A Hilbert space embedding of a distribution—in short, a kernel mean embedding—has
recently emerged as a powerful tool for machine learning and statistical inference. The basic …

The fundamental mathematical tools needed to understand machine learning include linear
algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability …

Recently, a new line of works has emerged to understand and improve self-attention in
Transformers by treating it as a kernel machine. However, existing works apply the methods …

We develop a variational framework to understand the properties of the functions learned by
neural networks fit to data. We propose and study a family of continuous-domain linear …

In a lot of real-world data mining and machine learning applications, data are provided by
multiple providers and each maintains private records of different feature sets about …

Characterizing the function spaces corresponding to neural networks can provide a way to
understand their properties. In this paper we discuss how the theory of reproducing kernel …

The past decade has seen increasing interest in applying Deep Learning (DL) to
Computational Science and Engineering (CSE). Driven by impressive results in applications …

Regularization addresses the ill-posedness of the training problem in machine learning or
the reconstruction of a signal from a limited number of measurements. The method is …

The aim of this expository paper is to explain to graduate students and beginning
researchers in the field of mathematics, statistics and engineering the fundamental concept …

In each iteration, the projection methods require computing at least one projection onto the
closed convex set. However, projections onto a general closed convex set are not easily …