Related papers: On Power-law Kernels, corresponding Reproducing Ke…

We study distributed learning with the least squares regularization scheme in a reproducing kernel Hilbert space (RKHS). By a divide-and-conquer approach, the algorithm partitions a data set into disjoint data subsets, applies the least…

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…

In this paper we consider the problems of supervised classification and regression in the case where attributes and labels are functions: a data is represented by a set of functions, and the label is also a function. We focus on the use of…

Obtaining reliable, adaptive confidence sets for prediction functions (hypotheses) is a central challenge in sequential decision-making tasks, such as bandits and model-based reinforcement learning. These confidence sets typically rely on…

We present a novel kernel over the space of probability measures based on the dual formulation of optimal regularized transport. We propose an Hilbertian embedding of the space of probabilities using their Sinkhorn potentials, which are…

We give two new global and algorithmic constructions of the reproducing kernel Hilbert space associated to a positive definite kernel. We further present ageneral positive definite kernel setting using bilinear forms, and we provide new…

Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…

Recent applications of kernel methods in machine learning have seen a renewed interest in the Laplacian kernel, due to its stability to the bandwidth hyperparameter in comparison to the Gaussian kernel, as well as its expressivity being…

We present several generative and predictive algorithms based on the RKHS (reproducing kernel Hilbert spaces) methodology, which, most importantly, are scale up efficiently with large datasets or high-dimensional data. It is well recognized…

This paper addresses the problem of regression to reconstruct functions, which are observed with superimposed errors at random locations. We address the problem in reproducing kernel Hilbert spaces. It is demonstrated that the estimator,…

Kernel-based methods offer a powerful and flexible mathematical framework for addressing histopolation problems. In histopolation, the available input data does not consist of pointwise function samples but of averages taken over intervals…

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,…

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…

In this paper, the framework of kernel machines with two layers is introduced, generalizing classical kernel methods. The new learning methodology provide a formal connection between computational architectures with multiple layers and the…

In many applications of machine learning, a large number of variables are considered. Motivated by machine learning of interacting particle systems, we consider the situation when the number of input variables goes to infinity. First, we…

This work constructs a hypothesis test for detecting whether an data-generating function $h: R^p \rightarrow R$ belongs to a specific reproducing kernel Hilbert space $\mathcal{H}_0$ , where the structure of $\mathcal{H}_0$ is only…

This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random…

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…

While deep neural networks (DNNs) and Gaussian Processes (GPs) are both popularly utilized to solve problems in reinforcement learning, both approaches feature undesirable drawbacks for challenging problems. DNNs learn complex nonlinear…

The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are rarely used and considered in numerical analysis due to their…