Morten Hjorth-Jensen
793 lines
47 KiB
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793 lines
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Applied Data Analysis and Machine Learning
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</a>
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</li>
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</ul>
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<p aria-level="2" class="caption" role="heading"><span class="caption-text">About the course</span></p>
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<li class="toctree-l1"><a class="reference internal" href="schedule.html">Teaching schedule with links to material</a></li>
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<p aria-level="2" class="caption" role="heading"><span class="caption-text">Review of Statistics with Resampling Techniques and Linear Algebra</span></p>
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<li class="toctree-l1"><a class="reference internal" href="statistics.html">1. Elements of Probability Theory and Statistical Data Analysis</a></li>
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<li class="toctree-l1"><a class="reference internal" href="linalg.html">2. Linear Algebra, Handling of Arrays and more Python Features</a></li>
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</ul>
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<p aria-level="2" class="caption" role="heading"><span class="caption-text">From Regression to Support Vector Machines</span></p>
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<ul class="nav bd-sidenav">
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<li class="toctree-l1"><a class="reference internal" href="chapter1.html">3. Linear Regression</a></li>
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<li class="toctree-l1"><a class="reference internal" href="chapter2.html">4. Ridge and Lasso Regression</a></li>
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<li class="toctree-l1"><a class="reference internal" href="chapter3.html">5. Resampling Methods</a></li>
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<li class="toctree-l1"><a class="reference internal" href="chapter4.html">6. Logistic Regression</a></li>
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<li class="toctree-l1"><a class="reference internal" href="chapteroptimization.html">7. Optimization, the central part of any Machine Learning algortithm</a></li>
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<li class="toctree-l1"><a class="reference internal" href="chapter5.html">8. Support Vector Machines, overarching aims</a></li>
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</ul>
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<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
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<ul class="nav bd-sidenav">
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<li class="toctree-l1"><a class="reference internal" href="chapter6.html">9. Decision trees, overarching aims</a></li>
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<li class="toctree-l1"><a class="reference internal" href="chapter7.html">10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</a></li>
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</ul>
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<p aria-level="2" class="caption" role="heading"><span class="caption-text">Dimensionality Reduction</span></p>
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<ul class="nav bd-sidenav">
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<li class="toctree-l1"><a class="reference internal" href="chapter8.html">11. Basic ideas of the Principal Component Analysis (PCA)</a></li>
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<li class="toctree-l1"><a class="reference internal" href="clustering.html">12. Clustering and Unsupervised Learning</a></li>
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</ul>
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<p aria-level="2" class="caption" role="heading"><span class="caption-text">Deep Learning Methods</span></p>
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<li class="toctree-l1"><a class="reference internal" href="chapter9.html">13. Neural networks</a></li>
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<li class="toctree-l1"><a class="reference internal" href="chapter10.html">14. Building a Feed Forward Neural Network</a></li>
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<li class="toctree-l1"><a class="reference internal" href="chapter11.html">15. Solving Differential Equations with Deep Learning</a></li>
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<li class="toctree-l1"><a class="reference internal" href="chapter12.html">16. Convolutional Neural Networks</a></li>
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<li class="toctree-l1"><a class="reference internal" href="chapter13.html">17. Recurrent neural networks: Overarching view</a></li>
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</ul>
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<p aria-level="2" class="caption" role="heading"><span class="caption-text">Weekly material, notes and exercises</span></p>
