Inferring time-varying graph structures from high-dimensional nodal observations is a fundamental problem arising in neuroscience, finance, climatology, and beyond. Two intrinsic challenges govern this problem: maintaining the temporal coherence of the latent graph across successive observation windows, and respecting the intrinsic Riemannian geometry of the symmetric positive definite manifold on which precision matrices naturally reside, a curved space whose geodesic structure departs fundamentally from that of the ambient Euclidean space. In this paper we propose dynamic estimation on the Grassmann manifold with a factor model (Degfm), a novel algorithm that jointly addresses both challenges. We model the time-varying precision matrix sequence as a low-rank-plus-diagonal structure governed by a latent elliptical graph factor model, which drastically reduces the effective parameter count and enables reliable estimation in the challenging small-sample regime. Temporal coherence is enforced through a Riemannian geodesic penalty defined on the Grassmann manifold, ensuring that the estimated graph trajectory is smooth with respect to the intrinsic geometry rather than the ambient Euclidean space. To solve the resulting non-convex optimization problem over Grassmann-manifold-valued sequences subject to the LRaD constraint, we derive an efficient Riemannian gradient descent algorithm that respects the manifold structure at every iterate and rigorously establish its convergence to a stationary point. Extensive experiments on both synthetic benchmarks and real-world datasets demonstrate that Degfm consistently outperforms state-of-the-art baselines across all evaluation metrics, confirming the practical effectiveness of the proposed framework.

Nonconvex and nonsmooth composite optimization problems with linear constraints have gained significant attention in practical applications. This paper proposes a hybrid stochastic Alternating Direction Method of Multipliers (ADMM) leveraging a novel hybrid estimator to solve such problems with expectation or finite-sum objective functions. Compared to existing double-loop stochastic ADMMs, our method features simpler updates enabled by a single-loop, single-sample framework, while avoiding the need for checkpoint selection. Under mild conditions, we analyze the explicit relationships between key parameters using refined Lyapunov functions and rigorously establish the sublinear convergence. To the best of our knowledge, our work is the first single-loop stochastic ADMM for solving both expectation and finite-sum problems while matching the best-known oracle complexity bound comparable to state-of-the-art double-loop stochastic ADMMs. Numerical experiments on several different nonconvex minimization tasks demonstrate the superior performance of the proposed method.

Jointly inferring latent node states and unknown network topology in nonlinear graphical dynamical systems is a fundamental yet largely unsolved problem, where the mutual entanglement of continuous states and discrete structure renders accurate recovery of either quantity critically dependent on the other. We propose Koopman-GKFA (Koopman Group-sparse Kalman Filter–ADMM), a unified framework that lifts nonlinear network dynamics into an approximately linear system via Koopman operator embedding with a separable node-wise dictionary, enabling optimal linear filtering for state estimation and provably convergent convex optimization for topology inference. Three theoretical contributions underpin the framework: (i) a structural homomorphism lemma proving that, under a separable-dictionary condition, block sparsity of the lifted coupling operator is isomorphic to the graph topology, providing the rigorous foundation for group-sparse regularization; (ii) a block-structured group-sparse ADMM topology subproblem with certified linear convergence, extended by an exponential forgetting factor to track time-varying topologies; and (iii) a three-term certified mean-squared error bound that decomposes total estimation error into Koopman truncation, observation noise, and topology residual components, with monotone consistency established as the dictionary dimension grows. Extensive experiments on synthetic benchmarks (Kuramoto oscillators, Hill-kinetics gene-regulatory networks) and real-world datasets (NGSIM US-101, DREAM4) demonstrate that Koopman-GKFA consistently outperforms EKF-, UKF-, and particle-filter-based joint estimators in both state estimation and topology recovery, while exhibiting polynomial computational scaling and strong robustness in high-dimensional nonlinear settings.

