English
Related papers

Related papers: Identifiability and Asymptotics in Learning Homoge…

200 papers

This paper studies the problem of state estimation for linear time-invariant descriptor systems in their most general form. The estimator is a system of ordinary differential equations (ODEs). We introduce the notion of partial causal…

Optimization and Control · Mathematics 2024-05-14 Juhi Jaiswal , Thomas Berger , Nutan K. Tomar

We present a new finite-time analysis of the estimation error of the Ordinary Least Squares (OLS) estimator for stable linear time-invariant systems. We characterize the number of observed samples (the length of the observed trajectory)…

Statistics Theory · Mathematics 2020-03-27 Yassir Jedra , Alexandre Proutiere

We study the problem of identification of linear dynamical system from a single trajectory, via excitations of isotropic Gaussian. In stark contrast with previously reported results, Ordinary Least Squares (OLS) estimator for even…

Statistics Theory · Mathematics 2023-05-23 Muhammad Abdullah Naeem , Miroslav Pajic

We study how to identify a class of continuous-time nonlinear systems defined by an ordinary differential equation affine in the unknown parameter. We define a notion of asymptotic consistency as $(n, h) \to (\infty, 0)$, and we achieve it…

Systems and Control · Electrical Eng. & Systems 2025-04-09 Simon Kuang , Xinfan Lin

We prove the support recovery for a general class of linear and nonlinear evolutionary partial differential equation (PDE) identification from a single noisy trajectory using $\ell_1$ regularized Pseudo-Least Squares model~($\ell_1$-PsLS).…

Numerical Analysis · Mathematics 2021-03-15 Yuchen He , Namjoon Suh , Xiaoming Huo , Sungha Kang , Yajun Mei

Identifying dynamical systems from experimental data is a notably difficult task. Prior knowledge generally helps, but the extent of this knowledge varies with the application, and customized models are often needed. Neural ordinary…

Systems and Control · Electrical Eng. & Systems 2023-01-13 Mona Buisson-Fenet , Valery Morgenthaler , Sebastian Trimpe , Florent Di Meglio

In engineering, accurately modeling nonlinear dynamic systems from data contaminated by noise is both essential and complex. Established Sequential Monte Carlo (SMC) methods, used for the Bayesian identification of these systems, facilitate…

Machine Learning · Statistics 2024-04-25 Joe D. Longbottom , Max D. Champneys , Timothy J. Rogers

Nonlinear ordinary differential equations (ODEs) are powerful tools for modeling real-world dynamical systems. However, propagating initial state uncertainty through nonlinear dynamics, especially when the ODE is unknown and learned from…

Systems and Control · Electrical Eng. & Systems 2026-02-06 Peter Amorese , Morteza Lahijanian

The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…

Machine Learning · Computer Science 2025-07-30 Rahul Golder , M. M. Faruque Hasan

We analyze a simple prefiltered variation of the least squares estimator for the problem of estimation with biased, semi-parametric noise, an error model studied more broadly in causal statistics and active learning. We prove an oracle…

Machine Learning · Computer Science 2019-02-05 Max Simchowitz , Ross Boczar , Benjamin Recht

The promising increase of Electric Vehicles (EVs) in our society poses a challenging problem on the impact assessment of their charging/discharging to power distribution grids. This paper addresses the assessment problem in a framework of…

Systems and Control · Electrical Eng. & Systems 2022-01-04 Haruki Tadano , Yoshihiko Susuki , Atsushi Ishigame

We consider the problem of learning the dynamics of autonomous linear systems (i.e., systems that are not affected by external control inputs) from observations of multiple trajectories of those systems, with finite sample guarantees.…

Systems and Control · Electrical Eng. & Systems 2022-09-27 Lei Xin , George Chiu , Shreyas Sundaram

This tutorial serves as an introduction to recently developed non-asymptotic methods in the theory of -- mainly linear -- system identification. We emphasize tools we deem particularly useful for a range of problems in this domain, such as…

Systems and Control · Electrical Eng. & Systems 2024-06-18 Ingvar Ziemann , Anastasios Tsiamis , Bruce Lee , Yassir Jedra , Nikolai Matni , George J. Pappas

We study the asymptotic properties of Lasso+mLS and Lasso+Ridge under the sparse high-dimensional linear regression model: Lasso selecting predictors and then modified Least Squares (mLS) or Ridge estimating their coefficients. First, we…

Statistics Theory · Mathematics 2014-01-14 Hanzhong Liu , Bin Yu

The dynamics of systems biological processes are usually modeled by a system of ordinary differential equations (ODEs) with many unknown parameters that need to be inferred from noisy and sparse measurements. Here, we introduce…

Quantitative Methods · Quantitative Biology 2022-02-04 Mitchell Daneker , Zhen Zhang , George Em Karniadakis , Lu Lu

This paper proposes a new algorithm for linear system identification from noisy measurements. The proposed algorithm balances a data fidelity term with a norm induced by the set of single pole filters. We pose a convex optimization problem…

Optimization and Control · Mathematics 2012-04-04 Parikshit Shah , Badri Narayan Bhaskar , Gongguo Tang , Benjamin Recht

We consider parameter estimation of ordinary differential equation (ODE) models from noisy observations. For this problem, one conventional approach is to fit numerical solutions (e.g., Euler, Runge--Kutta) of ODEs to data. However, such a…

Methodology · Statistics 2021-09-01 Takeru Matsuda , Yuto Miyatake

The paper studies distributed static parameter (vector) estimation in sensor networks with nonlinear observation models and noisy inter-sensor communication. It introduces \emph{separably estimable} observation models that generalize the…

Multiagent Systems · Computer Science 2012-05-21 Soummya Kar , Jose M. F. Moura , Kavita Ramanan

Misspecified models often provide useful information about the true data generating distribution. For example, if $y$ is a non-linear function of $x$ the least squares estimator $\hat{\beta}$ is an estimate of $\beta$, the slope of the best…

Methodology · Statistics 2017-05-17 James P. Long

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…

Statistics Theory · Mathematics 2008-12-22 Nicolas J-B. Brunel