Related papers: The interplay between system identification and ma…
Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation…
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…
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…
This paper generalizes regularized regression problems in a hyper-reproducing kernel Hilbert space (hyper-RKHS), illustrates its utility for kernel learning and out-of-sample extensions, and proves asymptotic convergence results for the…
Optimal experimental design seeks to determine the most informative allocation of experiments to infer an unknown statistical quantity. In this work, we investigate the optimal design of experiments for {\em estimation of linear functionals…
Regularized empirical risk minimization using kernels and their corresponding reproducing kernel Hilbert spaces (RKHSs) plays an important role in machine learning. However, the actually used kernel often depends on one or on a few…
Kernel methods are one of the cornerstones of learning-based control, modern system identification, surrogate modelling, and related fields. A key advantage of this class of learning and function approximation methods is the availability of…
Motivated by the growing interest in representation learning approaches that uncover the latent structure of high-dimensional data, this work proposes new algorithms for reconstruction-based manifold learning within Reproducing-Kernel…
We propose a new decentralized robust kernel-based learning algorithm within the framework of reproducing kernel Hilbert spaces (RKHSs) by utilizing a networked system that can be represented as a connected graph. The robust loss function…
The success of deep convolutional architectures is often attributed in part to their ability to learn multiscale and invariant representations of natural signals. However, a precise study of these properties and how they affect learning…
System identification, also known as learning forward models, transfer functions, system dynamics, etc., has a long tradition both in science and engineering in different fields. Particularly, it is a recurring theme in Reinforcement…
Learning convolution kernels in operators from data arises in numerous applications and represents an ill-posed inverse problem of broad interest. With scant prior information, kernel methods offer a natural nonparametric approach with…
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…
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…
Deep learning is a topic of considerable current interest. The availability of massive data collections and powerful software resources has led to an impressive amount of results in many application areas that reveal essential but hidden…
We propose a new point of view for regularizing deep neural networks by using the norm of a reproducing kernel Hilbert space (RKHS). Even though this norm cannot be computed, it admits upper and lower approximations leading to various…
This paper investigates a general regularization framework for unsupervised domain adaptation in vector-valued regression under the covariate shift assumption, utilizing vector-valued reproducing kernel Hilbert spaces (vRKHS). Covariate…
In a general context of positive definite kernels $k$, we develop tools and algorithms for sampling in reproducing kernel Hilbert space $\mathscr{H}$ (RKHS). With reference to these RKHSs, our results allow inference from samples; more…
Learning by interaction is the key to skill acquisition for most living organisms, which is formally called Reinforcement Learning (RL). RL is efficient in finding optimal policies for endowing complex systems with sophisticated behavior.…