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<li class="toctree-l1"><a class="reference internal" href="exercisesweek34.html">Exercises week 34</a></li>
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<li class="toctree-l1"><a class="reference internal" href="week34.html">Week 34: Introduction to the course, Logistics and Practicalities</a></li>
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<li class="toctree-l1"><a class="reference internal" href="exercisesweek35.html">Exercises week 35</a></li>
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<li class="toctree-l1"><a class="reference internal" href="week35.html">Week 35: From Ordinary Linear Regression to Ridge and Lasso Regression</a></li>
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<li class="toctree-l1"><a class="reference internal" href="exercisesweek36.html">Exercises week 36</a></li>
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<li class="toctree-l1"><a class="reference internal" href="week36.html">Week 36: Linear Regression and Statistical interpretations</a></li>
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<li class="toctree-l1"><a class="reference internal" href="exercisesweek37.html">Exercises week 37</a></li>
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<li class="toctree-l1"><a class="reference internal" href="week37.html">Week 37: Statistical interpretations and Resampling Methods</a></li>
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<li class="toctree-l1"><a class="reference internal" href="exercisesweek38.html">Exercises week 38</a></li>
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<li class="toctree-l1"><a class="reference internal" href="week38.html">Week 38: Logistic Regression and Optimization</a></li>
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<li class="toctree-l1"><a class="reference internal" href="exercisesweek39.html">Exercises week 39</a></li>
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<li class="toctree-l1"><a class="reference internal" href="week39.html">Week 39: Optimization and Gradient Methods</a></li>
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<li class="toctree-l1"><a class="reference internal" href="week40.html">Week 40: Gradient descent methods (continued) and start Neural networks</a></li>
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<li class="toctree-l1"><a class="reference internal" href="exercisesweek41.html">Exercises week 41</a></li>
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<li class="toctree-l1"><a class="reference internal" href="week41.html">Week 41 Neural networks and constructing a neural network code</a></li>
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<li class="toctree-l1"><a class="reference internal" href="exercisesweek42.html">Exercises week 42</a></li>
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<li class="toctree-l1"><a class="reference internal" href="week42.html">Week 42 Constructing a Neural Network code with examples</a></li>
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<li class="toctree-l1"><a class="reference internal" href="additionweek42.html">Exercises Week 42: Logistic Regression and Optimization, reminders from week 38 and week 40</a></li>
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<li class="toctree-l1"><a class="reference internal" href="week43.html">Week 43: Deep Learning: Constructing a Neural Network code and solving differential equations</a></li>
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<li class="toctree-l1"><a class="reference internal" href="exercisesweek43.html">Exercises week 43</a></li>
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<li class="toctree-l1"><a class="reference internal" href="week44.html">Week 44, Convolutional Neural Networks (CNN)</a></li>
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<li class="toctree-l1"><a class="reference internal" href="week45.html">Week 45, Convolutional Neural Networks (CCNs) and Recurrent Neural Networks (RNNs)</a></li>
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<li class="toctree-l1"><a class="reference internal" href="week46.html">Week 46: Decision Trees, Ensemble methods and Random Forests</a></li>
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<li class="toctree-l1"><a class="reference internal" href="week47.html">Week 47: From Decision Trees to Ensemble Methods, Random Forests and Boosting Methods</a></li>
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<li class="toctree-l1"><a class="reference internal" href="exercisesweek47.html">Exercise week 47</a></li>
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<li class="toctree-l1"><a class="reference internal" href="week48.html">Week 48: Gradient boosting and summary of course</a></li>
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<li class="toctree-l1"><a class="reference internal" href="exercisesweek48.html">Exercises week 48</a></li>
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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="project1.html">Project 1 on Machine Learning, deadline October 7 (midnight), 2024</a></li>
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<li class="toctree-l1 current active"><a class="current reference internal" href="#">Project 2 on Machine Learning, deadline November 4 (Midnight)</a></li>
