mhjensen
479 lines
19 KiB
HTML
479 lines
19 KiB
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<section>
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<!-- ------------------- main content ---------------------- -->
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<center><h1 style="text-align: center;">Data Analysis and Machine Learning: Representing data</h1></center> <!-- document title -->
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<p>
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<!-- author(s): Morten Hjorth-Jensen -->
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<center>
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<b>Morten Hjorth-Jensen</b> [1, 2]
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</center>
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<p> <br>
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<!-- institution(s) -->
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<center>[1] <b>Department of Physics, University of Oslo</b></center>
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<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
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<br>
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<p> <br>
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<center><h4>May 22, 2018</h4></center> <!-- date -->
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<br>
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<p>
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<center style="font-size:80%">
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<!-- copyright --> © 1999-2018, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
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</center>
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</section>
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<section>
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<h2 id="___sec0">Introduction </h2>
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<p>
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Statistics, data science and machine learning form important fields of
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research in modern science. They describe how to learn and make
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predictions from data, as well as allowing us to extract important
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correlations about physical process and the underlying laws of motion
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in large data sets. The latter, big data sets, appear
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frequently in essentially all disciplines, from the traditional Science,
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Technology, Mathematics and Engineering fields to Life Science, Law, education research,
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the Humanities and
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the Social Sciences. It has become more and more common to see
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research projects on big data in for example the Social
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Sciences where extracting patterns from complicated survey data is one of many research directions.
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Having a solid grasp of data analysis and machine learning
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is thus becoming central to scientific computing in many
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fields, and competences and skills within the fields of machine learning
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and scientific computing are nowadays strongly requested by many
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potential employers. The latter cannot be overstated, familiarity with
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machine learning has almost become a prerequisite for many of the most
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exciting employment opportunities, whether they are in bioinformatics,
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life science, physics or finance, in the private or the public
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sector. This author has had several students or met students who have
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been hired recently based on their skills and competences in
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scientific computing and data science, often with marginal knowledge
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of machine learning.
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<p>
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Machine learning is a subfield of computer science, and is closely
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related to computational statistics. It evolved from the study of
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pattern recognition in artificial intelligence (AI) research, and has
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made contributions to AI tasks like computer vision, natural language
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processing and speech recognition.
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Machine learning represents the
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science of giving computers the ability to learn without being
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explicitly programmed. The idea is that there exist generic
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algorithms which can be used to find patterns in a broad class of data
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sets without having to write code specifically for each problem. The
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algorithm will build its own logic based on the data.
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<p>
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Machine learning is an extremely rich field, in spite of its young age. The
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increases we have seen during the last three decades in computational
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capabilities have been followed by developments of methods and
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techniques for analyzing and handling large date sets, relying heavily
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on statistics, computer science and mathematics. The field is rather
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new and developing rapidly. Popular software packages written in
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Python for machine learning like <a href="http://scikit-learn.org/stable/" target="_blank">Scikit-learn</a>, <a href="https://www.tensorflow.org/" target="_blank">Tensorflow</a>,
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<a href="http://pytorch.org/" target="_blank">PyTorch</a> and <a href="https://keras.io/" target="_blank">Keras</a>, all freely available at their respective GitHub sites,
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encompass communities of developers in the thousands or more. And the number
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of code developers and contributors keeps increasing. Not all the
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algorithms and methods can be given a rigorous mathematical
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justification, opening up thereby large rooms for experimenting
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and trial and error and thereby exciting new developments.
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However, a solid command of linear algebra, multivariate theory,
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probability theory, statistical data analysis,
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understanding errors and Monte Carlo methods are central elements in a proper understanding of many of
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algorithms and methods we will discuss.
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</section>
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<section>
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<h2 id="___sec1">Learning outcomes </h2>
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<p>
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These lectures aim at giving you an overview of central aspects of
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statistical data analysis as well as some of the central algorithms
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used in machine learning. We will introduce a variety of central
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algorithms and methods essential for studies of data analysis and
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machine learning.
