mhjensen
632 lines
28 KiB
HTML
632 lines
28 KiB
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<section>
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<!-- ------------------- main content ---------------------- -->
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<center><h1 style="text-align: center;">Introduction to Applied Data Analysis and Machine Learning</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>Aug 13, 2019</h4></center> <!-- date -->
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<br>
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<h2 id="___sec0">Introduction </h2>
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<p>
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During the last two decades there has been a swift and amazing
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development of Machine Learning techniques and algorithms that impact
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many areas in not only Science and Technology but also the Humanities,
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Social Sciences, Medicine, Law, indeed, almost all possible
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disciplines. The applications are incredibly many, from self-driving
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cars to solving high-dimensional differential equations or complicated
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quantum mechanical many-body problems. Machine Learning is perceived
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by many as one of the main disruptive techniques nowadays.
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<p>
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Statistics, Data science and Machine Learning form important
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fields of research in modern science. They describe how to learn and
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make predictions from data, as well as allowing us to extract
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important correlations about physical process and the underlying laws
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of motion in large data sets. The latter, big data sets, appear
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frequently in essentially all disciplines, from the traditional
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Science, Technology, Mathematics and Engineering fields to Life
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Science, Law, education research, the Humanities and the Social
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Sciences.
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<p>
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It has become more
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and more common to see research projects on big data in for example
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the Social Sciences where extracting patterns from complicated survey
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data is one of many research directions. Having a solid grasp of data
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analysis and machine learning is thus becoming central to scientific
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computing in many fields, and competences and skills within the fields
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of machine learning and scientific computing are nowadays strongly
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requested by many potential employers. The latter cannot be
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overstated, familiarity with machine learning has almost become a
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prerequisite for many of the most exciting employment opportunities,
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whether they are in bioinformatics, life science, physics or finance,
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in the private or the public sector. This author has had several
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students or met students who have been hired recently based on their
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skills and competences in scientific computing and data science, often
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with marginal knowledge 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. Many of the methods we will study are also
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strongly rooted in basic mathematics and physics research.
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<p>
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Ideally, machine learning represents the science of giving computers
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the ability to learn without being explicitly programmed. The idea is
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that there exist generic algorithms which can be used to find patterns
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in a broad class of data sets without having to write code
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specifically for each problem. The algorithm will build its own logic
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based on the data. You should however always keep in mind that
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machines and algorithms are to a large extent developed by humans. The
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insights and knowledge we have about a specific system, play a central
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role when we develop a specific machine learning algorithm.
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<p>
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Machine learning is an extremely rich field, in spite of its young
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age. The increases we have seen during the last three decades in
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computational capabilities have been followed by developments of
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methods and techniques for analyzing and handling large date sets,
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relying heavily on statistics, computer science and mathematics. The
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field is rather new and developing rapidly. Popular software packages
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written in Python for machine learning like
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<a href="http://scikit-learn.org/stable/" target="_blank">Scikit-learn</a>,
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<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
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freely available at their respective GitHub sites, encompass
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communities of developers in the thousands or more. And the number of
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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 and
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trial and error and thereby exciting new developments. However, a
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solid command of linear algebra, multivariate theory, probability
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theory, statistical data analysis, understanding errors and Monte
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Carlo methods are central elements in a proper understanding of many
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of algorithms and methods we will discuss.
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<p>
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<center style="font-size:80%">
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<!-- copyright --> © 1999-2019, 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="___sec1">Learning outcomes </h2>
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<p>
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These sets of 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 exercises, 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 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
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statistical data analysis and its basic concepts such as expectation
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values, variance, covariance, correlation functions and errors, via
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well-known probability distribution functions like the 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 optimize (minimize) functions (the family of gradient descent methods)
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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, the bootstrapping
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and the jackknife methods and the infamous bias-variance tradeoff.
