Related papers: Debiasing Continuous-time Nonlinear Autoregression…
Asymptotic equivalence results for nonparametric regression experiments have always assumed that the variances of the observations are known. In practice, however the variance of each observation is generally considered to be an unknown…
This work considers methods for imposing sparsity in Bayesian regression with applications in nonlinear system identification. We first review automatic relevance determination (ARD) and analytically demonstrate the need to additional…
Exponential stability and solution estimates are investigated for a delay system $$ \dot{x}(t) - A(t)\dot{x}(g(t))=\sum_{k=1}^m B_k(t)x(h_k(t)) $$ of a neutral type, where $A$ and $B_k$ are $n\times n$ bounded matrix functions, and $g, h_k$…
Temporal data such as time series can be viewed as discretized measurements of the underlying function. To build a generative model for such data we have to model the stochastic process that governs it. We propose a solution by defining the…
A novel adaptive identifier is developed for nonlinear time-delay systems composed of linear, Lipschitz and non-Lipschitz components. To begin with, an identifier is designed for uncertain systems with a priori known delay values, and then…
We consider the problem of continuous-time policy evaluation. This consists in learning through observations the value function associated with an uncontrolled continuous-time stochastic dynamic and a reward function. We propose two…
Ordinary differential equations (ODE's) are widespread models in physics, chemistry and biology. In particular, this mathematical formalism is used for describing the evolution of complex systems and it might consist of high-dimensional…
Non-linear dynamical systems represent a compact, flexible, and robust tool for reactive motion generation. The effectiveness of dynamical systems relies on their ability to accurately represent stable motions. Several approaches have been…
To address the difficult problem of multi-step ahead prediction of non-parametric autoregressions, we consider a forward bootstrap approach. Employing a local constant estimator, we can analyze a general type of non-parametric time series…
Uncertainty is unavoidable in modeling dynamical systems and it may be represented mathematically by differential inclusions. In the past, we proposed an algorithm to compute validated solutions of differential inclusions; here we provide…
This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable…
We introduce a new approach for comparing the predictive accuracy of two nested models that bypasses the difficulties caused by the degeneracy of the asymptotic variance of forecast error loss differentials used in the construction of…
Ordinary differential equation models are used to describe dynamic processes across biology. To perform likelihood-based parameter inference on these models, it is necessary to specify a statistical process representing the contribution of…
Our aim in this paper is to investigate the asymptotic behavior of solutions of the perturbed linear fractional differential system. We show that if the original linear autonomous system is asymptotically stable then under the action of…
This work proposes a general strategy for solving possibly nonlinear problems arising from implicit time discretizations as a sequence of explicit solutions. The resulting sequence may exhibit instabilities similar to those of the base…
Non-autonomous differential equations are crucial for modeling systems influenced by external signals, yet fitting these models to data becomes particularly challenging when the signals change abruptly. To address this problem, we propose a…
The initial value problem of an integrable system, such as the Nonlinear Schr\" odinger equation, is solved by subjecting the linear eigenvalue problem arising from its Lax pair to inverse scattering, and, thus, transforming it to a matrix…
We discuss parametric estimation of a degenerate diffusion system from time-discrete observations. The first component of the degenerate diffusion system has a parameter $\theta_1$ in a non-degenerate diffusion coefficient and a parameter…
In this article, we study the dynamics of a nonlinear system governed by an ordinary differential equation under the combined influence of fast periodic sampling with period $\delta$ and small jump noise of size $\varepsilon, 0<…
We propose a new asymptotic test to assess the stationarity of a time series' mean that is applicable in the presence of both heteroscedasticity and short-range dependence. Our test statistic is composed of Gini's mean difference of local…