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<li class="toctree-l1"><a class="reference internal" href="project3.html">Project 3 on Machine Learning, deadline December 9 (midnight), 2024</a></li>
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<div id="jb-print-docs-body" class="onlyprint">
|
||
<h1>Project 2 on Machine Learning, deadline November 4 (Midnight)</h1>
|
||
<!-- Table of contents -->
|
||
<div id="print-main-content">
|
||
<div id="jb-print-toc">
|
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|
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<div>
|
||
<h2> Contents </h2>
|
||
</div>
|
||
<nav aria-label="Page">
|
||
<ul class="visible nav section-nav flex-column">
|
||
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#classification-and-regression-from-linear-and-logistic-regression-to-neural-networks">Classification and Regression, from linear and logistic regression to neural networks</a><ul class="nav section-nav flex-column">
|
||
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#part-a-write-your-own-stochastic-gradient-descent-code-first-step">Part a): Write your own Stochastic Gradient Descent code, first step</a></li>
|
||
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#part-b-writing-your-own-neural-network-code">Part b): Writing your own Neural Network code</a></li>
|
||
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#part-c-testing-different-activation-functions">Part c): Testing different activation functions</a></li>
|
||
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#part-d-classification-analysis-using-neural-networks">Part d): Classification analysis using neural networks</a></li>
|
||
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#part-e-write-your-logistic-regression-code-final-step">Part e): Write your Logistic Regression code, final step</a></li>
|
||
<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#part-f-critical-evaluation-of-the-various-algorithms">Part f) Critical evaluation of the various algorithms</a></li>
|
||
</ul>
|
||
</li>
|
||
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#background-literature">Background literature</a></li>
|
||
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#introduction-to-numerical-projects">Introduction to numerical projects</a></li>
|
||
<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#format-for-electronic-delivery-of-report-and-programs">Format for electronic delivery of report and programs</a></li>
|
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</ul>
|
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</nav>
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</div>
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</div>
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<article class="bd-article">
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<!-- HTML file automatically generated from DocOnce source (https://github.com/doconce/doconce/)
|
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doconce format html Project2.do.txt -->
|
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<!-- dom:TITLE: Project 2 on Machine Learning, deadline November 4 (Midnight) --><section class="tex2jax_ignore mathjax_ignore" id="project-2-on-machine-learning-deadline-november-4-midnight">
|
||
<h1>Project 2 on Machine Learning, deadline November 4 (Midnight)<a class="headerlink" href="#project-2-on-machine-learning-deadline-november-4-midnight" title="Link to this heading">#</a></h1>
|
||
<p><strong><a class="reference external" href="http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html">Data Analysis and Machine Learning FYS-STK3155/FYS4155</a></strong>, Department of Physics, University of Oslo, Norway</p>
|
||
<p>Date: <strong>Oct 8, 2024</strong></p>
|
||
<p>Copyright 1999-2024, <a class="reference external" href="http://www.uio.no/studier/emner/matnat/fys/FYS3155/index-eng.html">Data Analysis and Machine Learning FYS-STK3155/FYS4155</a>. Released under CC Attribution-NonCommercial 4.0 license</p>
|
||
<section id="classification-and-regression-from-linear-and-logistic-regression-to-neural-networks">
|
||
<h2>Classification and Regression, from linear and logistic regression to neural networks<a class="headerlink" href="#classification-and-regression-from-linear-and-logistic-regression-to-neural-networks" title="Link to this heading">#</a></h2>
|
||
<p>The main aim of this project is to study both classification and
|
||
regression problems by developing our own feed-forward neural network
|
||
(FFNN) code. We can reuse the regression algorithms studied in project</p>
|
||
<ol class="arabic simple">
|
||
<li><p>We will also include logistic regression for classification
|
||
problems and write our own FFNN code for studying both regression and
|
||
classification problems. The codes developed in project 1, including
|
||
bootstrap <strong>and/or</strong> cross-validation as well as the computation of the
|
||
mean-squared error and/or the <span class="math notranslate nohighlight">\(R2\)</span> or the accuracy score
|
||
(classification problems) functions can also be utilized in the
|
||
present analysis.</p></li>
|
||
</ol>
|
||
<p>The data sets that we propose here are (the default sets)</p>
|
||
<ul class="simple">
|
||