In aerospace target tracking and other physical sensing systems, decentralized sensor networks infer motion states from heterogeneous noisy observations, where nonlinear dynamics and sensing geometries make robust estimation challenging. Achieving optimal fusion becomes particularly difficult when measurement noises exhibit unknown cross-correlations. Conventional model-based fusion strategies (e.g., Covariance Intersection) guarantee consistency under such uncertainties but are conservative and often degrade fusion accuracy. To address this limitation, this paper proposes DIFNet, a decentralized information filtering neural network. DIFNet preserves the interpretable structure of the distributed extended information filter (DEIF) and uses lightweight Recurrent Neural Networks (RNNs) at sensor nodes to map local information vectors and matrices into fusion weights, thereby learning unknown noise-dependence effects from data. To ensure parameter consistency and communication efficiency, a Leader Gradient Descent (LGD) training strategy is incorporated. Extensive experiments on linear and nonlinear state-space models show that DIFNet significantly outperforms conservative baselines. Specifically, DIFNet reduces tracking Root Mean Square Error (RMSE) by approximately 25–30% compared with Covariance Intersection (CI) and approaches the theoretical exact-model upper bound, highlighting its potential for practical deployment in complex nonlinear physical sensing environments.

Set membership filter is a promising method to provide a bounding estimation containing the true state for dynamic systems with unknown but bounded noises. In this paper, we investigate the state bounding estimation problem of nonlinear dynamic systems with nonlinear state inequality constraints. Three types of ellipsoidal state bounding estimation methods are proposed by incorporating nonlinear state inequality constraints into nonlinear set membership filter. They are called model reduction method, system measurement method, and constraint dimension reduction method, respectively. We analyze the computation complexity of the three methods, which decrease in the order of model reduction method, system measurement method, and constraint dimension reduction method. Due to the nonlinearity of the dynamic systems, all the three methods are approximation algorithms and the state estimation accuracy cannot be analyzed explicitly. Consequently, a typical illustrative numerical experiment is conducted to compare the performance of the three methods. The results show that the accuracy increases in the order of the model reduction method, the constraint dimension reduction method, and the system measurement method.

Directional motion towards a specified destination is a common occurrence in physical processes and human societal activities. Utilizing this prior information can significantly improve the control and predictive performance of system models. This paper primarily focuses on reconstructing linear dynamic system models based on destination constraints in the set-valued framework. We treat destination constraints as inherent information in the state evolution process and employ convex optimization techniques to construct a coherent and robust state model. This refined model effectively captures the impact of destination constraints on the state evolution at each time step. Furthermore, we design an optimal weight matrix for the reconstructed model to ensure smoother and more natural trajectories of state evolution. We also analyze the theoretical guarantee of optimality for this weight matrix and the properties of the reconstructed model. Finally, simulation experiments verify that the reconstructed model has significant advantages over the unconstrained and unoptimized weighted models and constrains the evolution of state trajectories with different starting and ending points.

Reconstructing complex network topologies from data is a fundamental challenge in cybernetics and graph signal processing, with applications in neuroscience, sensor, and social networks. In practice, target-domain samples are scarce while heterogeneous source-domain data are abundant. Fusing these sources is challenging: Euclidean averaging works for homogeneous sources but degrades sharply as inter-source divergence grows, collapsing distinct geometries into an inflated, biased consensus. We exploit the Wasserstein metric's distribution-preserving properties to counter heterogeneity while preserving each source's intrinsic geometry. We propose MS-WDRO, a multi-source Wasserstein distributionally robust graph learning framework that fuses heterogeneous sources via their weighted Wasserstein barycenter, a geometrically principled nominal distribution, then builds an ambiguity ball around it to hedge residual uncertainty. Minimizing worst-case risk yields a tractable regularized Laplacian estimator solved efficiently via a provably convergent ADMM scheme. We establish non-asymptotic guarantees: a finite-sample concentration bound for the empirical barycenter, a pooling bias lower bound proving naive aggregation is suboptimal, and an out-of-sample excess risk bound decaying at a parametric rate with only logarithmic dependence on source count. To calibrate hyperparameters governing robustness, sparsity, and source fusion, we unroll the solver into a differentiable architecture trained end-to-end, achieving data-adaptive calibration beyond cross-validation while retaining interpretability. Experiments on synthetic benchmarks and the multi-site ABIDE I neuroimaging dataset show MS-WDRO consistently outperforms seven baselines in graph recovery, sample efficiency, and downstream diagnostic utility, with the largest gains in the sample-scarce regime.

