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Modern autonomous systems are purposed for many challenging scenarios, where agents will face unexpected events and complicated tasks. The presence of disturbance noise with control command and unknown inputs can negatively impact robot…

We consider the Kalman-filtering problem with multiple sensors which are connected through a communication network. If all measurements are delivered to one place called fusion center and processed together, we call the process centralized…

The ensemble Kalman filter (EnKF) is a reliable data assimilation tool for high-dimensional meteorological problems. On the other hand, the EnKF can be interpreted as a particle filter, and particle filters collapse in high-dimensional…

A sequential estimator based on the Ensemble Kalman Filter for Data Assimilation of fluid flows is presented in this research work. The main feature of this estimator is that the Kalman filter update, which relies on the determination of…

The Kalman filter (KF) is a widely-used algorithm for tracking dynamic systems that are captured by state space (SS) models. The need to fully describe a SS model limits its applicability under complex settings, e.g., when tracking based on…

We forecast a single time series using a high-dimensional set of predictors. When these predictors share common underlying dynamics, an approximate latent factor model provides a powerful characterization of their co-movements Bai(2003).…

The application of neural networks in modeling dynamic systems has become prominent due to their ability to estimate complex nonlinear functions. Despite their effectiveness, neural networks face challenges in long-term predictions, where…

We study sequential prediction of real-valued, arbitrary and unknown sequences under the squared error loss as well as the best parametric predictor out of a large, continuous class of predictors. Inspired by recent results from…

We provide a framework for computing the exact worst-case performance of any algorithm belonging to a broad class of oracle-based first-order methods for composite convex optimization, including those performing explicit, projected,…

Prediction of spatio-temporal chaotic systems is important in various fields, such as Numerical Weather Prediction (NWP). While data assimilation methods have been applied in NWP, machine learning techniques, such as Reservoir Computing…

We examine the problem of time delay estimation, or temporal calibration, in the context of multisensor data fusion. Differences in processing intervals and other factors typically lead to a relative delay between measurement updates from…

Online learning is a model of machine learning where the learner is trained on sequential feedback. We investigate worst-case error for the online learning of real functions that have certain smoothness constraints. Suppose that…

Federated learning (FL) has gain growing interests for its capability of learning from distributed data sources collectively without the need of accessing the raw data samples across different sources. So far FL research has mostly focused…

The research examined predicting short-duration traffic flow counts with the Kalman filtering technique (KFT), a computational filtering method. Short-term traffic prediction is an important tool for operation in traffic management and…

We present a practical implementation of the ensemble Kalman (EnKF) filter based on an iterative Sherman-Morrison formula. The new direct method exploits the special structure of the ensemble-estimated error covariance matrices in order to…

This paper is concerned with sequential filtering based stochastic optimization (FSO) approaches that leverage a probabilistic perspective to implement the incremental proximity method (IPM). The present FSO methods are derived based on the…

We present a theory-first framework that interprets inference-time adaptation in large language models (LLMs) as online Bayesian state estimation. Rather than modeling rapid adaptation as implicit optimization or meta-learning, we formulate…

The ensemble Kalman filter (EnKF) has become a standard methodology for state estimation in high-dimensional systems, yet its various stochastic and deterministic formulations often appear conceptually disconnected. In this paper, a unified…

We present an efficient and practical (polynomial time) algorithm for online prediction in unknown and partially observed linear dynamical systems (LDS) under stochastic noise. When the system parameters are known, the optimal linear…

State-of-the-art ensemble Kalman filtering (EnKF) algorithms require incorporating localization techniques to cope with the rank deficiency and the inherited spurious correlations in their error covariance matrices. Localization techniques…