Morten Hjorth-Jensen
723 lines
37 KiB
HTML
723 lines
37 KiB
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Applied Data Analysis and Machine Learning
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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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<p aria-level="2" class="caption" role="heading"><span class="caption-text">From Regression to Support Vector Machines</span></p>
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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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<p aria-level="2" class="caption" role="heading"><span class="caption-text">Decision Trees, Ensemble Methods and Boosting</span></p>
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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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<p aria-level="2" class="caption" role="heading"><span class="caption-text">Dimensionality Reduction</span></p>
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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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<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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<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 Gradient descent</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: Gradient descent 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: 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>
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<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="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="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="exercisesweek41.html">Exercises week 41</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="exercisesweek42.html">Exercises week 42</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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<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 6 (midnight), 2025</a></li>
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<li class="toctree-l1"><a class="reference internal" href="project2.html">Project 2 on Machine Learning, deadline November 10 (Midnight)</a></li>
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<div id="jb-print-docs-body" class="onlyprint">
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<h1>Applied Data Analysis and Machine Learning</h1>
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<!-- Table of contents -->
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<div id="jb-print-toc">
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<h2> Contents </h2>
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<ul class="visible nav section-nav flex-column">
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#introduction">Introduction</a></li>
|
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#learning-outcomes">Learning outcomes</a></li>
|
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#prerequisites-and-background">Prerequisites and background</a></li>
|
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#the-course-has-two-central-parts">The course has two central parts</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="#statistical-analysis-and-optimization-of-data">Statistical analysis and optimization of data</a></li>
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<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#machine-learning">Machine learning</a></li>
|
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</ul>
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</li>
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#required-technologies">Required Technologies</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="#python-installers">Python installers</a></li>
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<li class="toc-h3 nav-item toc-entry"><a class="reference internal nav-link" href="#useful-python-libraries">Useful Python libraries</a></li>
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</ul>
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</li>
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<article class="bd-article">
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<section class="tex2jax_ignore mathjax_ignore" id="applied-data-analysis-and-machine-learning">
|
||
<h1>Applied Data Analysis and Machine Learning<a class="headerlink" href="#applied-data-analysis-and-machine-learning" title="Link to this heading">#</a></h1>
|
||
<section id="introduction">
|
||
<h2>Introduction<a class="headerlink" href="#introduction" title="Link to this heading">#</a></h2>
|
||
