In this paper, we propose a distributed framework for reducing the dimensionality of high-dimensional, large-scale, heterogeneous matrix-variate time series data using a factor model. The data are first partitioned column-wise (or row-wise) and allocated to node servers, where each node estimates the row (or column) loading matrix via two-dimensional tensor PCA. These local estimates are then transmitted to a central server and aggregated, followed by a final PCA step to obtain the global row (or column) loading matrix estimator. Given the estimated loading matrices, the corresponding factor matrices are subsequently computed. Unlike existing distributed approaches, our framework preserves the latent matrix structure, thereby improving computational efficiency and enhancing information utilization. We also discuss row- and column-wise clustering procedures for settings in which the group memberships are unknown. Furthermore, we extend the analysis to unit-root nonstationary matrix-variate time series. Asymptotic properties of the proposed method are derived for the diverging dimension of the data in each computing unit and the sample size $T$. Simulation results assess the computational efficiency and estimation accuracy of the proposed framework, and real data applications further validate its predictive performance.

Extremely large-scale massive multiple-input multiple-output (XL-MIMO) is a key enabler for sixth-generation (6G) networks, offering massive spatial degrees of freedom. Despite these advantages, the coexistence of near-field and far-field effects in hybrid-field channels presents significant challenges for accurate estimation, where traditional methods often struggle to generalize effectively. In recent years, large language models (LLMs) have achieved impressive performance on downstream tasks via fine-tuning, aligning with the semantic communication shift toward task-oriented understanding over bit-level accuracy. Motivated by this, we propose Large Language Models for XL-MIMO Channel Estimation (LLM4XCE), a novel channel estimation framework that leverages the semantic modeling capabilities of large language models to recover essential spatial-channel representations for downstream tasks. The model integrates a carefully designed embedding module with Parallel Feature-Spatial Attention, enabling deep fusion of pilot features and spatial structures to construct a semantically rich representation for LLM input. By fine-tuning only the top two Transformer layers, our method effectively captures latent dependencies in the pilot data while ensuring high training efficiency. Extensive simulations demonstrate that LLM4XCE significantly outperforms existing state-of-the-art methods under hybrid-field conditions, achieving superior estimation accuracy and generalization performance.

Accurate real-time waypoints estimation for the UAV-based online Terrain Following during wildfire patrol missions is critical to ensuring flight safety and enabling wildfire detection. However, existing real-time filtering algorithms struggle to maintain accurate waypoints under measurement noise in nonlinear and time-varying systems, posing risks of flight instability and missed wildfire detections during UAV-based terrain following. To address this issue, a Residual Variance Matching Recursive Least Squares (RVM-RLS) filter, guided by a Residual Variance Matching Estimation (RVME) criterion, is proposed to adaptively estimate the real-time waypoints of nonlinear, time-varying UAV-based terrain following systems. The proposed method is validated using a UAV-based online terrain following system within a simulated terrain environment. Experimental results show that the RVM-RLS filter improves waypoints estimation accuracy by approximately 88$\%$ compared with benchmark algorithms across multiple evaluation metrics. These findings demonstrate both the methodological advances in real-time filtering and the practical potential of the RVM-RLS filter for UAV-based online wildfire patrol.

Accurate remote state estimation is a fundamental component of many autonomous and networked dynamical systems, where multiple decision-making agents interact and communicate over shared, bandwidth-constrained channels. These communication constraints introduce an additional layer of complexity, namely, the decision of when to communicate. This results in a fundamental trade-off between estimation accuracy and communication resource usage. Traditional extensions of classical estimation algorithms (e.g., the Kalman filter) treat the absence of communication as 'missing' information. However, silence itself can carry implicit information about the system's state, which, if properly interpreted, can enhance the estimation quality even in the absence of explicit communication. Leveraging this implicit structure, however, poses significant analytical challenges, even in relatively simple systems. In this paper, we propose CALM (Communication-Aware Learning and Monitoring), a novel learning-based framework that jointly addresses the dual challenges of communication scheduling and estimator design. Our approach entails learning not only when to communicate but also how to infer useful information from periods of communication silence. We perform comparative case studies on multiple benchmarks to demonstrate that CALM is able to decode the implicit coordination between the estimator and the scheduler to extract information from the instances of 'silence' and enhance the estimation accuracy.

Neural Information Processing Systems http://nips.cc/

Mutual Information (MI) is a fundamental metric for quantifying dependency between two random variables.

In many applications, observations are naturally grouped into different classes.

The success of machine learning methods heavily relies on having an appropriate representation for data at hand.

Stochastic state estimation methods for continuum robots (CRs) often struggle to balance accuracy and computational efficiency. While several recent works have explored sliding-window formulations for CRs, these methods are limited to simplified, discrete-time approximations and do not provide stochastic representations. In contrast, current stochastic filter methods must run at the speed of measurements, limiting their full potential. Recent works in continuous-time estimation techniques for CRs show a principled approach to addressing this runtime constraint, but are currently restricted to offline operation. In this work, we present a sliding-window filter (SWF) for continuous-time state estimation of CRs that improves upon the accuracy of a filter approach while enabling continuous-time methods to operate online, all while running at faster-than-real-time speeds. This represents the first stochastic SWF specifically designed for CRs, providing a promising direction for future research in this area.

High-dimensional regression often suffers from heavy-tailed noise and outliers, which can severely undermine the reliability of least-squares based methods. To improve robustness, we adopt a non-smooth Wilcoxon score based rank objective and incorporate structured group sparsity regularization, a natural generalization of the lasso, yielding a group lasso regularized rank regression method. By extending the tuning-free parameter selection scheme originally developed for the lasso, we introduce a data-driven, simulation-based tuning rule and further establish a finite-sample error bound for the resulting estimator. On the computational side, we develop a proximal augmented Lagrangian method for solving the associated optimization problem, which eliminates the singularity issues encountered in existing methods, thereby enabling efficient semismooth Newton updates for the subproblems. Extensive numerical experiments demonstrate the robustness and effectiveness of our proposed estimator against alternatives, and showcase the scalability of the algorithm across both simulated and real-data settings.