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<p>
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Hands-on projects and experimenting with data and algorithms plays a central role in
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these lectures, and our hope is, through the various
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projects and exercies, to expose you to fundamental
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research problems in these fields, with the aim to reproduce state of
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the art scientific results. You will learn to develop and
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structure large codes for studying these systems, get acquainted with
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computing facilities and learn to handle large scientific projects. A
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good scientific and ethical conduct is emphasized throughout the
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course. More specifically, you will
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<ol>
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<p><li> learn about basic data analysis, Bayesian statistics, Monte Carlo methods, data optimization and machine learning;</li>
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<p><li> be capable of extending the acquired knowledge to other systems and cases;</li>
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<p><li> Have an understanding of central algorithms used in data analysis and machine learning;</li>
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<p><li> Gain knowledge of central aspects of Monte Carlo methods, Markov chains, Gibbs samplers and their possible applications, from numerical integration to simulation of stock markets;</li>
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<p><li> Understand methods for regression and classification;</li>
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<p><li> Learn about neural network, genetic algorithms and Boltzmann machines;</li>
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<p><li> 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++, in addition to a basic knowledge of linear algebra (typically taught during the first one or two years of undergraduate studies).</li>
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</ol>
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<p>
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There are several topics we will cover here, spanning from a
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statistical data analysis and its basic concepts such expectation
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values, variance, covariance, correlation functions and errors, via
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well-known probability distribution functions like uniform
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distribution, the binomial distribution, the Poisson distribution and
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simple and multivariate normal distributions to central elements of
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Bayesian statistics and modeling. We will also remind the reader about
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central elements from linear algebra and standard methods based on
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linear algebra used to fit functions such Cubic splines and gradient
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methods for data optimization and the Singular-value decomposition and
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least square methods for parameterizing data.
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<p>
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We will also cover Monte Carlo methods, Markov chains, well-known
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algorithms for sampling stochastic events like the Metropolis-Hastings
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and Gibbs sampling methods. An important aspect of all our
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calculations is a proper estimation of errors. Here we will also
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discuss famous resampling techniques like the blocking, bootstrapping
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and jackknife methods.
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<p>
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The second part of the material covers several algorithms used in
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machine learning.
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</section>
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<section>
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<h2 id="___sec2">Types of Machine Learning </h2>
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<p>
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The approaches to machine learning are many, but are often split into two main categories.
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In <em>supervised learning</em> we know the answer to a problem,
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and let the computer deduce the logic behind it. On the other hand, <em>unsupervised learning</em>
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is a method for finding patterns and relationship in data sets without any prior knowledge of the system.
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Some authours also operate with a third category, namely <em>reinforcement learning</em>. This is a paradigm
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of learning inspired by behavioral psychology, where learning is achieved by trial-and-error,
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solely from rewards and punishment.
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<p>
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Another way to categorize machine learning tasks is to consider the desired output of a system.
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Some of the most common tasks are:
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<ul>
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<p><li> Classification: Outputs are divided into two or more classes. The goal is to produce a model that assigns inputs into one of these classes. An example is to identify digits based on pictures of hand-written ones. Classification is typically supervised learning.</li>
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<p><li> Regression: Finding a functional relationship between an input data set and a reference data set. The goal is to construct a function that maps input data to continuous output values.</li>
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<p><li> Clustering: Data are divided into groups with certain common traits, without knowing the different groups beforehand. It is thus a form of unsupervised learning.</li>
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</ul>
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<p>
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The methods we cover have three main topics in common, irrespective of
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whether we deal with supervised or unsupervised learning. The first
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ingredient is normally our data set, the second is a model which is
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normally a function of some parameters. The last ingredient is a
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so-called <b>cost</b> function which allows us to present an estimate on
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how good our model is in reproducing the data it is supposed to train.
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<p>
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Here we will build our machine learning approach on elements of the
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statistical foundation discussed above, with elements from data
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analysis, stochastic processes etc. We will discuss the following
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machine learning algorithms
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<ol>
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<p><li> Linear regression and its variants, in essence polynomial regression</li>
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<p><li> Decision tree algorithms, from simpler to more complex ones</li>
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<p><li> Nearest neighbors models</li>
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<p><li> Bayesian statistics and regression</li>
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<p><li> Support vector machines and finally various variants of</li>
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<p><li> Artifical neural networks and deep learning</li>
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</ol>
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</section>
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<section>
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<h2 id="___sec3">Why this text? </h2>
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</section>
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<section>
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<h2 id="___sec4">Choice of programming language </h2>
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</section>
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<section>
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<h2 id="___sec5">Data handling, machine learning and ethical aspects </h2>
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</section>
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<section>
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<h2 id="___sec6">Acknowledgements </h2>
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</section>
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<div style="position: absolute; bottom: 0px; left: 0; margin-left: 0px">
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<img src="somelogo.png">
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</div>
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end footer logo -->
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</body>
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</html>
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