Sequential change detection in high-dimensional dynamic networks has attracted growing attention in modern applications. A major challenge is that as network scale increases, limited sensing resources make it difficult to fully observe links at each time point, resulting in partial observability and complicating detection. To tackle this, we propose a Latent Bi-Transit Network (LBTN) that learns unobserved edge formation, latent node states, and the evolution mechanisms of dynamic networks. Based on LBTN, we design a variational Bayesian method to infer sparse node-level changes and employ a likelihood ratio test as the detection statistic. By further formulating the statistic as the reward function of a combinatorial multi-armed bandit (CMAB) problem, we develop a Thompson sampling strategy to adaptively select edges for observation, balancing exploration and exploitation. Comprehensive simulations and real-world experiments show that our method consistently outperforms existing baselines and its variants across diverse scenarios.

The rapid advancement of real-time data monitoring technologies has established functional data analysis as a crucial predictive tool across diverse applications. Despite progress in multivariate functional regression and principal component analysis, significant challenges persist in function-to-function regression and feature selection. These include the inaccurate selection of predictor variables from extensive predictors and flawed parameter estimation, which compromise the precision of function-based data predictions. This paper introduces the SPEVS-CC method, a novel canonical correlation-based feature selection technique specifically designed for function-on-function regression. By effectively decoupling variable selection from model fitting, the SPEVS-CC method enhances both adaptability and interpretability. Validated through rigorous experiments and real-world applications, including in the Shenzhen subway system, semiconductor manufacturing, and ocean climate, SPEVS-CC significantly reduces mean squared error, confirming its robustness and practical utility. This methodological breakthrough harmonizes variable selection with functional regression, providing unmatched interpretability and usability in industrial applications.

Metro system serves as the backbone for urban public transportation. Accurate passenger load prediction for the metro system plays a crucial role in metro service quality improvement, such as helping operators schedule train timetables and passengers plan their trips. However, existing works can only predict low‐grained passenger flows of origin‐destination (O‐D) paths or inflows/outflows of each station but cannot predict passenger load distribution over the whole metro network. To this end, this paper proposes an end‐to‐end inference framework, PIPE, for passenger load prediction of every metro segment between two adjacent stations, by only utilizing smart card data. In particular, PIPE includes two modules. The first is the core. It formulates the travel time distribution of each metro segment as a truncated Gaussian distribution. Since there might be several possible routes for certain O‐D paths, the population‐level travel time distribution of these O‐D paths would be a mixture of travel times of different routes. Considering the route preference may change over time, a dynamic truncated Gaussian mixture model is proposed for parameter inference of each truncated Gaussian distribution of each metro segment. The second module serves as the supplement, which compiles a bunch of methods for predicting passenger flows of O‐D paths. Built upon them, PIPE is able to predict the travel time that future passengers of each O‐D path will take for passing each metro segment and consequently can predict the passenger load of each metro segment in the short future. Numerical studies from Singapore’s metro system demonstrate the efficacy of our method.

Functional data have been gaining increasing popularity in the field of time series analysis. However, so far modeling heterogeneous multivariate functional time series remains a research gap. To fill it, this paper proposes a time-varying functional state space model (TV-FSSM). It uses functional decomposition to extract features of the functional observations, where the decomposition coefficients are regarded as latent states that evolve according to a tensor autoregressive model. This two-layer structure can on the one hand efficiently extract continuous functional features, and on the other provide a flexible and generalized description of data heterogeneity among different time points. An expectation maximization (EM) framework is developed for parameter estimation, where regularization and constraints are incorporated for better model interoperability. As the sample size grows, an incremental learning version of the EM algorithm is given to efficiently update the model parameters. Some model properties, including model identifiability conditions, convergence issues, time complexities, and bounds of its one-step-ahead prediction errors, are also presented. Extensive experiments on both real and synthetic datasets are performed to evaluate the predictive accuracy and efficiency of the proposed framework.

