# Introduction to statistical learning theory

# Introduction to statistical learning theory

Date

27 Feb 2019

6 Mar 2019

13 Mar 2019

20 Mar 2019

21 Mar 2019

Always at 12.00-14.00

Location

Aula C3-005, Campus Nord,

UPC

*Summary*

The theory of Machine Learning is a field that lies at the intersection of statistics, probability, computer science, and optimization. This mathematical theory is concerned with theoretical guarantees for machine learning algorithms. Over the last decades the statistical learning approach has been successfully applied to many problems of interest in machine learning, such as bioinformatics, computer vision, speech processing, robotics, and information retrieval. This success story crucially relies on a strong mathematical foundation.

The goal of this 10-hour course is to lay out some of the basic principles and introduce mathematical tools that help understand and analyze machine learning algorithms.

The focus will be on elements of empirical processes, concentration inequalities, kernel methods, and stochastic optimization of convex functions.

The course will be mostly of interest to PhD students in probability, statistics, optimization, and theoretical computer science. Only some basic background in probability at graduate level is required.

Date

27 Feb 2019

6 Mar 2019

13 Mar 2019

20 Mar 2019

21 Mar 2019

Always at 12.00-14.00

Location

Aula C3-005, Campus Nord,

UPC

*Summary*

The theory of Machine Learning is a field that lies at the intersection of statistics, probability, computer science, and optimization. This mathematical theory is concerned with theoretical guarantees for machine learning algorithms. Over the last decades the statistical learning approach has been successfully applied to many problems of interest in machine learning, such as bioinformatics, computer vision, speech processing, robotics, and information retrieval. This success story crucially relies on a strong mathematical foundation.

The goal of this 10-hour course is to lay out some of the basic principles and introduce mathematical tools that help understand and analyze machine learning algorithms.

The focus will be on elements of empirical processes, concentration inequalities, kernel methods, and stochastic optimization of convex functions.

The course will be mostly of interest to PhD students in probability, statistics, optimization, and theoretical computer science. Only some basic background in probability at graduate level is required.

With the support of

Gábor Lugosi, ICREA Research Professor, BGSMath – Universitat Pompeu Fabra

### Biosketch

Gábor Lugosi graduated in electrical engineering at the Technical University of Budapest in 1987, and received his Ph.D. from the Hungarian Academy of Sciences in 1991. Since 1996, he has been at the Department of Economics, Pompeu Fabra University, Barcelona. In 2006 he became an ICREA research professor.

### Research Interests

- Theory of machine learning
- Combinatorial statistics
- Inequalities in probability
- Random graphs and random structures
- Information theory

##### Syllabus

*Basic setup: *Elements of decision theory; Risk minimization.

*Concentration inequalities: *Concentration of sums of independent random variables; Random projections; Mean estimation; Concentration of functions of independent random variables.

*Empirical processes: *Uniform convergence of relative frequencies; Vapnik-Chervonenkis theory (Rademacher averages, VC-dimension); Empirical risk minimization;

Large-margin classifiers.

*Kernel methods: *Generalized linear regression and classification; Reproducing kernel Hilbert spaces; The kernel trick.

*Elements of convex optimization: *Stochastic optimization in machine learning; Stochastic gradient descent.

##### References

Shai Shalev-Shwartz and Shai Ben-David. *Understanding Machine Learning. From Theory to Algorithms*. Cambridge University Press, 2014.

Luc Devroye, László Györfi, Gábor Lugosi. *A Probabilistic Theory of Pattern Recognition*. Springer, 1996.

John Shawe-Taylor and Nello Crisianini. *Kernel Methods for Pattern Analysis. *Cambridge University Press, 2004.

Mehryar Mohri, Afshin Rostamizadeh, and Ameet Talwalkar. *Foundations of Machine Learning. *The MIT Press.

Martin Anthony and Peter L. Bartlett. *Neural Network Learning: Theoretical Foundations*. Cambridge University Press, 1999.