Interpolation and learning with scale dependent kernels

Title: Interpolation and learning with scale dependent kernels

Abstract:  We study the learning properties of nonparametric ridge-less least squares. In particular, we consider the common case of estimators defined by scale dependent (Matern) kernels, and focus on the role scale and smoothness. These estimators interpolate the data and the scale can be shown to control their stability to noise and sampling.  Larger scales, corresponding to smoother functions, improve stability with respect to sampling. However, smaller scales, corresponding to more complex functions, improve stability to noise. We will discuss to which extent these results can explain the learning curves observed for large overparameterized models.  Our analysis combines, probabilistic results with analytic techniques from interpolation theory.

Bio: Lorenzo Rosasco is  an assistant professor at  the University of Genova, Italy. He is also affiliated with  the Massachusetts Institute of Technology(MIT), where is a visiting professor, and with  the Istituto Italiano di Tecnologia (IIT), where he is an external collaborator. He is leading the efforts to establish the Laboratory for Computational and Statistical Learning (LCSL), born from a  collaborative agreement between  IIT and MIT. He received his PhD from the University of Genova in 2006. Dr. Rosasco has developed and analyzed methods to learn from small as well as large samples of high dimensional data, using analytical and probabilistic tools, within a multidisciplinary approach drawing concepts and techniques primarily from computer science but also from statistics, engineering and applied mathematics.

A full schedule for Fall 2021 Stochastics and Statistics Seminars can be found here: https://stat.mit.edu/seminars/upcoming/