<p>Probability theory and statistical methods play a central role in Science. Nowadays we are
|
||
surrounded by huge amounts of data. For example, there are more than one trillion web pages; more than one
|
||
hour of video is uploaded to YouTube every second, amounting to years of content every
|
||
day; the genomes of 1000s of people, each of which has a length of more than a billion base pairs, have
|
||
been sequenced by various labs and so on. This deluge of data calls for automated methods of data analysis,
|
||
which is exactly what machine learning aims at providing.</p>
|
||
</section>
|
||
<section id="learning-outcomes">
|
||
<h2>Learning outcomes<a class="headerlink" href="#learning-outcomes" title="Link to this heading">#</a></h2>
|
||
<p>This course aims at giving you insights and knowledge about many of the central algorithms used in Data Analysis and Machine Learning. The course is project based and through various numerical projects and weekly exercises you will be exposed to fundamental research problems in these fields, with the aim to reproduce state of the art scientific results. Both supervised and unsupervised methods will be covered. The emphasis is on a frequentist approach with an emphasis on predictions and correaltions. However, we will try, where appropriate, to link our machine learning models with a Bayesian approach as well. You will learn to develop and structure large codes for studying different cases where Machine Learning is applied to, get acquainted with computing facilities and learn to handle large scientific projects. A good scientific and ethical conduct is emphasized throughout the course. More specifically, after this course you will</p>
|
||
<ul class="simple">
|
||
<li><p>Learn about basic data analysis, statistical analysis, Bayesian statistics, Monte Carlo sampling, data optimization and machine learning;</p></li>
|
||
<li><p>Be capable of extending the acquired knowledge to other systems and cases;</p></li>
|
||
<li><p>Have an understanding of central algorithms used in data analysis and machine learning;</p></li>
|
||
<li><p>Understand linear methods for regression and classification, from ordinary least squares, via Lasso and Ridge to Logistic regression and Kernel regression;</p></li>
|
||
<li><p>Learn about neural networks and deep learning methods for supervised and unsupervised learning. Emphasis on feed forward neural networks, convolutional and recurrent neural networks;</p></li>
|
||
<li><p>Learn about about decision trees, random forests, bagging and boosting methods;</p></li>
|
||
<li><p>Learn about support vector machines and kernel transformations;</p></li>
|
||
<li><p>Reduction of data sets and unsupervised learning, from PCA to clustering;</p></li>
|
||
<li><p>Autoencoders and Reinforcement Learning;</p></li>
|
||
<li><p>Work on numerical projects to illustrate the theory. The projects play a central role and you are expected to know modern programming languages like Python or C++ and/or Fortran (Fortran2003 or later).</p></li>
|
||
</ul>
|
||
</section>
|
||
<section id="prerequisites-and-background">
|
||
<h2>Prerequisites and background<a class="headerlink" href="#prerequisites-and-background" title="Link to this heading">#</a></h2>
|
||
<p>Basic knowledge in programming and mathematics, with an emphasis on linear algebra. Knowledge of Python or/and C++ as programming languages is strongly recommended and experience with Jupyter notebooks is recommended. Required courses are the equivalents to the University of Oslo mathematics courses MAT1100, MAT1110, MAT1120 and at least one of the corresponding computing and programming courses INF1000/INF1110 or MAT-INF1100/MAT-INF1100L/BIOS1100/KJM-INF1100. Most universities offer nowadays a basic programming course (often compulsory) where Python is the recurring programming language.
|
||
We recommend also refreshing your knowledge on Statistics and Probability theory. The lecture notes at <a class="reference external" href="https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/intro.html">https://compphysics.github.io/MachineLearning/doc/LectureNotes/_build/html/intro.html</a> offer a review of Statistics and Probability theory.</p>
|
||
</section>
|
||
<section id="the-course-has-two-central-parts">
|
||
<h2>The course has two central parts<a class="headerlink" href="#the-course-has-two-central-parts" title="Link to this heading">#</a></h2>
|
||
<ol class="arabic simple">
|
||
<li><p>Statistical analysis and optimization of data</p></li>
|
||
<li><p>Machine learning</p></li>
|
||
</ol>
|
||
<section id="statistical-analysis-and-optimization-of-data">
|
||
<h3>Statistical analysis and optimization of data<a class="headerlink" href="#statistical-analysis-and-optimization-of-data" title="Link to this heading">#</a></h3>
