Related papers: Kernel-based models for system analysis
Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…
We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed…
We propose a new estimator for nonparametric binary choice models that does not impose a parametric structure on either the systematic function of covariates or the distribution of the error term. A key advantage of our approach is its…
Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…
Nonparametric feature selection in high-dimensional data is an important and challenging problem in statistics and machine learning fields. Most of the existing methods for feature selection focus on parametric or additive models which may…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
This paper presents a novel feature of the kernel-based system identification method. We prove that the regularized kernel-based approach for the estimation of a finite impulse response is equivalent to a robust least-squares problem with a…
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…
Estimating the dissipativity of nonlinear systems from empirical data is useful for the analysis and control of nonlinear systems, especially when an accurate model is unavailable. Based on a Koopman operator model of the nonlinear system…
This paper establishes a kernel-based framework for reconstructing data on manifolds, tailored to fit the dynamic-(d)MRI-data recovery problem. The proposed methodology exploits simple tangent-space geometries of manifolds in reproducing…
The linear quadratic regulator problem is central in optimal control and was investigated since the very beginning of control theory. Nevertheless, when it includes affine state constraints, it remains very challenging from the classical…
The basic idea of quantum computing is surprisingly similar to that of kernel methods in machine learning, namely to efficiently perform computations in an intractably large Hilbert space. In this paper we explore some theoretical…
Kernel-based nonparametric models have become very attractive for model-based control approaches for nonlinear systems. However, the selection of the kernel and its hyperparameters strongly influences the quality of the learned model.…
Signal processing tasks as fundamental as sampling, reconstruction, minimum mean-square error interpolation and prediction can be viewed under the prism of reproducing kernel Hilbert spaces. Endowing this vantage point with contemporary…
Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
Mean-field control problems have received continuous interest over the last decade. Despite being more intricate than in classical optimal control, the linear-quadratic setting can still be tackled through Riccati equations. Remarkably, we…
We present a data-driven method for computing approximate forward reachable sets using separating kernels in a reproducing kernel Hilbert space. We frame the problem as a support estimation problem, and learn a classifier of the support as…
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…
The kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the…