Related papers: Linear Model Regression on Time-series Data: Non-a…

Data-driven control of discrete-time and continuous-time systems is of tremendous research interest. In this paper, we explore data-driven optimal control of continuous-time linear systems using input-output data. Based on a density result,…

Empirical modelling often aims for the simplest model consistent with the data. A new technique is presented which quantifies the consistency of the model dynamics as a function of location in state space. As is well-known, traditional…

Time series forecasting is a fundamental tool with wide ranging applications, yet recent debates question whether complex nonlinear architectures truly outperform simple linear models. Prior claims of dominance of the linear model often…

Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…

Data-driven models are subject to model errors due to limited and noisy training data. Key to the application of such models in safety-critical domains is the quantification of their model error. Gaussian processes provide such a measure…

We present a stochastic constrained output-feedback data-driven predictive control scheme for linear time-invariant systems subject to bounded additive disturbances. The approach uses data-driven predictors based on an extension of Willems'…

Mathematical modeling of production systems is the foundation of all model-based approaches for production system analysis, design, improvement, and control. To construct such a model for the stochastic process of the production system more…

Time series forecasting has become a critical task due to its high practicality in real-world applications such as traffic, energy consumption, economics and finance, and disease analysis. Recent deep-learning-based approaches have shown…

We study the quadratic prediction error method -- i.e., nonlinear least squares -- for a class of time-varying parametric predictor models satisfying a certain identifiability condition. While this method is known to asymptotically achieve…

We introduce a generic class of dynamic nonlinear heterogeneous parameter models that incorporate individual and time fixed effects in both the intercept and slope. These models are subject to the incidental parameter problem, in that the…

Using a dynamical model to make predictions about a system has many sources of error. These can include errors in how the model was initialised but also errors in the dynamics of the model itself. For many applications in data assimilation,…

This work derives a residual-based a posteriori error estimator for reduced models learned with non-intrusive model reduction from data of high-dimensional systems governed by linear parabolic partial differential equations with control…

We study online prediction of bounded stationary ergodic processes. To do so, we consider the setting of prediction of individual sequences and build a deterministic regression tree that performs asymptotically as well as the best…

Linear dynamical systems are a fundamental and powerful parametric model class. However, identifying the parameters of a linear dynamical system is a venerable task, permitting provably efficient solutions only in special cases. This work…

The goal of this paper is to develop methodology for the systematic analysis of asymptotic statistical properties of data driven DRO formulations based on their corresponding non-DRO counterparts. We illustrate our approach in various…

This book is meant to provide an introduction to linear models and the theories behind them. Our goal is to give a rigorous introduction to the readers with prior exposure to ordinary least squares. In machine learning, the output is…

Linear Response theory aims to predict how added forcing alters the statistical properties of an unforced system. These kinds of questions have been studied predominantly for autonomous dynamical systems, yet many systems in the physical,…

One of the primary challenges of system identification is determining how much data is necessary to adequately fit a model. Non-asymptotic characterizations of the performance of system identification methods provide this knowledge. Such…

Modern applications have made ubiquitous high-dimensional data, especially time-dependent data, with more and more complicated structures, and it also has become more frequent to encounter the scenario of hierarchical relationships among…

Nonparametric regression problems with qualitative constraints such as monotonicity or convexity are ubiquitous in applications. For example, in predicting the yield of a factory in terms of the number of labor hours, the monotonicity of…