This paper proposes to learn Multi-task, Multi-modal Direct Acyclic Graphs (MM-DAGs), which are commonly observed in complex systems, e.g., traffic, manufacturing, and weather systems, whose variables are multi-modal with scalars, vectors, and functions. This paper takes the traffic congestion analysis as a concrete case, where a traffic intersection is usually regarded as a DAG. In a road network of multiple intersections, different intersections can only have someoverlapping and distinct variables observed. For example, a signalized intersection has traffic light-related variables, whereas unsignalized ones do not. This encourages the multi-task design: with each DAG as a task, the MM-DAG tries to learn the multiple DAGs jointly so that their consensus and consistency are maximized. To this end, we innovatively propose a multi-modal regression for linear causal relationship description of different variables. Then we develop a novel Causality Difference (CD) measure and its differentiable approximator. Compared with existing SOTA measures, CD can penalize the causal structural difference among DAGs with distinct nodes and can better consider the uncertainty of causal orders. We rigidly prove our design's topological interpretation and consistency properties. We conduct thorough simulations and one case study to show the effectiveness of our MM-DAG. The code is available under https://github.com/Lantian72/MM-DAG.

Abstract Individual passenger travel patterns have significant value in understanding passenger’s behavior, such as learning the hidden clusters of locations, time, and passengers. The learned clusters further enable commercially beneficial actions such as customized services, promotions, data-driven urban-use planning, peak hour discovery, and so on. However, the individualized passenger modeling is very challenging for the following reasons: 1) The individual passenger travel data are multi-dimensional spatiotemporal big data, including at least the origin, destination, and time dimensions; 2) Moreover, individualized passenger travel patterns usually depend on the external environment, such as the distances and functions of locations, which are ignored in most current works. This work proposes a multi-clustering model to learn the latent clusters along the multiple dimensions of Origin, Destination, Time, and eventually, Passenger (ODT-P). We develop a graph-regularized tensor Latent Dirichlet Allocation (LDA) model by first extending the traditional LDA model into a tensor version and then applies to individual travel data. Then, the external information of stations is formulated as semantic graphs and incorporated as the Laplacian regularizations; Furthermore, to improve the model scalability when dealing with massive data, an online stochastic learning method based on tensorized variational Expectation-Maximization algorithm is developed. Finally, a case study based on passengers in the Hong Kong metro system is conducted and demonstrates that a better clustering performance is achieved compared to state-of-the-arts with the improvement in point-wise mutual information index and algorithm convergence speed by a factor of two.

Time-varying dynamic Bayesian network (TVDBN) is essential for describing time-evolving directed conditional dependence structures in complex multivariate systems. In this article, we construct a TVDBN model, together with a score-based method for its structure learning. The model adopts a vector autoregressive (VAR) model to describe inter-slice and intra-slice relations between variables. By allowing VAR parameters to change segment-wisely over time, the time-varying dynamics of the network structure can be described. Furthermore, considering some external information can provide additional similarity information of variables. Graph Laplacian is further imposed to regularize similar nodes to have similar network structures. The regularized maximum a posterior estimation in the Bayesian inference framework is used as a score function for TVDBN structure evaluation, and the alternating direction method of multipliers (ADMM) with L-BFGS-B algorithm is used for optimal structure learning. Thorough simulation studies and a real case study are carried out to verify our proposed method’s efficacy and efficiency.

This article proposes a novel time-warped sparse non-negative factorization method for functional data analysis. The proposed method on the one hand guarantees the extracted basis functions and their coefficients to be positive and interpretable, and on the other hand is able to handle weakly correlated functions with different features. Furthermore, the method incorporates time warping into factorization and hence allows the extracted basis functions of different samples to have temporal deformations. An efficient framework of estimation algorithms is proposed based on a greedy variable selection approach. Numerical studies together with case studies on real-world data demonstrate the efficacy and applicability of the proposed methodology.