<li><p>Regression (fitting a continuous function). In this part you will need to bring back your results from project 1 and compare these with what you get from your Neural Network code to be developed here. The data sets could be</p></li>
|
||
</ul>
|
||
<p>a. A simple one-dimensional function or the Franke function or the terrain data from project 1, or data sets your propose. It could be a simpler function than the Franke function. We recommend testing a simpler function (see below). But if you wish to try more complex function, feel free to do so.</p>
|
||
<ul class="simple">
|
||
<li><p>Classification. Here you will also need to develop a Logistic regression code that you will use to compare with the Neural Network code. The data set we propose are the so-called <a class="reference external" href="https://www.kaggle.com/uciml/breast-cancer-wisconsin-data">Wisconsin Breat Cancer Data</a> data set of images representing various features of tumors. A longer explanation with links to the scientific literature can be found at the <a class="reference external" href="https://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+%28Diagnostic%29">Machine Learning repository of the University of California at Irvine</a>. Feel free to consult this site and the pertinent literature.</p></li>
|
||
</ul>
|
||
<p>You can find more information about this at the <a class="reference external" href="https://scikit-learn.org/stable/modules/generated/sklearn.datasets.load_breast_cancer.html">Scikit-Learn site</a> or at the <a class="reference external" href="https://archive.ics.uci.edu/ml/datasets/breast+cancer+wisconsin+(original)">University of California at Irvine</a>.</p>
|
||
<p>However, if you would like to study other data sets, feel free to
|
||
propose other sets. What we list here are mere suggestions from our
|
||
side. If you opt for another data set, consider using a set which has
|
||
been studied in the scientific literature. This makes it easier for
|
||
you to compare and analyze your results. Comparing with existing
|
||
results from the scientific literature is also an essential element of
|
||
the scientific discussion. The University of California at Irvine
|
||
with its Machine Learning repository at
|
||
<a class="reference external" href="https://archive.ics.uci.edu/ml/index.php">https://archive.ics.uci.edu/ml/index.php</a> is an excellent site to
|
||
look up for examples and
|
||
inspiration. <a class="reference external" href="https://www.kaggle.com/">Kaggle.com</a> is an equally
|
||
interesting site. Feel free to explore these sites.</p>
|
||
<p>We will start with a regression problem and we will reuse our codes from project 1 starting with writing our own Stochastic Gradient Descent (SGD) code.</p>
|
||
<section id="part-a-write-your-own-stochastic-gradient-descent-code-first-step">
|
||
<h3>Part a): Write your own Stochastic Gradient Descent code, first step<a class="headerlink" href="#part-a-write-your-own-stochastic-gradient-descent-code-first-step" title="Link to this heading">#</a></h3>
|
||
<p>In order to get started, we will now replace in our standard ordinary
|
||
least squares (OLS) and Ridge regression codes (from project 1) the
|
||
matrix inversion algorithm with our own gradient descent (GD) and SGD
|
||
codes. You can use the Franke function or the terrain data from
|
||
project 1. <strong>However, we recommend using a simpler function like</strong>
|
||
<span class="math notranslate nohighlight">\(f(x)=a_0+a_1x+a_2x^2\)</span> or higher-order one-dimensional polynomials.
|
||
You can obviously test your final codes against for example the Franke
|
||
function.</p>
|
||
<p>The exercise set for week 41 should help in solving this part of the project.</p>
|
||
<p>You should include in your analysis of the GD and SGD codes the following elements</p>
|
||
<ol class="arabic simple">
|
||
<li><p>A plain gradient descent with a fixed learning rate (you will need to tune it) using the analytical expression for the gradient.</p></li>
|
||
<li><p>Add momentum to the plain GD code and compare convergence with a fixed learning rate (you may need to tune the learning rate). Keep using the analytical expression for the gradient.</p></li>
|
||
<li><p>Repeat these steps for stochastic gradient descent with mini batches and a given number of epochs. Use a tunable learning rate as discussed in the lectures from weeks 39 and 40. Discuss the results as functions of the various parameters (size of batches, number of epochs etc). Use the analytical gradient.</p></li>
|
||
<li><p>Implement the Adagrad method in order to tune the learning rate. Do this with and without momentum for plain gradient descent and SGD.</p></li>
|
||
<li><p>Add RMSprop and Adam to your library of methods for tuning the learning rate.</p></li>
|
||
</ol>
|
||
<p>The lecture notes from <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/pub/week39/html/week39.html">weeks 39 and 40 contain more
|
||
details</a> and code examples. Feel free to use these examples.</p>
|
||
<ol class="arabic simple">
|
||
<li><p>Replace thereafter your analytical gradient with either <strong>Autograd</strong> or <strong>JAX</strong></p></li>
|
||
</ol>
|
||
<p><strong>Feel free to use codes on these methods from the lecture notes from week 39 and week 40</strong>.</p>
|
||
<p>In summary, you should
|
||