In real-world physical processes, motion scenarios with specific guidance or objectives are common, often involving uncertainties in both arrival time and destination. These dynamic models typically exhibit nonlinear characteristics, posing significant challenges in modeling and filtering. This paper addresses these challenges by introducing a novel approach. First, destination information is incorporated into the unconstrained nonlinear dynamic evolution process through an optimization-based method, resulting in a destination-constrained nonlinear dynamic system model applicable to both known and uncertain arrival times. Second, the theoretical properties of the reconstructed model are analyzed. Third, a comprehensive study of nonlinear filtering algorithms is conducted across four scenarios, considering uncertainties in both destination and arrival time. Notably, one of the proposed algorithms enables the joint estimation of both variables. Finally, simulation results validate the effectiveness and stability of the proposed model and algorithms.

Surface electromyography (sEMG) signals are widely used for motor intention estimation due to their non-invasive nature. However, real-world sEMG data often exhibit long-tailed distributions, and existing multi-expert fusion methods suffer from high prediction variance. To address these issues, we propose an Uncertainty-Aware Gaussian Cloud Dynamic Learning (UGDL) framework. It unifies uncertainty estimation, decision boundary calibration, and multi-expert fusion. First, we develop Extremum-Constrained Uncertainty Estimation (ECUE) to mitigate the exponential growth of evidence. ECUE employs an extremum-constrained mapping based on convex function properties in Dempster–Shafer Theory, enabling bounded and discriminative uncertainty estimation. Next, we introduce Uncertainty-aware Cloud Learning (UCL), which injects Gaussian perturbations into logits. The perturbation magnitude is dynamically determined by uncertainty, allowing adaptive feature expansion and refined decision boundary calibration. Finally, we propose Uncertainty-aware Best Linear Unbiased Estimation (UBLUE) for expert fusion. It models predictions as Gaussian distributions and uses uncertainty as standard deviation, yielding an optimal unbiased estimator under mild assumptions. Experiments on long-tailed datasets derived from NinaPro DB5 show that the proposed method consistently outperforms existing approaches, effectively alleviating class imbalance and reducing prediction variance.

This paper tackles the challenging problem of jointly inferring time-varying network topologies and imputing missing data from partially observed graph signals. We propose a unified non-convex optimization framework to simultaneously recover a sequence of graph Laplacian matrices while reconstructing the unobserved signal entries. Unlike conventional decoupled methods, our integrated approach facilitates a bidirectional flow of information between the graph and signal domains, yielding superior robustness, particularly in high missing-data regimes. To capture realistic network dynamics, we introduce a fused-lasso type regularizer on the sequence of Laplacians. This penalty promotes temporal smoothness by penalizing large successive changes, thereby preventing spurious variations induced by noise while still permitting gradual topological evolution. For solving the joint optimization problem, we develop an efficient Alternating Direction Method of Multipliers (ADMM) algorithm, which leverages the problem's structure to yield closed-form solutions for both the graph and signal subproblems. This design ensures scalability to large-scale networks and long time horizons. On the theoretical front, despite the inherent non-convexity, we establish a convergence guarantee, proving that the proposed ADMM scheme converges to a stationary point. Furthermore, we derive non-asymptotic statistical guarantees, providing high-probability error bounds for the graph estimator as a function of sample size, signal smoothness, and the intrinsic temporal variability of the graph. Extensive numerical experiments validate the approach, demonstrating that it significantly outperforms state-of-the-art baselines in both convergence speed and the joint accuracy of graph learning and signal recovery.