|
||
<p>The following topics will be covered</p>
|
||
<ul class="simple">
|
||
<li><p>Basic concepts, expectation values, variance, covariance, correlation functions and errors;</p></li>
|
||
<li><p>Simpler models, binomial distribution, the Poisson distribution, simple and multivariate normal distributions;</p></li>
|
||
<li><p>Central elements of Bayesian statistics and modeling;</p></li>
|
||
<li><p>Gradient methods for data optimization,</p></li>
|
||
<li><p>Monte Carlo methods, Markov chains, Gibbs sampling and Metropolis-Hastings sampling;</p></li>
|
||
<li><p>Estimation of errors and resampling techniques such as the cross-validation, blocking, bootstrapping and jackknife methods;</p></li>
|
||
<li><p>Principal Component Analysis (PCA) and its mathematical foundation</p></li>
|
||
</ul>
|
||
</section>
|
||
<section id="machine-learning">
|
||
<h3>Machine learning<a class="headerlink" href="#machine-learning" title="Link to this heading">#</a></h3>
|
||
<p>The following topics will be covered:</p>
|
||
<ul class="simple">
|
||
<li><p>Linear Regression and Logistic Regression;</p></li>
|
||
<li><p>Neural networks and deep learning, including convolutional and recurrent neural networks</p></li>
|
||
<li><p>Decisions trees, Random Forests, Bagging and Boosting</p></li>
|
||
<li><p>Support vector machines</p></li>
|
||
<li><p>Bayesian linear and logistic regression</p></li>
|
||
<li><p>Boltzmann Machines</p></li>
|
||
<li><p>Unsupervised learning Dimensionality reduction, PCA, k-means and clustering</p></li>
|
||
<li><p>Autoenconders</p></li>
|
||
</ul>
|
||
<p>Hands-on demonstrations, exercises and projects aim at deepening your understanding of these topics.</p>
|
||
<p>Computational aspects play a central role and you are
|
||
expected to work on numerical examples and projects which illustrate
|
||
the theory and various algorithms discussed during the lectures. We recommend strongly to form small project groups of 2-3 participants, if possible.</p>
|
||
</section>
|
||
</section>
|
||
<section id="required-technologies">
|
||
<h2>Required Technologies<a class="headerlink" href="#required-technologies" title="Link to this heading">#</a></h2>
|
||
<p>Course participants are expected to have their own laptops/PCs. We use <em>Git</em> as version control software and the usage of providers like <em>GitHub</em>, <em>GitLab</em> or similar are strongly recommended. If you are not familiar with Git as version control software, the following video may be of interest, see <a class="reference external" href="https://www.youtube.com/watch?v=RGOj5yH7evk&amp;ab_channel=freeCodeCamp.org">https://www.youtube.com/watch?v=RGOj5yH7evk&ab_channel=freeCodeCamp.org</a></p>
|
||
<p>We will make extensive use of Python as programming language and its
|
||
myriad of available libraries. You will find
|
||
Jupyter notebooks invaluable in your work. You can run <em>R</em>
|
||
codes in the Jupyter/IPython notebooks, with the immediate benefit of
|
||
visualizing your data. You can also use compiled languages like C++,
|
||
Rust, Julia, Fortran etc if you prefer. The focus in these lectures will be
|
||
on Python.</p>
|
||
<p>If you have Python installed and you feel
|
||
pretty familiar with installing different packages, we recommend that
|
||
you install the following Python packages via <em>pip</em> as</p>
|
||
<ul class="simple">
|
||
<li><p>pip install numpy scipy matplotlib ipython scikit-learn mglearn sympy pandas pillow</p></li>
|
||
</ul>
|
||
<p>For OSX users we recommend, after having installed Xcode, to
|
||
install <em>brew</em>. Brew allows for a seamless installation of additional
|
||
software via for example</p>
|
||
<ul class="simple">
|
||
<li><p>brew install python3</p></li>
|
||
</ul>
|
||
<p>For Linux users, with its variety of distributions like for example the widely popular Ubuntu distribution,
|
||
you can use <em>pip</em> as well and simply install Python as</p>
|
||
<ul class="simple">
|
||
<li><p>sudo apt-get install python3</p></li>
|
||
</ul>
|
||
<section id="python-installers">
|
||
<h3>Python installers<a class="headerlink" href="#python-installers" title="Link to this heading">#</a></h3>
|
||
<p>If you don’t want to perform these operations separately and venture
|
||
into the hassle of exploring how to set up dependencies and paths, we
|
||
recommend two widely used distrubutions which set up all relevant
|
||
dependencies for Python, namely</p>
|
||
<ul class="simple">
|
||
<li><p>Anaconda:<a class="reference external" href="https://docs.anaconda.com/">https://docs.anaconda.com/</a>,</p></li>
|
||
</ul>
|
||
<p>which is an open source
|
||