perform an analysis of the results for OLS and Ridge regression as
|
||
function of the chosen learning rates, the number of mini-batches and
|
||
epochs as well as algorithm for scaling the learning rate. You can
|
||
also compare your own results with those that can be obtained using
|
||
for example <strong>Scikit-Learn</strong>’s various SGD options. Discuss your
|
||
results. For Ridge regression you need now to study the results as functions of the hyper-parameter <span class="math notranslate nohighlight">\(\lambda\)</span> and
|
||
the learning rate <span class="math notranslate nohighlight">\(\eta\)</span>. Discuss your results.</p>
|
||
<p>You will need your SGD code for the setup of the Neural Network and
|
||
Logistic Regression codes. You will find the Python <a class="reference external" href="https://seaborn.pydata.org/generated/seaborn.heatmap.html">Seaborn
|
||
package</a>
|
||
useful when plotting the results as function of the learning rate
|
||
<span class="math notranslate nohighlight">\(\eta\)</span> and the hyper-parameter <span class="math notranslate nohighlight">\(\lambda\)</span> when you use Ridge
|
||
regression. Since you will use different gradient descent methods, you can also add Lasse regression. This is however optional. How to code Lasso regression is discussed in the lecture notes from week 40.</p>
|
||
<p>We recommend reading chapter 8 on optimization from the textbook of Goodfellow, Bengio and Courville at <a class="reference external" href="https://www.deeplearningbook.org/">https://www.deeplearningbook.org/</a>. This chapter contains many useful insights and discussions on the optimization part of machine learning.</p>
|
||
</section>
|
||
<section id="part-b-writing-your-own-neural-network-code">
|
||
<h3>Part b): Writing your own Neural Network code<a class="headerlink" href="#part-b-writing-your-own-neural-network-code" title="Link to this heading">#</a></h3>
|
||
<p>Your aim now, and this is the central part of this project, is to
|
||
write your own Feed Forward Neural Network code implementing the back
|
||
propagation algorithm discussed in the lecture slides from <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/pub/week41/ipynb/week41.ipynb">week 41</a> and
|
||
<a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/pub/week42/ipynb/week42.ipynb">week 42</a>.</p>
|
||
<p>We will focus on a regression problem first and study either the simple second-order polynomial from part a) or the
|
||
Franke function or terrain data (or both or other data sets) from
|
||
project 1.</p>
|
||
<p>Discuss again your choice of cost function.</p>
|
||
<p>Write an FFNN code for regression with a flexible number of hidden
|
||
layers and nodes using the Sigmoid function as activation function for
|
||
the hidden layers. Initialize the weights using a normal
|
||
distribution. How would you initialize the biases? And which
|
||
activation function would you select for the final output layer?</p>
|
||
<p>Train your network and compare the results with those from your OLS and Ridge Regression codes from project 1 if you use the Franke function or the terrain data.
|
||
You should test your results against a similar code using <strong>Scikit-Learn</strong> (see the examples in the above lecture notes from weeks 41 and 42) or <strong>tensorflow/keras</strong> or <strong>Pytorch</strong> (for Pytorch, see Raschka et al.’s text chapters 12 and 13).</p>
|
||
<p>Comment your results and give a critical discussion of the results
|
||
obtained with the Linear Regression code and your own Neural Network
|
||
code.<br />
|
||
Make an analysis of the regularization parameters and the learning rates employed to find the optimal MSE and <span class="math notranslate nohighlight">\(R2\)</span> scores.</p>
|
||
<p>A useful reference on the back progagation algorithm is Nielsen’s book at <a class="reference external" href="http://neuralnetworksanddeeplearning.com/">http://neuralnetworksanddeeplearning.com/</a>. It is an excellent
|
||
read.</p>
|
||
</section>
|
||
<section id="part-c-testing-different-activation-functions">
|
||
<h3>Part c): Testing different activation functions<a class="headerlink" href="#part-c-testing-different-activation-functions" title="Link to this heading">#</a></h3>
|
||
<p>You should now also test different activation functions for the hidden layers. Try out the Sigmoid, the RELU and the Leaky RELU functions and discuss your results. You may also study the way you initialize your weights and biases.</p>
|
||
</section>
|
||
<section id="part-d-classification-analysis-using-neural-networks">
|
||
<h3>Part d): Classification analysis using neural networks<a class="headerlink" href="#part-d-classification-analysis-using-neural-networks" title="Link to this heading">#</a></h3>
|
||
<p>With a well-written code it should now be easy to change the
|
||
activation function for the output layer.</p>
|
||
<p>Here we will change the cost function for our neural network code
|
||
developed in parts b) and c) in order to perform a classification analysis.</p>
|
||
<p>We will here study the Wisconsin Breast Cancer data set. This is a typical binary classification problem with just one single output, either True or Fale, <span class="math notranslate nohighlight">\(0\)</span> or <span class="math notranslate nohighlight">\(1\)</span> etc.
