class="reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/EvaluationGrading/EvaluationForm.md">https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/EvaluationGrading/EvaluationForm.md</a>.</p>
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<p>Furthermore, at
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<a class="reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/ReportExample/">https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/ReportExample/</a>
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you can find examples of previous reports. How to write reports will
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also be discussed during the various lab sessions. Please do ask us if you are in doubt.</p>
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<p>When using codes and material from other sources, you should refer to these in the bibliography of your report, indicating wherefrom you for example
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got the code, whether this is from the lecture notes, softwares like
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Scikit-Learn, TensorFlow, PyTorch or other sources. These should
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always be cited correctly. How to cite some of the libraries is often
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indicated from their corresponding GitHub sites or websites, see for example how to cite Scikit-Learn at <a class="reference external" href="https://scikit-learn.org/dev/about.html">https://scikit-learn.org/dev/about.html</a>.</p>
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<p>We enocurage you to use tools like
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<a class="reference external" href="https://openai.com/chatgpt/">ChatGPT</a> in writing the report. If you use for example ChatGPT,
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<a class="reference external" href="https://openai.com/chatgpt/">ChatGPT</a> or similar in writing the report. If you use for example ChatGPT,
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please do cite it properly and include (if possible) your questions and answers as an addition to the report. This can
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be uplodaed to for example your website, GitHub/GitLab or similar as supplemental material.</p>
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<p>On scaling, we recommend reading the following section from the scikit-learn software description, see <a class="reference external" href="https://scikit-learn.org/stable/auto_examples/preprocessing/plot_all_scaling.html#plot-all-scaling-standard-scaler-section">https://scikit-learn.org/stable/auto_examples/preprocessing/plot_all_scaling.html#plot-all-scaling-standard-scaler-section</a></p>
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be uploaded to for example your website, GitHub/GitLab or similar as supplemental material.</p>
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</div>
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<div class="section" id="regression-analysis-and-resampling-methods">
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<h2>Regression analysis and resampling methods<a class="headerlink" href="#regression-analysis-and-resampling-methods" title="Permalink to this headline">¶</a></h2>
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<p>The main aim of this project is to study in more detail various
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regression methods, including the Ordinary Least Squares (OLS) method.
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In addition to the scientific part, in this course we want also to
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give you an experience in writing scientific reports. The format for
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the delivery of your answers is namely that of a scientific report. At
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for example
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<a class="reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/EvaluationGrading/EvaluationForm.md">https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/EvaluationGrading/EvaluationForm.md</a>
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we detail how to write a report. Furthermore, at
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<a class="reference external" href="https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/ReportExample/">https://github.com/CompPhysics/MachineLearning/blob/master/doc/Projects/ReportExample/</a>
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you can find examples of previous reports. How to write reports will
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also be discussed during the various lab sessions.</p>
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give you an experience in writing scientific reports.</p>
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<p><strong>A small recommendation when developing the codes here</strong>. Instead of
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jumping on to the two-dimensional function described below, we
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recommend to do the code development and testing with a simpler
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@@ -682,6 +681,7 @@ which polynomial fits the data best.</p>
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</div>
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</div>
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</div>
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<p>If you wish to compare your results with other on the Franke function or other popular functions tested with linear regression, see the list in Figure 1 of the article by Cook et al at <a class="reference external" href="https://arxiv.org/abs/2401.11694">https://arxiv.org/abs/2401.11694</a>.</p>
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</div>
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<div class="section" id="part-a-ordinary-least-square-ols-on-the-franke-function">
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<h3>Part a) : Ordinary Least Square (OLS) on the Franke function<a class="headerlink" href="#part-a-ordinary-least-square-ols-on-the-franke-function" title="Permalink to this headline">¶</a></h3>
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@@ -728,6 +728,7 @@ data and say test data. An accepted rule of thumb is to use
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approximately <span class="math notranslate nohighlight">\(2/3\)</span> to <span class="math notranslate nohighlight">\(4/5\)</span> of the data as training data.</p>
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<p>You can easily reuse the solutions to your exercises from week 35 and week 36.
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See also the lecture slides from week 35 and week 36.</p>
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<p>On scaling, we recommend reading the following section from the scikit-learn software description, see <a class="reference external" href="https://scikit-learn.org/stable/auto_examples/preprocessing/plot_all_scaling.html#plot-all-scaling-standard-scaler-section">https://scikit-learn.org/stable/auto_examples/preprocessing/plot_all_scaling.html#plot-all-scaling-standard-scaler-section</a>.</p>
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</div>
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<div class="section" id="part-b-adding-ridge-regression-for-the-franke-function">
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<h3>Part b): Adding Ridge regression for the Franke function<a class="headerlink" href="#part-b-adding-ridge-regression-for-the-franke-function" title="Permalink to this headline">¶</a></h3>
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@@ -854,16 +855,14 @@ You can follow the code example in the jupyter-book at <a class="reference exter
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</div>
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<div class="section" id="part-f-cross-validation-as-resampling-techniques-adding-more-complexity">
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<h3>Part f): Cross-validation as resampling techniques, adding more complexity<a class="headerlink" href="#part-f-cross-validation-as-resampling-techniques-adding-more-complexity" title="Permalink to this headline">¶</a></h3>
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<p>The aim here is to write your own code for another widely popular
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<p>The aim here is to implement another widely popular
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resampling technique, the so-called cross-validation method.</p>
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<p>Implement the <span class="math notranslate nohighlight">\(k\)</span>-fold cross-validation algorithm (write your own
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code) and evaluate again the MSE function resulting
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from the test folds. You can compare your own code with that from
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<strong>Scikit-Learn</strong> if needed.</p>
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code or use the functionality of <strong>Scikit-Learn</strong>) and evaluate again the MSE function resulting
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from the test folds.</p>
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<p>Compare the MSE you get from your cross-validation code with the one
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you got from your <strong>bootstrap</strong> code. Comment your results. Try <span class="math notranslate nohighlight">\(5-10\)</span>
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folds. You can also compare your own cross-validation code with the
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one provided by <strong>Scikit-Learn</strong>.</p>
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folds.</p>
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<p>In addition to using the ordinary least squares method, you should include both Ridge and Lasso regression.</p>
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</div>
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<div class="section" id="part-g-analysis-of-real-data">
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