Related papers: Towards a representer theorem for identification o…
In this paper we provide a finite-sample and an infinite-sample representer theorem for the concatenation of (linear combinations of) kernel functions of reproducing kernel Hilbert spaces. These results serve as mathematical foundation for…
System identification is a key enabling component for the implementation of quantum technologies, including quantum control. In this paper, we consider the class of passive linear input-output systems, and investigate several basic…
This manuscript presents an algorithm for obtaining an approximation of a nonlinear high order control affine dynamical system. Controlled trajectories of the system are leveraged as the central unit of information via embedding them in…
This paper introduces a computational framework to identify nonlinear input-output operators that fit a set of system trajectories while satisfying incremental integral quadratic constraints. The data fitting algorithm is thus regularized…
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…
We consider a general regularised interpolation problem for learning a parameter vector from data. The well known representer theorem says that under certain conditions on the regulariser there exists a solution in the linear span of the…
In this work, the problem of learning Koopman operator of a discrete-time autonomous system is considered. The learning problem is formulated as a constrained regularized empirical loss minimization in the infinite-dimensional space of…
The necessary and sufficient conditions for existence of a generalized representer theorem are presented for learning Hilbert space-valued functions. Representer theorems involving explicit basis functions and Reproducing Kernels are a…
Passive systems are characterized by their inability to generate energy internally, providing a powerful tool for modeling physical phenomena. Additionally, algebraically encoding passivity in the system description can be advantageous. For…
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…
In this work, we consider the problem of learning nonlinear operators that correspond to discrete-time nonlinear dynamical systems with inputs. Given an initial state and a finite input trajectory, such operators yield a finite output…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
The notion of reproducing kernel Hilbert space (RKHS) has emerged in system identification during the past decade. In the resulting framework, the impulse response estimation problem is formulated as a regularized optimization defined on an…
The representer theorem is a cornerstone of kernel methods, which aim to estimate latent functions in reproducing kernel Hilbert spaces (RKHSs) in a nonparametric manner. Its significance lies in converting inherently infinite-dimensional…
In this paper, we propose a definition of phase for a class of stable nonlinear systems called semi-sectorial systems, from an input-output perspective. The definition involves the Hilbert transform as a critical instrument to complexify…
This work presents a nonparametric framework for dissipativity learning in reproducing kernel Hilbert spaces, which enables data-driven certification of stability and performance properties for unknown nonlinear systems without requiring an…
We consider a general regularised interpolation problem for learning a parameter vector from data. The well known representer theorem says that under certain conditions on the regulariser there exists a solution in the linear span of the…
We introduce a complex-valued counterpart of the representer theorem in machine learning. We study several learning and minimization problems in reproducing kernel Hilbert spaces (RKHSs), with the aim of identifying appropriate input-output…
Learning models of dynamical systems characterized by specific stability properties is of crucial importance in applications. Existing results mainly focus on linear systems or some limited classes of nonlinear systems and stability…
Based on direct integrals, a framework allowing to integrate a parametrised family of reproducing kernels with respect to some measure on the parameter space is developed. By pointwise integration, one obtains again a reproducing kernel…