Distributionally Robust Optimization (DRO) offers reliable solutions under data uncertainty and often yields superior out-of-sample performance. It has long been popular and widely studied in machine learning and engineering. Classical approaches to DRO typically rely on general-purpose solvers or deterministic methods, which become inefficient for large-scale settings. Although a first-order deterministic method has been proposed for Wasserstein distributionally robust logistic regression (DRLR), solving the β-subproblem remains the primary computational bottleneck. Consequently, the design of efficient algorithms, such as stochastic ones for large-scale DRO, remains an active research direction. In this paper, we propose two efficient stochastic methods to solve the β-subproblem of Wasserstein DRLR: SGD-LP-ADMM and SVRG-LP-ADMM. Both methods exploit stochastic gradient estimators to significantly reduce per-iteration complexity while maintaining convergence guarantees. We theoretically establish an $\mathcal{O}(1/\sqrt t )$ convergence rate for SGD-LP-ADMM and an accelerated $\mathcal{O}(1/\sqrt t )$ one for SVRG-LP-ADMM using the variance-reduced technique. Empirical evaluations on both synthetic and real-world datasets demonstrate that SVRG-LP-ADMM attains faster convergence and higher accuracy than existing baselines, with significantly lower computational cost, highlighting its effectiveness for robust learning in large-scale scenarios.

Cooperative and non-cooperative localization frequently arise together in wireless sensor networks, particularly when sensor positions are uncertain and targets are unable to communicate with the network. While joint processing can eliminate the delay in target estimation found in sequential approaches, it introduces complex variable coupling, posing challenges in both modeling and optimization. This paper presents a joint modeling approach that formulates cooperative and non-cooperative localization as a single optimization problem. To address the resulting coupling, we introduce auxiliary variables that enable structural decoupling and distributed computation. Building on this formulation, we develop the Scaled Proximal Alternating Direction Method of Multipliers for Joint Cooperative and Non-Cooperative Localization (SP-ADMM-JCNL). Leveraging the problem's structured design, we provide theoretical guarantees that the algorithm generates a sequence converging globally to the Karush-Kuhn-Tucker (KKT) point of the reformulated problem and further to a critical point of the original non-convex objective function, with a sublinear rate of O(1/T). Experiments on both synthetic and benchmark datasets demonstrate that SP-ADMM-JCNL achieves accurate and reliable localization performance.

Medical phrase grounding is crucial for identifying relevant regions in medical images based on phrase queries, facilitating accurate image analysis and diagnosis. However, current methods rely on manual extraction of key phrases from medical reports, reducing efficiency and increasing the workload for clinicians. Additionally, the lack of model confidence estimation limits clinical trust and usability. In this paper, we introduce a novel task-Medical Report Grounding (MRG)-which aims to directly identify diagnostic phrases and their corresponding grounding boxes from medical reports in an end-to-end manner. To address this challenge, we propose uMedGround, a a robust and reliable framework that leverages a multimodal large language model to predict diagnostic phrases by embedding a unique token, < $\mathtt {BOX}$BOX >, into the vocabulary to enhance detection capabilities. A vision encoder-decoder processes the embedded token and input image to generate grounding boxes. Critically, uMedGround incorporates an uncertainty-aware prediction model, significantly improving the robustness and reliability of grounding predictions. Experimental results demonstrate that uMedGround outperforms state-of-the-art medical phrase grounding methods and fine-tuned large visual-language models, validating its effectiveness and reliability. This study represents a pioneering exploration of the MRG task, marking the first-ever endeavor in this domain. Additionally, we demonstrate the applicability of uMedGround in medical visual question answering and class-based localization tasks, where it highlights visual evidence aligned with key diagnostic phrases, supporting clinicians in interpreting various types of textual inputs, including free-text reports, visual question answering queries, and class labels.

We explore the increasingly important task of jointly inferring multiple graph structures from nodal observations. Unlike traditional approaches that assume full access to signal data, our method is designed for more realistic scenarios where only a subset of nodes is observed. Under the assumption that the signals from these partially observed nodes are smooth and that the networks exhibit similar connectivity patterns, we introduce a flexible structural fusion regularization that simultaneously captures common and unique topological patterns across graphs by leveraging a Gram matrix formulation to encode various similarity measures. To address the resulting computational challenges, we develop an efficient algorithm based on the alternating direction method of multipliers (ADMM). Finally, the superior performance of the proposed method is demonstrated through simulated and real data examples.

