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…

Abstract:  Self-supervised learning is an increasingly popular approach for learning representations of data that can be used for downstream representation tasks. A practical advantage of self-supervised learning is that it can be used on unlabeled data. However, even when labels are available, self-supervised learning can be competitive with the more "traditional" approach of supervised learning.…

Abstract: Matrix completion is the study of recovering an underlying matrix from a sparse subset of noisy observations. Traditionally, it is assumed that the entries of the matrix are “missing completely atrandom” (MCAR), i.e., each entry is revealed at random, independent of everything else, with uniform probability. This is likely unrealistic due to the presence…