Related papers: On Reproducing Kernel Banach Spaces: Generic Defin…
For many machine learning problem settings, particularly with structured inputs such as sequences or sets of objects, a distance measure between inputs can be specified more naturally than a feature representation. However, most standard…
We consider a general regularised interpolation problem for learning a parameter vector from data. The well known representer theorem says that under certain conditions on the regulariser there exists a solution in the linear span of the…
We propose a novel Bayesian methodology for inference in functional linear and logistic regression models based on the theory of reproducing kernel Hilbert spaces (RKHS's). We introduce general models that build upon the RKHS generated by…
The empirical success of deep convolutional networks on tasks involving high-dimensional data such as images or audio suggests that they can efficiently approximate certain functions that are well-suited for such tasks. In this paper, we…
Cauchy-de Branges spaces are Hilbert spaces of entire functions defined in terms of Cauchy transforms of discrete measures on the plane and generalizing the classical de Branges theory. We consider extensions of two important properties of…
This paper presents two models of neural-networks and their training applicable to neural networks of arbitrary width, depth and topology, assuming only finite-energy neural activations; and a novel representor theory for neural networks in…
Universal kernels, whose Reproducing Kernel Hilbert Space is dense in the space of continuous functions are of great practical and theoretical interest. In this paper, we introduce an explicit construction of universal kernels on compact…
The performance of adaptive estimators that employ embedding in reproducing kernel Hilbert spaces (RKHS) depends on the choice of the location of basis kernel centers. Parameter convergence and error approximation rates depend on where and…
Given a publicly available pool of machine learning models constructed for various tasks, when a user plans to build a model for her own machine learning application, is it possible to build upon models in the pool such that the previous…
Multiscale Models are known to be successful in uncovering and analyzing the structures in data at different resolutions. In the current work we propose a feature driven Reproducing Kernel Hilbert space (RKHS), for which the associated…
Reproducing kernel Hilbert spaces (RKHSs) are key elements of many non-parametric tools successfully used in signal processing, statistics, and machine learning. In this work, we aim to address three issues of the classical RKHS based…
We study reproducing kernels, and associated reproducing kernel Hilbert spaces (RKHSs) $\mathscr{H}$ over infinite, discrete and countable sets $V$. In this setting we analyze in detail the distributions of the corresponding Dirac…
This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…
This paper provides a self-contained exposition of coorbit spaces associated to integrable group representations and quasi-Banach function spaces, and at the same time extends and simplifies previous work. The main results provide an…
This paper ist concerned with recent progress in the context of coorbit space theory. Based on a square integrable group representation, the coorbit theory provides new families of associated smoothness spaces, where the smoothness of a…
This paper investigates the critical role of eigenalignments between the kernel matrix and learning targets in achieving robust generalization in learning problems. We establish a direct connection between generalization performance in…
This short technical report presents some learning theory results on vector-valued reproducing kernel Hilbert space (RKHS) regression, where the input space is allowed to be non-compact and the output space is a (possibly…
We give a complete characterization of Riesz bases of normalized reproducing kernels in the small Fock spaces $\mathcal{F}^2_{\varphi}$, the spaces of entire functions $f$ such that $f\mathrm{e}^{-\varphi} \in L^{2}(\mathbb{C})$, where…
Margin-based learning, exemplified by linear and kernel methods, is one of the few classical settings where generalization guarantees are independent of the number of parameters. This makes it a central case study in modern highly…
Applying machine learning to biological sequences - DNA, RNA and protein - has enormous potential to advance human health, environmental sustainability, and fundamental biological understanding. However, many existing machine learning…