Dictionary learning (DL) is a pivotal task in machine learning and signal processing, involving extracting representative features from a given dataset. However, conventional DL models are known to be highly sensitive to outliers. To circumvent this issue, we introduce a new and robust DL model based on unbalanced optimal transport (UOT). Compared to DL models based on conventional robust distances and the Wasserstein distance, our model not only captures and leverages the structural information within the data but also demonstrates strong resilience to outliers. By employing the structure of the proposed robust DL model, we develop a novel hybrid block coordinate descent (BCD) algorithm. The proposed algorithm maintains computational tractability by exploiting special block structures of the subproblems. In addition, we establish the convergence of our algorithm without the Lipschitz smooth condition. Through extensive experimentation, we validate our theoretical results and demonstrate the effectiveness of the proposed method on synthetic data, MNIST data, Olivetti faces dataset, and hyperspectral images (HSIs) datasets.

This paper considers the distributed group target tracking (DGTT) problem under sensors with limited and different field of views (FoVs). Usually, for the tracking of groups, targets within groups are closely spaced and move in a coordinated manner. These groups can split or merge, and the numbers of targets in groups may be large, which lead to more challenging issues related to data association, filtering and computational complexities. Particularly, these challenges may be further complicated in distributed fusion system architectures. To deal with these difficulties, we propose a consensus-based DGTT method within the belief propagation (BP) framework, which introduces undetected targets inside the FoV or new targets outside the FoV and performs the probabilistic track association via BP. Meanwhile, the obtained track association probabilities make it possible to exploit a probabilistic consensus fusion scheme for fusing local target densities. Furthermore, the proposed method exhibits computational scalability scaling only linearly on the numbers of group partitions, local measurements and neighboring sensors, and scaling quadratically on the number of targets. Numerical results validate the performance of the proposed method.

Traditional maneuvering target tracking algorithms assume that the target motion model is either fixed or limited in number. For high-speed and highly maneuvering targets, the tracker's performance degrades rapidly when the model set fails to adequately encompass the maneuvering mode or when there is a substantial deviation. Therefore, we propose a novel maneuvering target tracking method based on a random motion model. This algorithm employs a random model to describe the target maneuver, which is more widely applicable than traditional algorithms and remains more stable when the target maneuver is not covered by the model set. Additionally, in cases where the model set of the Interacting Multiple Model algorithm (IMM) does not align with the actual maneuvering state, the new method exhibits a smaller tracking error compared to IMM and shows no divergence trend. Finally, we combine IMM and the random motion model to propose an Integrated Random Interacting Multiple Model algorithm (IRIMM). The performance of the IRIMM algorithm closely matches that of IMM when provided with a perfectly accurate model set and significantly improves tracking effectiveness and stability when the model is incorrect.

Tracking multiple targets with unknown measurement-to-target association and uncertain target dynamics is a significant problem that arises in various applications such as surveillance monitoring and intelligent transportation systems. In this paper, we propose an enhanced multi-model multi-scan data association algorithm to address the problem of tracking multiple maneuvering targets. First, we use a probabilistic graphical model to represent the joint distribution of the dynamic model indices, target state, and multi-scan data association variables. This formulation transforms the inference of marginal distributions into a Bethe free energy (BFE) problem. Next, to transform the BFE problem into a convex one, we demonstrate that the BFE function can be made convex through re-weighting. Additionally, we decompose the re-weighted BFE function into a block-wise sum form. We prove that under certain regularization conditions, each block of the re-weighted BFE is convex, ensuring convergence of the primal–dual coordinate ascent algorithm to the minimum of the overall re-weighted BFE. Finally, we provide a particle implementation of the proposed algorithm, accompanied by an analysis of its complexity. Simulation results indicate that the proposed algorithm exhibits favorable performance when compared to both the single-model multi-scan algorithm and the multi-model single-scan algorithm.