Recovering incomplete multidimensional tensor-structured data is a fundamental task in many real-world applications. Smoothness-constrained low-rank tensor factorization effectively captures global and long-range correlations, but often struggles to characterize short-scale, high-frequency, or locally varying structures. We propose GLSKF, a complementary Generalized Least Squares Kernelized Tensor Factorization framework, for multidimensional spatiotemporal data completion. GLSKF additively integrates a covariance-regularized low-rank global component with an explicitly modeled locally correlated residual component under a GLS objective, enabling effective modeling of both global dependencies and localized variations. A covariance norm regularizer encodes spatiotemporal dependencies in both components: structured covariances are imposed on the latent factor columns to enforce smoothness in the global factorization, whereas compactly supported sparse kernels are used to model local correlations in the residual. We develop an alternating least squares algorithm with blockwise linear-system updates that exploit the Kronecker structure of the covariance matrices under missing data and facilitate fast conjugate gradient solves. Additional computational gains are obtained by exploiting the sparsity and Toeplitz structure of the local residual covariance matrices for efficient matrix-vector multiplications. We evaluate GLSKF on four real-world multidimensional data-completion tasks: traffic speed imputation, color image completion, digital video recovery, and MRI data reconstruction. Experimental results demonstrate that GLSKF achieves superior reconstruction performance and favorable scalability across a range of tensor completion tasks, supporting its broad applicability to multidimensional data completion.

In real-world scenarios, spatiotemporal traffic data frequently experiences dual degradation from missing values and noise caused by sensor malfunctions and communication failures. Therefore, effective data recovery methods are essential to ensure the reliability of downstream data-driven applications. while classical tensor completion methods have been widely adopted, they are incapable of modeling noise, making them unsuitable for complex scenarios involving simultaneous data missingness and noise interference. ExistingRobust Tensor Completion(RTC) approaches offer potential solutions by separately modeling the actual tensor data and noise. However, their effectiveness is often constrained by the over-relaxation of convex rank surrogates and the suboptimal utilization of local consistency. To address these limitations, we introduce the gradient tensor nuclear$\ell _{1}$-$\ell _{2}$norm via a non-convex tensor rank surrogate and an advanced feature fusion strategy, and integrate it into the RTC framework to propose theRobust Tensor Completion via Gradient Tensor Nuclear$\ell _{1}$-$\ell _{2}$Norm(RTC-GTNLN) model. The proposed model not only fully exploits both global low-rankness and local consistency without a trade-off parameter, but also effectively handles the dual degradation challenges of missing data and noise in traffic data. Extensive experiments conducted on multiple real-world traffic datasets demonstrate that the RTC-GTNLN model consistently outperforms existing state-of-the-art methods in complex recovery scenarios involving simultaneous missing values and noise. The code is available athttps://github.com/HaoShu2000/RTC-GTNLN

Traffic data analysis often faces challenges such as missing data and anomalies, significantly limiting accurate understanding and forecasting of traffic patterns. To address these challenges, our study introduces the anti-circulant-structured tensor Robust Matrix Completion (circ-RMC), a novel approach to enhance spatiotemporal traffic flow data analysis. Traditional Robust Matrix Completion (RMC) methods struggle with continuous missing data and often overlook local traffic dynamics due to the assumption on global data. Our proposed circ-RMC overcomes these limitations by integrating the Short-Time Fourier Transform (STFT) with RMC, enabling more accurate data completion and anomaly detection in the time-frequency domain. This method uniquely analyzes traffic flow as a multivariate time series matrix, using STFT to detect localized changes in traffic patterns over time. The resulting time-frequency spectra are then organized into an anti-circulant-structured tensor, capturing intricate correlations across different locations. In addition, the model is adept at detecting continuous anomalous behavior caused by special events. Formulated as an optimization problem, this method employs the Alternating Direction Method of Multipliers (ADMM) for efficient resolution. Tested against real-world taxi passenger flow and bike-sharing records, circ-RMC outperforms existing methodologies in completing missing data and identifying traffic anomalies. This approach contributes to traffic management and urban planning by providing complete datasets for downstream traffic-related tasks and offering researchers a tool to understand and explore travel behaviors.

