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$C^*$-algebra-valued kernels could pave the way for the next generation of kernel machines. To further our fundamental understanding of learning with $C^*$-algebraic kernels, we propose a new class of positive definite kernels based on the…

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…

Motivated by the inherent heterogeneity observed in many functional or imaging datasets, this paper focuses on subgroup learning in functional or image responses. While change-plane analysis has demonstrated empirical success in practice,…

In this paper we investigate and compare different gradient algorithms designed for the domain expression of the shape derivative. Our main focus is to examine the usefulness of kernel reproducing Hilbert spaces for PDE constrained shape…

We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves…

In this paper, we study the asymptotic properties of regularized least squares with indefinite kernels in reproducing kernel Krein spaces (RKKS). By introducing a bounded hyper-sphere constraint to such non-convex regularized risk…

Accurate energy demand forecasting is crucial for sustainable and resilient energy development. To meet the Net Zero Representative Concentration Pathways (RCP) $4.5$ scenario in the DACH countries, increased renewable energy production,…

We construct a space of vector fields that are normal to differentiable curves in the plane. Its basis functions are defined via saddle point variational problems in reproducing kernel Hilbert spaces (RKHSs). First, we study the properties…

In nonparametric classification and regression problems, regularized kernel methods, in particular support vector machines, attract much attention in theoretical and in applied statistics. In an abstract sense, regularized kernel methods…

In this paper we combine the theory of reproducing kernel Hilbert spaces with the field of collocation methods to solve boundary value problems with special emphasis on reproducing property of kernels. From the reproducing property of…

We develop a comprehensive framework for spatio-temporal prediction of time-varying vector fields using operator-valued reproducing kernel Hilbert spaces (OV RKHS). By integrating Sobolev regularity with Koopman operator theory, we…

In supervised learning, the output variable to be predicted is often represented as a function, such as a spectrum or probability distribution. Despite its importance, functional output regression remains relatively unexplored. In this…

Face Recognition (FR) has been the interest to several researchers over the past few decades due to its passive nature of biometric authentication. Despite high accuracy achieved by face recognition algorithms under controlled conditions,…

Reliable uncertainty quantification for causal effects is crucial in various applications, but remains difficult in nonparametric models, particularly for continuous treatments. We introduce IMPspec, a Gaussian process (GP) framework for…

The aim of this study is to present a good modernistic strategy for solving some well-known classes of Lane-Emden type singular differential equations. The proposed approach is based on the reproducing kernel Hilbert space (RKHS) and…

We consider a class of infinite-dimensional singular stochastic control problems. These can be thought of as spatial monotone follower problems and find applications in spatial models of production and climate transition. Let…

We present a unified theoretical and computational framework for constructing reproducing kernels tailored to transport equations and adapted to Koopman eigenfunctions of nonlinear dynamical systems. These eigenfunctions satisfy a…

The reproducing kernel Hilbert space (RKHS) embedding of distributions offers a general and flexible framework for testing problems in arbitrary domains and has attracted considerable amount of attention in recent years. To gain insights…

Support Vector Machines (SVMs) rely heavily on the choice of the kernel function to map data into high-dimensional feature spaces. While the Gaussian Radial Basis Function (RBF) is the industry standard, its exponential decay makes it…

It is often said that control and estimation problems are in duality. Recently, in (Aubin-Frankowski,2021), we found new reproducing kernels in Linear-Quadratic optimal control by focusing on the Hilbert space of controlled trajectories,…