Related papers: A Behavioral Framework for Data-Driven Modeling of…

We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to…

This work presents a purely data-driven, wavelet-based framework for modal identification and reduced-order modeling of mechanical systems with assumed linear dynamics characterized by closely spaced modes with classical or non-classical…

A Hilbert space embedding of a distribution---in short, a kernel mean embedding---has recently emerged as a powerful tool for machine learning and inference. The basic idea behind this framework is to map distributions into a reproducing…

This paper develops a novel mathematical framework for collaborative learning by means of geometrically inspired kernel machines which includes statements on the bounds of generalisation and approximation errors, and sample complexity. For…

We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that…

This paper introduces a solution to the problem of selecting dynamically (online) the ``optimal'' p-norm to combat outliers in linear adaptive filtering without any knowledge on the probability density function of the outliers. The proposed…

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…

Theoretical studies have proven that the Hilbert space has remarkable performance in many fields of applications. Frames in tensor product of Hilbert spaces were introduced to generalize the inner product to high-order tensors. However,…

We develop a mathematical framework to address a broad class of metric and preference learning problems within a Hilbert space. We obtain a novel representer theorem for the simultaneous task of metric and preference learning. Our key…

Reproducing kernel Hilbert spaces (RKHSs) are special Hilbert spaces in one-to-one correspondence with positive definite maps called kernels. They are widely employed in machine learning to reconstruct unknown functions from sparse and…

In this paper, we present a data-driven representation for linear parameter-varying (LPV) systems, which can be used for direct data-driven analysis and control of such systems. Specifically, we use the behavioral approach to develop a…

These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…

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…

Continuous-time stochastic processes underlie many natural and engineered systems. In healthcare, autonomous driving, and industrial control, direct interaction with the environment is often unsafe or impractical, motivating offline…

Kernel mean embeddings, a widely used technique in machine learning, map probability distributions to elements of a reproducing kernel Hilbert space (RKHS). For supervised learning problems, where input-output pairs are observed, the…

Representations that can compactly and effectively capture the temporal evolution of semantic content are important to computer vision and machine learning algorithms that operate on multi-variate time-series data. We investigate such…

This paper introduces a new framework for quantifying predictive uncertainty for both data and models that relies on projecting the data into a Gaussian reproducing kernel Hilbert space (RKHS) and transforming the data probability density…

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…

While Koopman operator lifts a nonlinear system into an infinite-dimensional function space and represents it as a linear dynamics, its definition is restricted to autonomous systems, i.e., does not incorporate inputs or disturbances. To…

In this article, we develop a kernel-based framework for constructing dynamic, pathdependent trading strategies under a mean-variance optimisation criterion. Building on the theoretical results of (Muca Cirone and Salvi, 2025), we…