Related papers: Error bounds for numerical differentiation using k…
In this paper we investigate the approximation properties of kernel interpolants on manifolds. The kernels we consider will be obtained by the restriction of positive definite kernels on $\R^d$, such as radial basis functions (RBFs), to a…
Depth measures are powerful tools for defining level sets in emerging, non--standard, and complex random objects such as high-dimensional multivariate data, functional data, and random graphs. Despite their favorable theoretical properties,…
In this article we study the field of Hilbertian metrics and positive definit (pd) kernels on probability measures, they have a real interest in kernel methods. Firstly we will make a study based on the Alpha-Beta-divergence to have a…
We prove H\"older regularity for a general class of parabolic integro-differential equations, which (strictly) includes many previous results. We present a proof which avoids the use of a convex envelop as well as give a new covering…
Spectral enhancement -- which aims to undo spectral broadening -- leads to integral equations which are ill-posed and require special regularisation techniques for their solution. Even when an optimal regularisation technique is used,…
Edge detection is widely and fundamental feature used in various algorithms in computer vision to determine the edges in an image. The edge detection algorithm is used to determine the edges in an image which are further used by various…
Sliced Stein discrepancy (SSD) and its kernelized variants have demonstrated promising successes in goodness-of-fit tests and model learning in high dimensions. Despite their theoretical elegance, their empirical performance depends…
Kernel techniques are among the most popular and flexible approaches in data science allowing to represent probability measures without loss of information under mild conditions. The resulting mapping called mean embedding gives rise to a…
This article provides a practical introduction to kernel discrepancies, focusing on the Maximum Mean Discrepancy (MMD), the Hilbert-Schmidt Independence Criterion (HSIC), and the Kernel Stein Discrepancy (KSD). Various estimators for these…
We study kernel functions, and associated reproducing kernel Hilbert spaces $\mathscr{H}$ over infinite, discrete and countable sets $V$. Numerical analysis builds discrete models (e.g., finite element) for the purpose of finding…
Model selection when designing deep learning systems for specific use-cases can be a challenging task as many options exist and it can be difficult to know the trade-off between them. Therefore, we investigate a number of state of the art…
In this paper, we correct an upper bound, presented in~\cite{hs-11}, on the generalisation error of classifiers learned through multiple kernel learning. The bound in~\cite{hs-11} uses Rademacher complexity and has an\emph{additive}…
We derive concentration inequalities for the supremum norm of the difference between a kernel density estimator (KDE) and its point-wise expectation that hold uniformly over the selection of the bandwidth and under weaker conditions on the…
This paper presents a new perspective on the identification at infinity for the intercept of the sample selection model as identification at the boundary via a transformation of the selection index. This perspective suggests generalizations…
Quantum kernel methods have emerged as a promising approach for leveraging high-dimensional feature spaces in machine learning, particularly in domains where classical kernel methods face scalability limitations. In this work, we present…
The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…
In deep learning models, learning more with less data is becoming more important. This paper explores how neural networks with normalized Radial Basis Function (RBF) kernels can be trained to achieve better sample efficiency. Moreover, we…
Recent works have introduced methods to estimate segmentation performance without ground truth, relying solely on neural network softmax outputs. These techniques hold potential for intuitive output quality control. However, such…
We present estimators for smooth Hilbert-valued parameters, where smoothness is characterized by a pathwise differentiability condition. When the parameter space is a reproducing kernel Hilbert space, we provide a means to obtain efficient,…
In a previous paper it was shown that a machine learning regression problem can be solved within the framework of random function theory, with the optimal kernel analytically derived from symmetry and indifference principles and coinciding…