distribution of the Python and R programming languages for large-scale
|
||
data processing, predictive analytics, and scientific computing, that
|
||
aims to simplify package management and deployment. Package versions
|
||
are managed by the package management system <em>conda</em>.</p>
|
||
<ul class="simple">
|
||
<li><p>Enthought canopy:<a class="reference external" href="https://www.enthought.com/product/canopy/">https://www.enthought.com/product/canopy/</a></p></li>
|
||
</ul>
|
||
<p>is a Python
|
||
distribution for scientific and analytic computing distribution and
|
||
analysis environment, available for free and under a commercial
|
||
license.</p>
|
||
<p>Furthermore, Google’s Colab:<a class="reference external" href="https://colab.research.google.com/notebooks/welcome.ipynb">https://colab.research.google.com/notebooks/welcome.ipynb</a> is a free Jupyter notebook environment that requires
|
||
no setup and runs entirely in the cloud. Try it out!</p>
|
||
</section>
|
||
<section id="useful-python-libraries">
|
||
<h3>Useful Python libraries<a class="headerlink" href="#useful-python-libraries" title="Link to this heading">#</a></h3>
|
||
<p>Here we list several useful Python libraries we strongly recommend (if you use anaconda many of these are already there)</p>
|
||
<ul class="simple">
|
||
<li><p><em>NumPy</em>:<a class="reference external" href="https://www.numpy.org/">https://www.numpy.org/</a> is a highly popular library for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays</p></li>
|
||
<li><p><em>The pandas</em>:<a class="reference external" href="https://pandas.pydata.org/">https://pandas.pydata.org/</a> library provides high-performance, easy-to-use data structures and data analysis tools</p></li>
|
||
<li><p><em>Xarray</em>:<a class="reference external" href="http://xarray.pydata.org/en/stable/">http://xarray.pydata.org/en/stable/</a> is a Python package that makes working with labelled multi-dimensional arrays simple, efficient, and fun!</p></li>
|
||
<li><p><em>Scipy</em>:<a class="reference external" href="https://www.scipy.org/">https://www.scipy.org/</a> (pronounced “Sigh Pie”) is a Python-based ecosystem of open-source software for mathematics, science, and engineering.</p></li>
|
||
<li><p><em>Matplotlib</em>:<a class="reference external" href="https://matplotlib.org/">https://matplotlib.org/</a> is a Python 2D plotting library which produces publication quality figures in a variety of hardcopy formats and interactive environments across platforms.</p></li>
|
||
<li><p><em>Autograd</em>:<a class="github reference external" href="https://github.com/HIPS/autograd">HIPS/autograd</a> can automatically differentiate native Python and Numpy code. It can handle a large subset of Python’s features, including loops, ifs, recursion and closures, and it can even take derivatives of derivatives of derivatives</p></li>
|
||
<li><p><em>JAX</em> <a class="reference external" href="https://jax.readthedocs.io/en/latest/index.html">https://jax.readthedocs.io/en/latest/index.html</a> has now more or less replaced <em>Autograd</em>.
|
||
JAX is Autograd and XLA, brought together for high-performance numerical computing and machine learning research.
|
||
It provides composable transformations of Python+NumPy programs: differentiate, vectorize, parallelize, Just-In-Time compile to GPU/TPU, and more.</p></li>
|
||
<li><p><em>SymPy</em>:<a class="reference external" href="https://www.sympy.org/en/index.html">https://www.sympy.org/en/index.html</a> is a Python library for symbolic mathematics.</p></li>
|
||
<li><p><em>scikit-learn</em>:<a class="reference external" href="https://scikit-learn.org/stable/">https://scikit-learn.org/stable/</a> has simple and efficient tools for machine learning, data mining and data analysis</p></li>
|
||
<li><p><em>TensorFlow</em>:<a class="reference external" href="https://www.tensorflow.org/">https://www.tensorflow.org/</a> is a Python library for fast numerical computing created and released by Google</p></li>
|
||
<li><p><em>Keras</em>:<a class="reference external" href="https://keras.io/">https://keras.io/</a> is a high-level neural networks API, written in Python and capable of running on top of TensorFlow, CNTK, or Theano</p></li>
|
||
<li><p>And many more such as <em>pytorch</em>:<a class="reference external" href="https://pytorch.org/">https://pytorch.org/</a>, <em>Theano</em>:<a class="reference external" href="https://pypi.org/project/Theano/">https://pypi.org/project/Theano/</a> etc</p></li>
|
||
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<li class="toc-h2 nav-item toc-entry"><a class="reference internal nav-link" href="#introduction">Introduction</a></li>
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