This paper is an attempt to bridge the conceptual gaps between researchers working on the
two widely used approaches based on positive definite kernels: Bayesian learning or …

The population loss of trained deep neural networks often follows precise power-law scaling
relations with either the size of the training dataset or the number of parameters in the …

Flexible estimation of heterogeneous treatment effects lies at the heart of many statistical
applications, such as personalized medicine and optimal resource allocation. In this article …

Along with the rapid development and wide application of information technology, human
society has entered the information era. In this era, people live and work in cyberspace …

Teacher-student models provide a framework in which the typical-case performance of high-
dimensional supervised learning can be described in closed form. The assumptions of …

It has been hypothesized that quantum computers may lend themselves well to applications
in machine learning. In the present work, we analyze function classes defined via quantum …

We study the generalization properties of ridge regression with random features in the
statistical learning framework. We show for the first time that $ O (1/\sqrt {n}) $ learning …

We study Nyström type subsampling approaches to large scale kernel methods, and prove
learning bounds in the statistical learning setting, where random sampling and high …

We show that kernel-based quadrature rules for computing integrals can be seen as a
special case of random feature expansions for positive definite kernels, for a particular …

We study a decomposition-based scalable approach to kernel ridge regression, and show
that it achieves minimax optimal convergence rates under relatively mild conditions. The …