NB: Postponed, new date tba. Talk: Learning adaptive and multi-scale representation and reconstruction operators by Dr. Lorenzo Rosasco
Dr. Lorenzo has unfortunately been caught in flight delays, and because of this we will have to postpone the event. A new date for this talk will be announced shortly. Our apologies for any inconvenience caused.
Dr. Rosasco leads the Laboratory for Computational and Statistical Learning, a joint machine learning laboratory between the Istituto Italiano di Tecnologia (IIT) and the Massachusetts Institute of Technology (MIT). He is associate professor at the University of Genova and a visiting professor at the MIT. He received his PhD from the University of Genova in 2006 and has been visiting student at the Toyota Technological Institute at Chicago and at the Center for Biological and Computational Learning at MIT. He held a research scientist position at MIT between 2006 and 2009, working together with Tomaso Poggio.
His research focuses on studying theory and algorithms for machine learning. Dr. Rosasco has developed and analyzed methods to learn from small as well as large samples of high dimensional data. He is known for his foundational work in machine learning as well as the development of sound machine learning algorithms, based on spectral methods and convex optimization.
We consider the problem of learning representation/reconstruction operators from data sampled from a fixed unknown probability distribution. We describe and analyze procedures based on piecewise constant and linear approximation approaches. In particular, we analyze piecewise constant approximations, by comparing K-Means with a new multi-scale vector quantization algorithm that can be seen as a geometric analogue of decision trees. Further, we consider piecewise linear approximations comparing K-Flats and Geometric Multi-resolution Analysis proposed by Maggioni and colleagues. While our approach is general, a special case of interest is the one where the data distribution is supported on a low dimensional manifold embedded in a high-dimensional space. In this view, the considered approaches can be considered as a form of manifold learning. Also, the obtained representation/reconstruction operators can be contrasted to those obtained by classic dictionary learning approaches such as sparse coding. These latter connections will be discussed in details.
In collaboration with G. Canas, E. Cecini and E. De Vito.