|
||
You find more information about this at the <a class="reference external" href="https://scikit-learn.org/stable/modules/generated/sklearn.datasets.load_breast_cancer.html">Scikit-Learn
|
||
site</a> or at the <a class="reference external" href="https://archive.ics.uci.edu/ml/datasets/breast+cancer+wisconsin+(original)">University of California
|
||
at Irvine</a>.</p>
|
||
<p>To measure the performance of our classification problem we use the
|
||
so-called <em>accuracy</em> score. The accuracy is as you would expect just
|
||
the number of correctly guessed targets <span class="math notranslate nohighlight">\(t_i\)</span> divided by the total
|
||
number of targets, that is</p>
|
||
<div class="math notranslate nohighlight">
|
||
\[
|
||
\text{Accuracy} = \frac{\sum_{i=1}^n I(t_i = y_i)}{n} ,
|
||
\]</div>
|
||
<p>where <span class="math notranslate nohighlight">\(I\)</span> is the indicator function, <span class="math notranslate nohighlight">\(1\)</span> if <span class="math notranslate nohighlight">\(t_i = y_i\)</span> and <span class="math notranslate nohighlight">\(0\)</span>
|
||
otherwise if we have a binary classification problem. Here <span class="math notranslate nohighlight">\(t_i\)</span>
|
||
represents the target and <span class="math notranslate nohighlight">\(y_i\)</span> the outputs of your FFNN code and <span class="math notranslate nohighlight">\(n\)</span> is simply the number of targets <span class="math notranslate nohighlight">\(t_i\)</span>.</p>
|
||
<p>Discuss your results and give a critical analysis of the various parameters, including hyper-parameters like the learning rates and the regularization parameter <span class="math notranslate nohighlight">\(\lambda\)</span> (as you did in Ridge Regression), various activation functions, number of hidden layers and nodes and activation functions.</p>
|
||
<p>As stated in the introduction, it can also be useful to study other
|
||
datasets.</p>
|
||
<p>Again, we strongly recommend that you compare your own neural Network
|
||
code for classification and pertinent results against a similar code using <strong>Scikit-Learn</strong> or <strong>tensorflow/keras</strong> or <strong>pytorch</strong>.</p>
|
||
</section>
|
||
<section id="part-e-write-your-logistic-regression-code-final-step">
|
||
<h3>Part e): Write your Logistic Regression code, final step<a class="headerlink" href="#part-e-write-your-logistic-regression-code-final-step" title="Link to this heading">#</a></h3>
|
||
<p>Finally, we want to compare the FFNN code we have developed with
|
||
Logistic regression, that is we wish to compare our neural network
|
||
classification results with the results we can obtain with another
|
||
method.</p>
|
||
<p>Define your cost function and the design matrix before you start writing your code.
|
||
Write thereafter a Logistic regression code using your SGD algorithm. You can also use standard gradient descent in this case, with a learning rate as hyper-parameter.
|
||
Study the results as functions of the chosen learning rates.
|
||
Add also an <span class="math notranslate nohighlight">\(l_2\)</span> regularization parameter <span class="math notranslate nohighlight">\(\lambda\)</span>. Compare your results with those from your FFNN code as well as those obtained using <strong>Scikit-Learn</strong>’s logistic regression functionality.</p>
|
||
<p>The weblink here <a class="reference external" href="https://medium.com/ai-in-plain-english/comparison-between-logistic-regression-and-neural-networks-in-classifying-digits-dc5e85cd93c3">https://medium.com/ai-in-plain-english/comparison-between-logistic-regression-and-neural-networks-in-classifying-digits-dc5e85cd93c3</a>compares logistic regression and FFNN using the so-called MNIST data set. You may find several useful hints and ideas from this article.</p>
|
||
</section>
|
||
<section id="part-f-critical-evaluation-of-the-various-algorithms">
|
||
<h3>Part f) Critical evaluation of the various algorithms<a class="headerlink" href="#part-f-critical-evaluation-of-the-various-algorithms" title="Link to this heading">#</a></h3>
|
||
<p>After all these glorious calculations, you should now summarize the
|
||
various algorithms and come with a critical evaluation of their pros
|
||
and cons. Which algorithm works best for the regression case and which
|
||
is best for the classification case. These codes can also be part of
|
||
your final project 3, but now applied to other data sets.</p>
|
||
</section>
|
||
</section>
|
||
<section id="background-literature">
|
||
<h2>Background literature<a class="headerlink" href="#background-literature" title="Link to this heading">#</a></h2>
|
||
<ol class="arabic simple">
|
||
<li><p>The text of Michael Nielsen is highly recommended, see Nielsen’s book at <a class="reference external" href="http://neuralnetworksanddeeplearning.com/">http://neuralnetworksanddeeplearning.com/</a>. It is an excellent read.</p></li>