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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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<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
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two main categories. In <em>supervised learning</em> we know the answer to a
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problem, and let the computer deduce the logic behind it. On the other
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hand, <em>unsupervised learning</em> is a method for finding patterns and
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relationship in data sets without any prior knowledge of the system.
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Some authours also operate with a third category, namely
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<em>reinforcement learning</em>. This is a paradigm of learning inspired by
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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
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desired output of a system. 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 (which can be subdivided into
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training and test data), the second item is a model which is normally
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a function of some parameters. The model reflects our knowledge of
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the system (or lack thereof). As an example, if we know that our data
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show a behavior similar to what would be predicted by a polynomial,
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fitting our data to a polynomial of some degree would then determin
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our model.
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<p>
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The last ingredient is a so-called <b>cost</b>
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function which allows us to present an estimate on how good our model
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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</li>
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<p><li> Decision tree algorithms, from single trees to random forests</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, including convolutional neural networks and Bayesian neural networks</li>
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<p><li> Networks for unsupervised learning using for example reduced Boltzmann machines.</li>
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</ol>
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<h2 id="___sec3">Choice of programming language </h2>
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<p>
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Python plays nowadays a central role in the development of machine
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learning techniques and tools for data analysis. In particular, seen
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the wealth of machine learning and data analysis libraries written in
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Python, easy to use libraries with immediate visualization(and not the
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least impressive galleries of existing examples), the popularity of the
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Jupyter notebook framework with the possibility to run <b>R</b> codes or
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compiled programs written in C++, and much more made our choice of
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programming language for this series of lectures easy. However,
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since the focus here is not only on using existing Python libraries such
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as <b>Scikit-Learn</b> or <b>Tensorflow</b>, but also on developing your own
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algorithms and codes, we will as far as possible present many of these
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algorithms either as a Python codes or C++ or Fortran (or other languages) codes.
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<p>
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The reason we also focus on compiled languages like C++ (or
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Fortran), is that Python is still notoriously slow when we do not
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utilize highly streamlined computational libraries like
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<a href="http://www.netlib.org/lapack/" target="_blank">Lapack</a> or other numerical libraries
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written in compiled languages (many of these libraries are written in
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Fortran). Although a project like <a href="https://numba.pydata.org/" target="_blank">Numba</a>
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holds great promise for speeding up the unrolling of lengthy loops, C++
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and Fortran are presently still the performance winners. Numba gives
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you potentially the power to speed up your applications with high
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performance functions written directly in Python. In particular,
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array-oriented and math-heavy Python code can achieve similar
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performance to C, C++ and Fortran. However, even with these speed-ups,
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for codes involving heavy Markov Chain Monte Carlo analyses and
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optimizations of cost functions, C++/C or Fortran codes tend to
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outperform Python codes.
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<p>
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Presently thus, the community tends to let
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code written in C++/C or Fortran do the heavy duty numerical
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number crunching and leave the post-analysis of the data to the above
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mentioned Python modules or software packages. However, with the developments taking place in for example the Python community, and seen
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the changes during the last decade, the above situation may change swiftly in the not too distant future.
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<p>
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Many of the examples we discuss in this series of lectures come with
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existing data files or provide code examples which produce the data to
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be analyzed. Most of the applications we will discuss deal with
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small data sets (less than a terabyte of information) and can easily
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be analyzed and tested on standard off the shelf laptops you find in general
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stores.
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<h2 id="___sec4">Data handling, machine learning and ethical aspects </h2>
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<p>
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In most of the cases we will study, we will either generate the data
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to analyze ourselves (both for supervised learning and unsupervised
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learning) or we will recur again and again to data present in say
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<b>Scikit-Learn</b> or <b>Tensorflow</b>. Many of the examples we end up
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dealing with are from a privacy and data protection point of view,
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rather inoccuous and boring results of numerical
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calculations. However, this does not hinder us from developing a sound
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ethical attitude to the data we use, how we analyze the data and how
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we handle the data.
