In this paper, the vector-valued regular functions are extended to the locally convex space. The residues theory of the functions in the locally convex space is achieved. Thereby the Cauchy theory and ...

Abstract: Kernel methods are among the most popular techniques in machine learning. From a regularization theory perspective, they provide a natural choice for the hypotheses space and the ...

The methods here apply to continuous functions that are finite compositions of simple "scientific calculator" operations, but may be nonsmooth. Operator overloading is used to automatically apply ...

Abstract: In this article, we study the generalization performance of multitask learning (MTL) by considering MTL as a learning process of vector-valued functions (VFs). We will answer two theoretical ...

Convex analysis plays a fundamental role in mathematics. In this paper, we extend the concept of convexity to vector-valued functions in Banach lattices. We introduce the notion of “order convexity” ...