Related papers: Nonlinear Probabilistic Forecast Reconciliation
We study how the degree of nonlinearity in the input data affects the optimal design of reservoir computers, focusing on how closely the model's nonlinearity should align with that of the data. By reducing minimal RCs to a single tunable…
Calibration ensures that probabilistic forecasts meaningfully capture uncertainty by requiring that predicted probabilities align with empirical frequencies. However, many existing calibration methods are specialized for post-hoc…
Model-based filtering is often carried out while subject to an imperfect model, as learning partially-observable stochastic systems remains a challenge. Recent work on Bayesian inference found that tempering the likelihood or full posterior…
Koopman-based methods leverage a nonlinear lifting to enable linear regression techniques. Consequently, data generation, learning and prediction is performed through the lens of this lifting, giving rise to a nonlinear manifold that is…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
Many filters have been proposed in recent decades for the nonlinear state estimation problem. The linearization-based extended Kalman filter (EKF) is widely applied to nonlinear industrial systems. As EKF is limited in accuracy and…
We develop a predictive inference procedure that combines conformal prediction (CP) with unconditional quantile regression (QR) -- a commonly used tool in econometrics that involves regressing the recentered influence function (RIF) of the…
We demonstrate that the forecasting combination puzzle is a consequence of the methodology commonly used to produce forecast combinations. By the combination puzzle, we refer to the empirical finding that predictions formed by combining…
The ensemble Kalman filter (EnKF) (Evensen, 2009) has proven effective in quantifying uncertainty in a number of challenging dynamic, state estimation, or data assimilation, problems such as weather forecasting and ocean modeling. In these…
We are interested in ensemble methods to solve multi-objective optimization problems. An ensemble Kalman method is proposed to solve a formulation of the nonlinear problem using a weighted function approach. An analysis of the mean field…
Reliably characterizing the full conditional distribution of a multivariate response variable given a set of covariates is crucial for trustworthy decision-making. However, misspecified or miscalibrated multivariate models may yield a poor…
This paper develops a sequential-linearization feedback optimization framework for driving nonlinear dynamical systems to an optimal steady state. A fundamental challenge in feedback optimization is the requirement of accurate first-order…
Achieving highly accurate dynamic or simulator models that are close to the real robot can facilitate model-based controls (e.g., model predictive control or linear-quadradic regulators), model-based trajectory planning (e.g., trajectory…
Traditional filtering algorithms for state estimation -- such as classical Kalman filtering, unscented Kalman filtering, and particle filters - show performance degradation when applied to nonlinear systems whose uncertainty follows…
We consider the problem of state estimation in dynamical systems and propose a different mechanism for handling unmodeled system uncertainties. Instead of injecting random process noise, we assign different weights to measurements so that…
We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system's process and measurement uncertainty.…
Quantifying forecast uncertainty is a key aspect of state-of-the-art numerical weather prediction and data assimilation systems. Ensemble-based data assimilation systems incorporate state-dependent uncertainty quantification based on…
Perturbation-based explanations are widely utilized to enhance the transparency of modern machine-learning models. However, their reliability is often compromised by the unknown model behavior under the specific perturbations used. This…
This expository paper discusses Bayesian decision analysis perspectives on problems of constrained forecasting. Foundational and pedagogic discussion contrasts decision analytic approaches with the traditional, but typically inappropriate,…
Recently, the prediction-correction method has been developed to solve nonlinear convex optimization problems. However, its convergence rate is often poor since large regularization parameters are set to ensure convergence conditions. In…