Overview of course material: Data Analysis and Machine Learning

Morten Hjorth-Jensen [1, 2]

[1] Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University, USA [2] Department of Physics (office FV308), University of Oslo, Norway

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Basic introduction to the course with schedule etc

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Introduction to Data Analysis and Machine Learning

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Getting started with Machine Learning

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Review of central linear algebra elements

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Monte Carlo methods and elements of probability theory

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Splines and Gradient methods

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Regression Methods

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Logistic Regression

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Neural Networks

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Elements of Bayesian theory

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Decision trees, from simple to random ones

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Support Vector Machines

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Unsupervised Learning, Boltzmann Machines

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Python and Scikit Learn, a short guide

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Teach yourself C++

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Projects and Exercises Fall 2018

Course content

Probability theory and statistical methods play a central role in science. Nowadays we are surrounded by huge amounts of data. For example, there are about one trillion web pages; more than one hour of video is uploaded to YouTube every second, amounting to 10 years of content every day; the genomes of 1000s of people, each of which has a length of \( 3.8\times 10^9 \) 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 provides. In this course the approach is to define machine learning as a set of methods that can automatically detect patterns in data, and then use the uncovered patterns to predict future data, or to perform other kinds of decision making under uncertainty. Since many of these problems can be studied using tools of probability theory, the aim of this course is to expose you to central methods in probability theory linked with machine learning.

This course covers thus topics like Monte Carlo methods and Markov chains, Bayesian statistics, error estimates, various linear methods, optimization of data and error analysis and central algorithms in machine learning. The course has several numerical projects and numerical exercises that are meant to illustrate the theory.

Learning outcomes

The course introduces a variety of central algorithms and methods essential for studies of data analysis and machine learning. The course is project based and through the various projects, normally three, the students will be exposed to fundamental research problems in these fields, with the aim to reproduce state of the art scientific results. The students will learn to develop and structure large codes for studying these systems, 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

Learn about basic data analysis, Bayesian statistics, Monte Carlo methods, data optimization and machine learning;
Be capable of extending the acquired knowledge to other systems and cases;
Have an understanding of central algorithms used in data analysis and machine learning;
Have a basic knowledge of Bayesian statistics and learning and common distributions;
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;
Understand linear methods for regression and classification;
Learn about neural network, genetic algorithms and Boltzmann machines;
Work on numerical projects to illustrate the theory. The projects play a central role and students are expected to know modern programming languages like Python or C++.

Prerequisites

Basic knowledge in programming and numerics. 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-INF1xxx.

The course has two central parts

Statistical analysis and optimization of data
Machine learning

Statistical analysis and optimization of data

The following topics will be covered

Basic concepts, expectation values, variance, covariance, correlation functions and errors;
Review of linear algebra methods;
Splines and conjugate gradient methods for data optimization;
Simpler models, binomial distribution, the Poisson distribution, simple and multivariate normal distributions;
Central elements of Bayesian statistics and modeling;
Monte Carlo methods, Markov chains, Metropolis-Hastings algorithm, ergodicity;
Linear methods for regression and classification;
Estimation of errors using blocking, bootstrapping and jackknife methods;
Practical optimization using Singular-value decomposition and least squares for parameterizing data.

Machine learning

The following topics will be covered

Gaussian and Dirichlet processes;
Decision trees and nearest neighbors;
Support vector machines;
Boltzmann machines;
Neural networks;
Genetic algorithms.

All the above topics will be supported by examples, hands-on exercises and project work.

Other textbooks

General learning book on statistical analysis:

Christian Robert and George Casella, Monte Carlo Statistical Methods, Springer
Peter Hoff, A first course in Bayesian statistical models, Springer

General Machine Learning Books:

Kevin Murphy, Machine Learning: A Probabilistic Perspective, MIT Press
Christopher M. Bishop, Pattern Recognition and Machine Learning, Springer
David J.C. MacKay, Information Theory, Inference, and Learning Algorithms, Cambridge University Press
Trevor Hastie, Robert Tibshirani, and Jerome Friedman, The Elements of Statistical Learning, Springer
David Barber, Bayesian Reasoning and Machine Learning, Cambridge University Press

Teaching schedule Fall 2018

Acronyms for textbooks and references to chapter

Week and days	Topics to be covered	Projects, exercises and deadlines	Reading assignments	Lab activities
Week 34	Introduction and regression analysis	Exercises TBD	HTF chapters 1-3 and lecture notes	No lab first week
Week 35	Regression analysis	Exercises TBD	HTF chapter 3 and lecture notes	Introduction to Git, GitHub and Python software, Python technicalities and work on exercises
Week 36	Regression analysis and nearest neighbors	Exercises TBD	HTF chapters 3, 4 and 13 and lecture notes	Work on exercises
Week 37	Classification and logistic regression	Presentation of Project 1, deadline October 1	HTF chapter 4 and lecture notes	Work on project 1
Week 38	Optimization methods	Exercises and project 1	HTF chapter 5 and lecture notes	Work on project 1, deadline October 1
Week 39	Statistics, Bayesian statistics	Project 1	Lecture notes	Work on Project 1
Week 40	Statistics, Monte Carlo and Randow walks	Presentation of project 2, deadline November 5	Lecture notes	Deadline project 1, October 1
Week 41	Statistics, Monte Carlo, Gibbs and Metropolis sampling	Project 2	Lecture notes	Work on project 2
Week 42	Neural networks	Project 2	HTF chapter 11 and lecture notes	Work on project 2
Week 43	Neural networks	Project 2	HTF chapter 11 and lecture notes	Work on project 2
Week 44	Neural networks	Project 2	HTF chapter 11 and lecture notes	Work on project 2
Week 45	Support Vector Machines	Presentation and discussion of project 3	HTF chapter 12 and lecture notes	Deadline project 2 November 5
Week 46	Decision trees	Project 3	HTF chapter 9 and lecture notes	Work on project 3
Week 47	Unsupervised learning, Boltzmann machines	Project 3	HTF chapter 14 and lecture notes	Work on project 3
Week 48	Unsupervised learning, summary of course and final workshop	Project 3	Lecture notes	Final workshop with presentation of project 3