## Tutorial

"Advances of statistical learning and applications to computer vision"

### Speakers: Francesca Odone, Ernesto De Vito

## Outline

The goal of this tutorial is to provide a comprehensive introduction to a
large class of statistical learning algorithms in the supervised setting with
applications to a variety of computer vision problems.
As for the theoretical aspects, having as a guide regularized least squares,
we will introduce a new class of algorithms dened in terms of lter functions
on the kernel matrix. We will give some examples and we discuss the
theoretical and computational properties. Finally we will briefly present algorithms
that enforce the sparsity of the solution by means of l1 constraints.
As for the applications to computer vision we will suggest applications to
some filter algorithms that are simpler to implement and to tune than other
kernel methods (such as SVMs). We will also discuss how methods that enforce
sparsity can be used for feature selection, and compare this approach
to state-of-the-art feature selection (e.g., Adaboost) and dimensionality reduction
methods (e.g., PCA) , on the well known face detection framework.
We plan to balance theory and application aspects.
## Tentative table of contents

Theory
- Review of the regularized least squares algorithm by a filter point of view
- Filter functions: theoretical properties
- Examples of filter function and corresponding algorithms with discussion
of the properties (consistency and computational complexity)
- Sparsity on the feature versus sparsity on the examples
- Lasso Algorithm and Elastic Net Algorithm.

Applications
- Filter functions for image classification
- Feature selection methods applied to face detection

## Potential target audience

It includes graduate students and researchers of the field as well as interested
students/researchers new to the field, with a background on linear algebra.
## Biography of the presenters

**Ernesto De Vito** received a Laura degree in Physics in 1991 and a PhD in
Mathematical Physics in 1995. In 1997 he has been researcher at Department
of Mathematics of University of Modena. Since 2006 he is researcher
at Department of Mathematics of University of Genova.

His main research interests focus on the theoretical properties of statistical
learning theory both in the supervised and unsupervised setting. Ernesto De
Vito has published a book and more than 30 papers in refereed journals and
in proceedings of international conferences on simmetry in quantum theory,
wavelet analysis, learning theory and inverse problems.

http://www.dima.unige.it/~devito

**Francesca Odone** received a Laurea degree in Information Science in 1997
and a PhD in Computer Science in 2002, both from the University of Genova,
Italy. She was with Heriot-Watt University, Edinburgh, UK, in 1997 as a
research associate, and in 1999 as a visiting PhD student. From 2002 to
2005 she has been researcher at the Italian Institute for Solid State Physics
(INFM). Since January 2006 she is assistant professor (ricercatore) at the
Department of Computing and Information Sciences of the University of
Genova.

Her main research interests are related to various aspects of computer vision
and statistical learning and, in particular, to the interconnections between
the two disciplines, including image and scene understanding and perception.
On these topics, Francesca Odone has published more than 30 papers in
refereed journals and in proceedings of international conferences, symposia,
and book chapters.
http://www.disi.unige.it/person/OdoneF