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<p>
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The most immediate and simplest possible ethical aspects deal with our
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approach to the scientific process. Nowadays, with version control
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software like <a href="https://git-scm.com/" target="_blank">Git</a> and various online
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repositories like <a href="https://github.com/" target="_blank">Github</a>,
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<a href="https://about.gitlab.com/" target="_blank">Gitlab</a> etc, we can easily make our codes
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and data sets we have used, freely and easily accessible to a wider
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community. This helps us almost automagically in making our science
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reproducible. The large open-source development communities involved
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in say <a href="http://scikit-learn.org/stable/" target="_blank">Scikit-Learn</a>,
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<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>, are
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all excellent examples of this. The codes can be tested and improved
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upon continuosly, helping thereby our scientific community at large in
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developing data analysis and machine learning tools. It is much
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easier today to gain traction and acceptance for making your science
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reproducible. From a societal stand, this is an important element
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since many of the developers are employees of large public institutions like
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universities and research labs. Our fellow taxpayers do deserve to get
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something back for their bucks.
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<p>
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However, this more mechanical aspect of the ethics of science (in
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particular the reproducibility of scientific results) is something
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which is obvious and everybody should do so as part of the dialectics of
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science. The fact that many scientists are not willing to share their codes or
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data is detrimental to the scientific discourse.
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<p>
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Before we proceed, we should add a disclaimer. Even though
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we may dream of computers developing some kind of higher learning
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capabilities, at the end (even if the artificial intelligence
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community keeps touting our ears full of fancy futuristic avenues), it is we, yes you reading these lines,
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who end up constructing and instructing, via various algorithms, the
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machine learning approaches. Self-driving cars for example, rely on sofisticated
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programs which take into account all possible situations a car can
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encounter. In addition, extensive usage of training data from GPS
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information, maps etc, are typically fed into the software for
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self-driving cars. Adding to this various sensors and cameras that
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feed information to the programs, there are zillions of ethical issues
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which arise from this.
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<p>
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For self-driving cars, where basically many of the standard machine
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learning algorithms discussed here enter into the codes, at a certain
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stage we have to make choices. Yes, we , the lads and lasses who wrote
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a program for a specific brand of a self-driving car. As an example,
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all carmakers have as their utmost priority the security of the
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driver and the accompanying passengers. A famous European carmaker, which is
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one of the leaders in the market of self-driving cars, had <b>if</b>
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statements of the following type: suppose there are two obstacles in
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front of you and you cannot avoid to collide with one of them. One of
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the obstacles is a monstertruck while the other one is a kindergarten
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|
class trying to cross the road. The self-driving car algo would then
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opt for the hitting the small folks instead of the monstertruck, since
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the likelihood of surving a collision with our future citizens, is
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much higher.
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<p>
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This leads to serious ethical aspects. Why should we
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opt for such an option? Who decides and who is entitled to make such
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choices? Keep in mind that many of the algorithms you will encounter in
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this series of lectures or hear about later, are indeed based on
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simple programming instructions. And you are very likely to be one of
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the people who may end up writing such a code. Thus, developing a
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sound ethical attitude to what we do, an approach well beyond the
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simple mechanistic one of making our science available and
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|
reproducible, is much needed. The example of the self-driving cars is
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just one of infinitely many cases where we have to make choices. When
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|
you analyze data on economic inequalities, who guarantees that you are
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not weighting some data in a particular way, perhaps because you dearly want a
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specific conclusion which may support your political views?
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<p>
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We do not have the answers here, nor will we venture into a deeper
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discussions of these aspects, but we want you think over these topics
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in a more overarching way. A statistical data analysis with its dry
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numbers and graphs meant to guide the eye, does not necessarily
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|
reflect the truth, whatever that is. As a scientist, and after a
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|
university education, you are supposedly a better citizen, with an
|
|
improved critical view and understanding of the scientific method, and
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|
perhaps some deeper understanding of the ethics of science at
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|
large. Use these insights. Be a critical citizen. You owe it to our
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society.
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</section>
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