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Model-based reinforcement learning has the potential to be more sample efficient than model-free approaches. However, existing model-based methods are vulnerable to model bias, which leads to poor generalization and asymptotic performance…

Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning…

Quantifying uncertainty is important for actionable predictions in real-world applications. A crucial part of predictive uncertainty quantification is the estimation of epistemic uncertainty, which is defined as an integral of the product…

This paper studies a data-driven predictive control for a class of control-affine systems which is subject to uncertainty. With the accessibility to finite sample measurements of the uncertain variables, we aim to find controls which are…

Many applications of machine learning methods involve an iterative protocol in which data are collected, a model is trained, and then outputs of that model are used to choose what data to consider next. For example, one data-driven approach…

Traditional statistical estimation, or statistical inference in general, is static, in the sense that the estimate of the quantity of interest does not change the future evolution of the quantity. In some sequential estimation problems…

Modern data-driven applications that make real-time decisions increasingly depend on advanced sensors which use pre-stored calibration data. In such applications, accurate characterization of sensor output uncertainty is important for…

This paper studies identification and estimation of a class of dynamic models in which the decision maker (DM) is uncertain about the data-generating process. The DM surrounds a benchmark model that he or she fears is misspecified by a set…

Scientific imaging problems are often severely ill-posed, and hence have significant intrinsic uncertainty. Accurately quantifying the uncertainty in the solutions to such problems is therefore critical for the rigorous interpretation of…

This work develops a measurement-driven and model-based formal verification approach, applicable to systems with partly unknown dynamics. We provide a principled method, grounded on reachability analysis and on Bayesian inference, to…

This book chapter introduces the principles and practical applications of uncertainty quantification in machine learning. It explains how to identify and distinguish between different types of uncertainty and presents methods for…

Machine learning (ML) and deep learning models are extensively used for parameter optimization and regression problems. However, not all inverse problems in ML are ``identifiable,'' indicating that model parameters may not be uniquely…

Bayesian inference is a popular approach to calibrating uncertainties, but it can underpredict such uncertainties when model misspecification is present, impacting its reliability to inform decision making. Recently, the statistics and…

Quantifying and reducing uncertainty in Earth system model parameterizations is essential to improving their reliability in decision-making. Forward uncertainty propagation is used to derive parameter sensitivity but requires physically…

Modern weather forecast models perform uncertainty quantification using ensemble prediction systems, which collect nonparametric statistics based on multiple perturbed simulations. To provide accurate estimation, dozens of such…

The reliability assessment of a machine learning model's prediction is an important quantity for the deployment in safety critical applications. Not only can it be used to detect novel sceneries, either as out-of-distribution or anomaly…

Uncertainty quantification is essential for scientific analysis, as it allows for the evaluation and interpretation of variability and reliability in complex systems and datasets. In their original form, multivariate statistical regression…

This paper presents a new robust data-driven predictive control scheme for unknown linear time-invariant systems by using input-state-output or input-output data based on whether the state is measurable. To remove the need for the…

While several methods for predicting uncertainty on deep networks have been recently proposed, they do not readily translate to large and complex datasets. In this paper we utilize a simplified form of the Mixture Density Networks (MDNs) to…

Obtaining accurate estimates of machine learning model uncertainties on newly predicted data is essential for understanding the accuracy of the model and whether its predictions can be trusted. A common approach to such uncertainty…