Related papers: Regularized system identification using orthonorma…
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…
In Optimal Recovery, the task of learning a function from observational data is tackled deterministically by adopting a worst-case perspective tied to an explicit model assumption made on the functions to be learned. Working in the…
This paper develops a frequentist solution to the functional calibration problem, where the value of a calibration parameter in a computer model is allowed to vary with the value of control variables in the physical system. The need of…
The reproducing kernel Hilbert space (RKHS) embedding method is a recently introduced estimation approach that seeks to identify the unknown or uncertain function in the governing equations of a nonlinear set of ordinary differential…
We introduce a renormalization procedure which allows us to study in a unified and concise way different properties of the irrational rotations on the unit circle $\beta \mapsto \set{\alpha+\beta}$, $\alpha \in \R\setminus \Q$. In…
Regularized system identification is the major advance in system identification in the last decade. Although many promising results have been achieved, it is far from complete and there are still many key problems to be solved. One of them…
A structure-preserving kernel ridge regression method is presented that allows the recovery of nonlinear Hamiltonian functions out of datasets made of noisy observations of Hamiltonian vector fields. The method proposes a closed-form…
We consider conditions on a given system $\mathcal{F}$ of vectors in Hilbert space $\mathcal{H}$, forming a frame, which turn $\mathcal{H}$ into a reproducing kernel Hilbert space. It is assumed that the vectors in $\mathcal{F}$ are…
Modern computational models in supervised machine learning are often highly parameterized universal approximators. As such, the value of the parameters is unimportant, and only the out of sample performance is considered. On the other hand…
Many problems arising in control require the determination of a mathematical model of the application. This has often to be performed starting from input-output data, leading to a task known as system identification in the engineering…
Models that contain intersample behavior are important for control design of systems with slow-rate outputs. The aim of this paper is to develop a system identification technique for fast-rate models of systems where only slow-rate output…
Spectral approximation and variational inducing learning for the Gaussian process are two popular methods to reduce computational complexity. However, in previous research, those methods always tend to adopt the orthonormal basis functions,…
In the absence of explicit regularization, Kernel "Ridgeless" Regression with nonlinear kernels has the potential to fit the training data perfectly. It has been observed empirically, however, that such interpolated solutions can still…
Estimating the innovation probability density is an important issue in any regression analysis. This paper focuses on functional autoregressive models. A residual-based kernel estimator is proposed for the innovation density. Asymptotic…
An ill-posed inverse problem of autoconvolution type is investigated. This inverse problem occurs in nonlinear optics in the context of ultrashort laser pulse characterization. The novelty of the mathematical model consists in a physically…
This paper focuses on the use of the theory of Reproducing Kernel Hilbert Spaces in the statistical analysis of replicated point processes. We show that spatial point processes can be observed as random variables in a Reproducing Kernel…
We study the estimation and prediction of functional autoregressive~(FAR) processes, a statistical tool for modeling functional time series data. Due to the infinite-dimensional nature of FAR processes, the existing literature addresses its…
We explore the issues of identification for nonlinear Impulse Response Functions in nonlinear dynamic models and discuss the settings in which the problem can be mitigated. In particular, we introduce the nonlinear autoregressive…
We study recursive regularized learning algorithms in the reproducing kernel Hilbert space (RKHS) with non-stationary online data streams. We introduce the concept of random Tikhonov regularization path and decompose the tracking error of…
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…