Related papers: Mathematical foundations of stable RKHSs

In this paper, we consider the problem of system identification when side-information is available on the steady-state (or DC) gain of the system. We formulate a general nonparametric identification method as an infinite-dimensional…

We generalize Jan Willems' behavioral approach to a class of discrete-time nonlinear systems in a vector-valued reproducing kernel Hilbert space (RKHS). Apart from linear time-invariant systems, this class covers nonlinear systems modeled…

Learning models of dynamical systems characterized by specific stability properties is of crucial importance in applications. Existing results mainly focus on linear systems or some limited classes of nonlinear systems and stability…

A reproducing kernel Hilbert space (RKHS) has four well-known easily derived properties. Since these properties are usually not emphasized as a simple means of gaining insight into RKHS structure, they are singled out and proved in this…

Weighted log-rank tests are arguably the most widely used tests by practitioners for the two-sample problem in the context of right-censored data. Many approaches have been considered to make weighted log-rank tests more robust against a…

Score-based kernelised Stein discrepancy (KSD) tests have emerged as a powerful tool for the goodness of fit tests, especially in high dimensions; however, the test performance may depend on the choice of kernels in an underlying…

This work reports a novel multi-frame Bundle Adjustment (BA) framework called RKHS-BA. It uses continuous landmark representations that encode RGB-D/LiDAR and semantic observations in a Reproducing Kernel Hilbert Space (RKHS). With a…

A different route to identification of time-invariant linear systems has been recently proposed which does not require committing to a specific parametric model structure. Impulse responses are described in a nonparametric Bayesian…

Let $(X,\mu)$ be a strictly-positive Borel measure space. We show that the modes of convergence in a reproducing kernel Hilbert (RKHS) space, pointwise, weak and strong are all equivalents. From this we describe some important consequences…

Ridgeless regression has garnered attention among researchers, particularly in light of the ``Benign Overfitting'' phenomenon, where models interpolating noisy samples demonstrate robust generalization. However, kernel ridgeless regression…

Consider the problem: given the data pair $(\mathbf{x}, \mathbf{y})$ drawn from a population with $f_*(x) = \mathbf{E}[\mathbf{y} | \mathbf{x} = x]$, specify a neural network model and run gradient flow on the weights over time until…

Supervised learning in reproducing kernel Hilbert space (RKHS) and vector-valued RKHS (vvRKHS) has been investigated for more than 30 years. In this paper, we provide a new twist to this rich literature by generalizing supervised learning…

Hierarchical data pervades diverse machine learning applications, including natural language processing, computer vision, and social network analysis. Hyperbolic space, characterized by its negative curvature, has demonstrated strong…

We develop a stochastic approximation framework for learning nonlinear operators between infinite-dimensional spaces utilizing general Mercer operator-valued kernels. Our framework encompasses two key classes: (i) compact kernels, which…

There exists a plethora of parametric models for positive definite kernels, and their use is ubiquitous in disciplines as diverse as statistics, machine learning, numerical analysis, and approximation theory. Usually, the kernel parameters…

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…

Learning in the reproducing kernel Hilbert space (RKHS) such as the support vector machine has been recognized as a promising technique. It continues to be highly effective and competitive in numerous prediction tasks, particularly in…

In this paper, we consider the coefficient-based regularized distribution regression which aims to regress from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS), where the regularization is put on…

Compositional data, such as human gut microbiomes, consist of non-negative variables whose only the relative values to other variables are available. Analyzing compositional data such as human gut microbiomes needs a careful treatment of…

In this paper, we present a unified approach to function approximation in reproducing kernel Hilbert spaces (RKHS) that establishes a previously unrecognized optimality property for several well-known function approximation techniques, such…