|
||
<li><p>Goodfellow, Bengio and Courville, Deep Learning at <a class="reference external" href="https://www.deeplearningbook.org/">https://www.deeplearningbook.org/</a>. Here we recommend chapters 6, 7 and 8</p></li>
|
||
<li><p>Raschka et al. at <a class="reference external" href="https://sebastianraschka.com/blog/2022/ml-pytorch-book.html">https://sebastianraschka.com/blog/2022/ml-pytorch-book.html</a>. Here we recommend chapters 11, 12 and 13.</p></li>
|
||
</ol>
|
||
</section>
|
||
<section id="introduction-to-numerical-projects">
|
||
<h2>Introduction to numerical projects<a class="headerlink" href="#introduction-to-numerical-projects" title="Link to this heading">#</a></h2>
|
||
<p>Here follows a brief recipe and recommendation on how to write a report for each
|
||
project.</p>
|
||
<ul class="simple">
|
||
<li><p>Give a short description of the nature of the problem and the eventual numerical methods you have used.</p></li>
|
||
<li><p>Describe the algorithm you have used and/or developed. Here you may find it convenient to use pseudocoding. In many cases you can describe the algorithm in the program itself.</p></li>
|
||
<li><p>Include the source code of your program. Comment your program properly.</p></li>
|
||
<li><p>If possible, try to find analytic solutions, or known limits in order to test your program when developing the code.</p></li>
|
||
<li><p>Include your results either in figure form or in a table. Remember to label your results. All tables and figures should have relevant captions and labels on the axes.</p></li>
|
||
<li><p>Try to evaluate the reliabilty and numerical stability/precision of your results. If possible, include a qualitative and/or quantitative discussion of the numerical stability, eventual loss of precision etc.</p></li>
|
||
<li><p>Try to give an interpretation of you results in your answers to the problems.</p></li>
|
||
<li><p>Critique: if possible include your comments and reflections about the exercise, whether you felt you learnt something, ideas for improvements and other thoughts you’ve made when solving the exercise. We wish to keep this course at the interactive level and your comments can help us improve it.</p></li>
|
||
<li><p>Try to establish a practice where you log your work at the computerlab. You may find such a logbook very handy at later stages in your work, especially when you don’t properly remember what a previous test version of your program did. Here you could also record the time spent on solving the exercise, various algorithms you may have tested or other topics which you feel worthy of mentioning.</p></li>
|
||
</ul>
|
||
</section>
|
||
<section id="format-for-electronic-delivery-of-report-and-programs">
|
||
<h2>Format for electronic delivery of report and programs<a class="headerlink" href="#format-for-electronic-delivery-of-report-and-programs" title="Link to this heading">#</a></h2>
|
||
<p>The preferred format for the report is a PDF file. You can also use DOC or postscript formats or as an ipython notebook file. As programming language we prefer that you choose between C/C++, Fortran2008 or Python. The following prescription should be followed when preparing the report:</p>
|
||
<ul class="simple">
|
||
<li><p>Use Canvas to hand in your projects, log in at <a class="reference external" href="https://www.uio.no/english/services/it/education/canvas/">https://www.uio.no/english/services/it/education/canvas/</a> with your normal UiO username and password.</p></li>
|
||
<li><p>Upload <strong>only</strong> the report file or the link to your GitHub/GitLab or similar typo of repos! For the source code file(s) you have developed please provide us with your link to your GitHub/GitLab or similar domain. The report file should include all of your discussions and a list of the codes you have developed. Do not include library files which are available at the course homepage, unless you have made specific changes to them.</p></li>
|
||
<li><p>In your GitHub/GitLab or similar repository, please include a folder which contains selected results. These can be in the form of output from your code for a selected set of runs and input parameters.</p></li>
|
||
</ul>
|
||
<p>Finally,
|
||
we encourage you to collaborate. Optimal working groups consist of
|
||
2-3 students. You can then hand in a common report.</p>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#classification-and-regression-from-linear-and-logistic-regression-to-neural-networks">Classification and Regression, from linear and logistic regression to neural networks</a><ul class="nav section-nav flex-column">
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<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#part-a-write-your-own-stochastic-gradient-descent-code-first-step">Part a): Write your own Stochastic Gradient Descent code, first step</a></li>
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