The course covers the foundations as well as the recent advances in Computational Learning with particular emphasis on the analysis of high dimensional data and focusing on a set of core techniques, namely regularization methods. See the synopsis and the syllabus for more details

Understanding how intelligence works and how it can be emulated in machines has been an elusive problem for decades and it is arguably one of the biggest challenges in modern science. Learning, its principles, and computational implementations are at the very core of this endeavor. Only recently we have been able, for the first time, to develop  artificial intelligence systems able to solve complex tasks that were considered out of reach for several decades. Modern cameras can recognize faces, and smart phones recognize people voice, car provided with cameras can detect pedestrians and ATM machines can automatically read checks.  In most cases at the root of these success stories there are machine learning algorithms, that is, softwares that  are trained rather than programmed to solve a task. 

Among the variety of approaches and ideas in modern computational learning, we focus on a core class of methods, namely regularization methods, which represent a  fundamental set of concepts and techniques allowing to treat in a unified way a huge  class of diverse approaches, while providing the tools to design new ones. Starting from classical notions of smoothness, shrinkage and margin,  we will cover state of the art techniques based on the concepts of geometry  (e.g. manifold learning), sparsity, low rank, allowing to design algorithm for tasks such as supervised learning,  feature selection, structured prediction, multitask learning and model selection.
Practical applications will be discussed, primarily from the field of computational vision. 
   
The classes will focus on algorithmic and methodological aspects, while trying to give an idea of the underlying theoretical underpinnings.

Slides of the classes will be posted on this website and scribes of most classes, as well as other material, can be found on the 9.520 course webpage at MIT.

The course will cover the following topics:

• Introduction to machine learning - first part and second part
• Reproducing Kernel Hilbert Spaces and Tikhonov Regularization - slides
• Regularized Least Squares and Support Vector Machines - slides
• Spectral methods for supervised learning - slides
• Sparsity-based learning - slides
• Multiple Kernel Learning - slides
• Manifold regularization - slides
• Multitask learning - slides

General references are

To pass the exam you have to gain a total of at least 20 points. Extra points may buy you better a grade. We envision three possibilities:

1. Solve problems from the proposed set (46 possible point ) for a total of 10/46 points. AND write a short report 2 pages+ references on one of the subject treated in class.
2. Write a report 6 pages+ references on one of the subject treated in class.
3. Solve problems from the proposed set (46 possible point ) for a total of 20/46 points.