Related papers: A Generalized Representer Theorem for Hilbert Spac…

Gaussian Radial Basis Function (RBF) Kernels are the most-often-employed kernels in artificial intelligence and machine learning routines for providing optimally-best results in contrast to their respective counter-parts. However, a little…

We consider positive semidefinite kernels valued in the $*$-algebra of adjointable operators on a VE-space (Vector Euclidean space) and that are invariant under actions of $*$-semigroups. A rather general dilation theorem is stated and…

The standard approach for dealing with the ill-posedness of the training problem in machine learning and/or the reconstruction of a signal from a limited number of measurements is regularization. The method is applicable whenever the…

Most machine learning theory and practice is concerned with learning a single task. In this thesis it is argued that in general there is insufficient information in a single task for a learner to generalise well and that what is required…

In respect of b-linear functional, Riesz representation theorem in n-Hilbert space have been proved. We define b-sesquilinear functional in n-Hilbert space and establish the polarization identities. A generalized form of the Schwarz…

This paper investigates a general regularization framework for unsupervised domain adaptation in vector-valued regression under the covariate shift assumption, utilizing vector-valued reproducing kernel Hilbert spaces (vRKHS). Covariate…

Reproducing kernel Hilbert spaces provide a foundational framework for kernel-based learning, where regularization and interpolation problems admit finite-dimensional solutions through classical representer theorems. Many modern learning…

In this work, we consider the problem of learning nonlinear operators that correspond to discrete-time nonlinear dynamical systems with inputs. Given an initial state and a finite input trajectory, such operators yield a finite output…

A major problem in system identification is the incorporation of prior knowledge about the physical properties of the given system, such as stability, positivity and passivity. In this paper, we present first steps towards tackling this…

A lot of the recent success in natural language processing (NLP) has been driven by distributed vector representations of words trained on large amounts of text in an unsupervised manner. These representations are typically used as general…

We present a Representer Theorem result for a large class of weak formulation problems. We provide examples of applications of our formulation both in traditional machine learning and numerical methods as well as in new and emerging…

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 inverse problems with total variation-like regularization in…

A general theory of reproducing kernels and reproducing kernel Hilbert spaces on a right quaternionic Hilbert space is presented. Positive operator valued measures and their connection to a class of generalized quaternionic coherent states…

Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However,…

Stochastic models share many characteristics with generic parametric models. In some ways they can be regarded as a special case. But for stochastic models there is a notion of weak distribution or generalised random variable, and the same…

In many instances one has to deal with parametric models. Such models in vector spaces are connected to a linear map. The reproducing kernel Hilbert space and affine- / linear- representations in terms of tensor products are directly…

We discuss a general method to learn data representations from multiple tasks. We provide a justification for this method in both settings of multitask learning and learning-to-learn. The method is illustrated in detail in the special case…

Of theories for why large-scale machine learning models generalize despite being vastly overparameterized, which of their assumptions are needed to capture the qualitative phenomena of generalization in the real world? On one hand, we find…

Lurie's representability theorem gives necessary and sufficient conditions for a functor to be an almost finitely presented derived geometric stack. We establish several variants of Lurie's theorem, making the hypotheses easier to verify…

In this work, we establish a representation theorem for multivariable totally symmetric functions: a multisymmetric continuous function must be the composition of a continuous function and a set of generators of the multisymmetric…