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Optimal control problems naturally arise in many scientific applications where one wishes to steer a dynamical system from a certain initial state $\mathbf{x}_0$ to a desired target state $\mathbf{x}^*$ in finite time $T$. Recent advances…

Machine Learning · Computer Science 2022-09-20 Lucas Böttcher , Thomas Asikis

We consider the problem of parameter estimation for a system of ordinary differential equations from noisy observations on a solution of the system. In case the system is nonlinear, as it typically is in practical applications, an analytic…

Statistics Theory · Mathematics 2012-07-27 Shota Gugushvili , Chris A. J. Klaassen

Ordinary differential equations (ODEs) are commonly used to model dynamic behavior of a system. Because many parameters are unknown and have to be estimated from the observed data, there is growing interest in statistics to develop…

Statistics Theory · Mathematics 2010-01-13 Xin Qi , Hongyu Zhao

Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex probability distributions. While such models have achieved…

Statistics Theory · Mathematics 2023-09-06 Youssef Marzouk , Zhi Ren , Sven Wang , Jakob Zech

Regularization is a popular technique in machine learning for model estimation and avoiding overfitting. Prior studies have found that modern ordered regularization can be more effective in handling highly correlated, high-dimensional data…

Machine Learning · Computer Science 2019-11-01 Mahammad Humayoo , Xueqi Cheng

Debiased inference for high-dimensional regression models has received substantial recent attention to ensure regularized estimators have valid inference. All existing methods focus on achieving Neyman orthogonality through explicitly…

Methodology · Statistics 2025-12-16 Yi Wang , Yuhao Deng , Yu Gu , Yuanjia Wang , Donglin Zeng

In real-world problems, uncertainties (e.g., errors in the measurement, precision errors) often lead to poor performance of numerical algorithms when not explicitly taken into account. This is also the case for control problems, where…

Optimization and Control · Mathematics 2020-12-18 Carlos Ignacio Hernández Castellanos , Sina Ober-Blöbaum , Sebastian Peitz

We consider the problem of estimating parameters of stochastic differential equations (SDEs) with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally…

Methodology · Statistics 2015-09-09 Libo Sun , Chihoon Lee , Jennifer A. Hoeting

Nonlinear optimal control is vital for numerous applications but remains challenging for unknown systems due to the difficulties in accurately modelling dynamics and handling computational demands, particularly in high-dimensional settings.…

Systems and Control · Electrical Eng. & Systems 2024-12-03 Zhexuan Zeng , Ruikun Zhou , Yiming Meng , Jun Liu

Mathematical modelling is a widely used approach to understand and interpret clinical trial data. This modelling typically involves fitting mechanistic mathematical models to data from individual trial participants. Despite the widespread…

Pharmacokinetic modeling using ordinary differential equations (ODEs) has an important role in dose optimization studies, where dosing must balance sustained therapeutic efficacy with the risk of adverse side effects. Such ODE models…

Methodology · Statistics 2025-06-30 Yuxuan Zhao , Samuel W. K. Wong

Interactive fixed effects are routinely controlled for in linear panel models. While an analogous fixed effects (FE) estimator for nonlinear models has been available in the literature (Chen, Fernandez-Val and Weidner, 2021), it sees much…

Econometrics · Economics 2026-03-25 Andrei Zeleneev , Weisheng Zhang

In a recent article, we presented a framework to control nonlinear partial differential equations (PDEs) by means of Koopman operator based reduced models and concepts from switched systems. The main idea was to transform a control system…

Optimization and Control · Mathematics 2019-05-15 Sebastian Peitz

Applications of structural equation models (SEMs) are often restricted to linear associations between variables. Maximum likelihood (ML) estimation in non-linear models may be complex and require numerical integration. Furthermore, ML…

Methodology · Statistics 2019-03-15 Klaus Kähler Holst , Esben Budtz-Jørgensen

We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…

Systems and Control · Electrical Eng. & Systems 2024-07-16 Simon Kuang , Xinfan Lin

Ordinary and stochastic differential equations (ODEs and SDEs) are widely used to model continuous-time processes across various scientific fields. While ODEs offer interpretability and simplicity, SDEs incorporate randomness, providing…

Methodology · Statistics 2025-05-20 Qingchuan Sun , Susanne Ditlevsen

Linear mixed models with large imbalanced crossed random effects structures pose severe computational problems for maximum likelihood estimation and for Bayesian analysis. The costs can grow as fast as $N^{3/2}$ when there are N…

Methodology · Statistics 2017-05-30 K. Gao , A. B. Owen

In this work, we consider an optimal control problem subject to a nonlinear PDE constraint and apply it to the regularized $p$-Laplace equation. To this end, a reduced unconstrained optimization problem in terms of the control variable is…

Numerical Analysis · Mathematics 2020-06-29 Bernhard Endtmayer , Ulrich Langer , Ira Neitzel , Winnifried Wollner , Thomas Wick

This paper investigates new ways of estimating and identifying causal, noncausal, and mixed causal-noncausal autoregressive models driven by a non-Gaussian error sequence. We do not assume any parametric distribution function for the…

Econometrics · Economics 2022-11-28 Alain Hecq , Daniel Velasquez-Gaviria

Nonlinear mixed effects models have received a great deal of attention in the statistical literature in recent years because of their flexibility in handling longitudinal studies, including human immunodeficiency virus viral dynamics,…

Methodology · Statistics 2021-09-28 Fernanda L. Schumacher , Dipak K. Dey , Victor H. Lachos