In order to represent the semantics and concepts better, the ontology, as an efficient model,
has penetrated into all research areas of the computer science and information technology …

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 …

Recently, there has been emerging interest in constructing reproducing kernel Banach
spaces (RKBS) for applied and theoretical purposes such as machine learning, sampling …

We characterize the solution of a broad class of convex optimization problems that address
the reconstruction of a function from a finite number of linear measurements. The underlying …

This article studies constructions of reproducing kernel Banach spaces (RKBSs) which may
be viewed as a generalization of reproducing kernel Hilbert spaces (RKHSs). A key point is …

The representer theorem plays an outsized role in a large class of learning problems. It
provides a means to reduce infinite dimensional optimization problems to tractable finite …

Targeting at sparse learning, we construct Banach spaces B of functions on an input space
X with the following properties:(1) B possesses an ℓ1 norm in the sense that B is …

Robustness and stability of image-reconstruction algorithms have recently come under
scrutiny. Their importance to medical imaging cannot be overstated. We review the known …

Despite their ubiquity in core AI fields like natural language processing, the mechanics of
deep attention-based neural networks like the Transformer model are not fully understood …