Class Times:Monday and Wednesday: 1:00pm - 2:30pmUnits:3-0-9 H,G Location:46-3189Instructors:Tomaso Poggio (TP), Lorenzo Rosasco (LR), Carlo Ciliberto (CC), Charlie Frogner (CF), Georgios Evangelopoulos (GE).

Office Hours:Friday 2-3 pm in 46-5156, CBCL lounge (by appointment) Email Contact :9.520@mit.edu Previous Class:FALL 2013 Further Info:9.520 is currently NOTusing the Stellar system

Course descriptionThe class covers foundations and recent advances of Machine Learning in the framework of Statistical Learning Theory.

Understanding intelligence and how to replicate it in machines is arguably one of the greatest problems in science. Learning, its principles and computational implementations, is at the very core of intelligence. During the last decade, for the first time, we have been able to develop artificial intelligence systems that can solve complex tasks previously considered out of reach. Modern cameras recognize faces, and smart phones voice commands, cars can see and detect pedestrians and ATM machines automatically read checks. The machine learning algorithms that are at the roots of these success stories are trained with labeled examples rather than programmed to solve a task. Among the approaches in modern machine learning, the course focus is on regularization techniques, that are key to high- dimensional supervised learning. Regularization methods allow to treat in a unified way a large number of diverse approaches, while providing tools to design new ones.

Starting from classical methods such as Regularization Networks and Support Vector Machines, the course covers state of the art techniques based on the concepts of geometry (aka manifold learning), sparsity and a variety of algorithms for supervised learning (batch and online), feature selection, structured prediction and multitask learning.

The final part of the course is new and will focus on connections between Radial Basis Functions and deep learning networks. We will also introduce new techniques for the (unsupervised) learning of data representation. In particular we will present a new theory (M-theory) of hierarchical architectures, motivated by the visual cortex, that might suggest how to learn, in an unsupervised way, data representation that can lower the sample complexity of a final supervised learning stage.

The goal of this class is to provide students with the knowledge needed to use and develop effective machine learning solutions to challenging problems.

## We will make extensive use of linear algebra, basic functional analysis (we cover the essentials in class and during the math-camp), basic concepts in probability theory and concentration of measure (also covered in class and during the mathcamp). Students are expected to be familiar with MATLAB.

Prerequisites## Requirements for grading (other than attending lectures) are: 2 problems sets, and a final project.

Grading

Problem SetsNote:for the Problems that require to write code and run experiments, submit via email to 9.520@mit.edu your MATLAB code by the due date.

## The final project can be either a Wikipedia entry or a research project (we recommend a Wikipedia entry).

Projects

We envision 2 kinds of research project:For the Wikipedia article, we suggest a short one using the Wikipedia standard article format; for the research project you should use this template. Reports should be 8 pages maximum, including references. Additional material can be included in the appendix.

Applications: evaluate an algorithm on some interesting problem of your choice;Theory and Algorithms: study theoretically or empirically some new machine learning algorithm/problem.

SyllabusFollow the link for each class to find a detailed description, suggested readings, and class slides. Some of the later classes may be subject to reordering or rescheduling.

Class Date Title Instructor(s)

## There is no textbook for this course. All the required information will be presented in the slides associated with each class. The books/papers listed below are useful general reference reading, especially from the theoretical viewpoint. A list of suggested readings will also be provided separately for each class.

Reading List## Primary References

- Bousquet, O., S. Boucheron and G. Lugosi.
Introduction to Statistical Learning Theory. Advanced Lectures on Machine Learning Lecture Notes in Artificial Intelligence 3176, 169-207. (Eds.) Bousquet, O., U. von Luxburg and G. Ratsch, Springer, Heidelberg, Germany (2004)- F. Cucker and S. Smale.
On The Mathematical Foundations of Learning. Bulletin of the American Mathematical Society, 2002.- F. Cucker and D-X. Zhou.
Learning theory: an approximation theory viewpoint.Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, Cambridge, 2007.- L. Devroye, L. Gyorfi, and G. Lugosi.
A Probabilistic Theory of Pattern Recognition.Springer, 1997.- T. Evgeniou and M. Pontil and T. Poggio.
Regularization Networks and Support Vector Machines.Advances in Computational Mathematics, 2000.- T. Poggio and S. Smale.
The Mathematics of Learning: Dealing with Data.Notices of the AMS, 2003- I. Steinwart and A. Christmann.
Support vector machines.Springer, New York, 2008.- V. N. Vapnik.
Statistical Learning Theory.Wiley, 1998.- V. N. Vapnik.
The Nature of Statistical Learning Theory.Springer, 1995.- N. Cristianini and J. Shawe-Taylor.
Introduction To Support Vector Machines.Cambridge, 2000.## Background Mathematics References

- A. N. Kolmogorov and S. V. Fomin,
Introductory Real Analysis, Dover Publications, 1975.- A. N. Kolmogorov and S. V. Fomin,
Elements of the Theory of Functions and Functional Analysis, Dover Publications, 1999.- Luenberger,
Optimization by Vector Space Methods, Wiley, 1969.## Neuroscience Related References

- Serre, T., L. Wolf, S. Bileschi, M. Riesenhuber and T. Poggio. "
Object Recognition with Cortex-like Mechanisms", IEEE Transactions on Pattern Analysis and Machine Intelligence, 29, 3, 411-426, 2007.- Serre, T., A. Oliva and T. Poggio."
A Feedforward Architecture Accounts for Rapid Categorization", Proceedings of the National Academy of Sciences (PNAS), Vol. 104, No. 15, 6424-6429, 2007.- S. Smale, L. Rosasco, J. Bouvrie, A. Caponnetto, and T. Poggio. "
Mathematics of the Neural Response", Foundations of Computational Mathematics, Vol. 10, 1, 67-91, June 2009.