Related papers: The interplay between system identification and ma…

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…

Motivated by applications to the study of stochastic processes, we introduce a new analysis of positive definite kernels $K$, their reproducing kernel Hilbert spaces (RKHS), and an associated family of feature spaces that may be chosen in…

Random Forests and Gradient Boosting are among the most effective algorithms for supervised learning on tabular data. Both belong to the class of tree-based ensemble methods, where predictions are obtained by aggregating many randomized…

Safe autonomous driving critically depends on how well the ego-vehicle can predict the trajectories of neighboring vehicles. To this end, several trajectory prediction algorithms have been presented in the existing literature. Many of these…

In statistical learning, identifying underlying structures of true target functions based on observed data plays a crucial role to facilitate subsequent modeling and analysis. Unlike most of those existing methods that focus on some…

Nonlinearities in piezoelectric systems can arise from internal factors such as nonlinear constitutive laws or external factors like realizations of boundary conditions. It can be difficult or even impossible to derive detailed models from…

Traditionally, kernel methods rely on the representer theorem which states that the solution to a learning problem is obtained as a linear combination of the data mapped into the reproducing kernel Hilbert space (RKHS). While elegant from…

Studying the reliability of complex systems using machine learning techniques involves facing a series of technical and practical challenges, ranging from the intrinsic nature of the system and data to the difficulties in modeling and…

Nonlocal operators with integral kernels have become a popular tool for designing solution maps between function spaces, due to their efficiency in representing long-range dependence and the attractive feature of being resolution-invariant.…

A model for the prediction of functional time series is introduced, where observations are assumed to be continuous random functions. We model the dependence of the data with a nonstandard autoregressive structure, motivated in terms of the…

We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of…

This paper considers different facets of the interplay between reproducing kernel Hilbert spaces (RKHS) and stable analysis/synthesis processes: First, we analyze the structure of the reproducing kernel of a RKHS using frames and…

Algorithmic verification of realistic systems to satisfy safety and other temporal requirements has suffered from poor scalability of the employed formal approaches. To design systems with rigorous guarantees, many approaches still rely on…

Metric learning from a set of triplet comparisons in the form of "Do you think item h is more similar to item i or item j?", indicating similarity and differences between items, plays a key role in various applications including image…

Motivated by the need of processing functional-valued data, or more general, operatorvalued data, we introduce the notion of the operator reproducing kernel Hilbert space (ORKHS). This space admits a unique operator reproducing kernel which…

We develop novel learning rates for conditional mean embeddings by applying the theory of interpolation for reproducing kernel Hilbert spaces (RKHS). We derive explicit, adaptive convergence rates for the sample estimator under the…

Is it possible to understand the intricacies of a dynamical system not solely from its input/output pattern, but also by observing the behavior of other systems within the same class? This central question drives the study presented in this…

This paper addresses the covariate shift problem in the context of nonparametric regression within reproducing kernel Hilbert spaces (RKHSs). Covariate shift arises in supervised learning when the input distributions of the training and…

In this paper we investigate the connection between supervised learning and linear inverse problems. We first show that a linear inverse problem can be view as a function approximation problem in a reproducing kernel Hilbert space (RKHS)…

Dynamical models identified from data are frequently employed in control system design. However, decoupling system identification from controller synthesis can result in situations where no suitable controller exists after a model has been…