Large Language Models (LLMs) have recently demonstrated significant potential in the field of time series forecasting, offering impressive capabilities in handling complex temporal data. However, their robustness and reliability in real-world applications remain under-explored, particularly concerning their susceptibility to adversarial attacks. In this paper, we introduce a targeted adversarial attack framework for LLM-based time series forecasting. By employing both gradient-free and black-box optimization methods, we generate minimal yet highly effective perturbations that significantly degrade the forecasting accuracy across multiple datasets and LLM architectures. Our experiments, which include models like LLMTime with GPT-3.5, GPT-4, LLaMa, and Mistral, TimeGPT, and TimeLLM show that adversarial attacks lead to much more severe performance degradation than random noise, and demonstrate the broad effectiveness of our attacks across different LLMs. The results underscore the critical vulnerabilities of LLMs in time series forecasting, highlighting the need for robust defense mechanisms to ensure their reliable deployment in practical applications. The code repository can be found at \url{https://github.com/JohnsonJiang1996/AdvAttack_LLM4TS.}

Long-term urban mobility predictions play a crucial role in the effective management of urban facilities and services. Conventionally, urban mobility data has been structured as spatiotemporal videos, treating longitude and latitude grids as fundamental pixels. Consequently, video prediction methods, relying on Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs), have been instrumental in this domain. In our research, we introduce a fresh perspective on urban mobility prediction. Instead of oversimplifying urban mobility data as traditional video data, we regard it as a complex multivariate time series. This perspective involves treating the time-varying values of each grid in each channel as individual time series. To tackle the prediction of these time series, we present the Super-Multivariate Urban Mobility Transformer (SUMformer), which utilizes a specially designed attention mechanism to calculate temporal and cross-variable correlations and reduce computational costs stemming from a large number of time series. SUMformer also employs low-frequency filters to extract essential information for long-term predictions. Furthermore, SUMformer is structured with a temporal patch merge mechanism, forming a hierarchical framework that enables the capture of multi-scale correlations. Consequently, it excels in urban mobility pattern modeling and long-term prediction, outperforming current state-of-the-art methods across five real-world datasets. The code is available at:https://github.com/Chengyui/SUMformer.

Spatiotemporal traffic data (STTD) displays complex correlational structures. Extensive advanced techniques have been designed to capture these structures for effective forecasting. However, because STTD is often massive in scale, practitioners need to strike a balance between effectiveness and efficiency using computationally efficient models. An alternative paradigm based on multilayer perceptron (MLP) called MLP-Mixer has the potential for both simplicity and effectiveness. Taking inspiration from its success in other domains, we propose an adapted version, named NexuSQN, for STTD forecast at scale. We first identify the challenges faced when directly applying MLP-Mixers as series- and window-wise multivaluedness. To distinguish between spatial and temporal patterns, the concept of ST-contextualization is then proposed. Our results surprisingly show that this simple-yet-effective solution can rival SOTA baselines when tested on several traffic benchmarks. Furthermore, NexuSQN has demonstrated its versatility across different domains, including energy and environment data, and has been deployed in a collaborative project with Baidu to predict congestion in megacities like Beijing and Shanghai. Our findings contribute to the exploration of simple-yet-effective models for real-world STTD forecasting.

Travel time estimation is a key task in navigation apps and web mapping services. Existing deterministic and probabilistic methods, based on the assumption of trip independence, predominantly focus on modeling individual trips while overlooking trip correlations. However, real-world conditions frequently introduce strong correlations between trips, influenced by external and internal factors such as weather and the tendencies of drivers. To address this, we propose a deep hierarchical joint probabilistic model,ProbETA, for travel time estimation, capturing both inter-trip and intra-trip correlations. The joint distribution of travel times across multiple trips is modeled as a low-rank multivariate Gaussian, parameterized by learnable link representations estimated using the empirical Bayes approach. We also introduce a data augmentation method based on trip sub-sampling, allowing for fine-grained gradient backpropagation when learning link representations. During inference, our model estimates the probability distribution of travel time for a queried trip, conditional on spatiotemporally adjacent completed trips. Evaluation on two real-world GPS trajectory datasets demonstrates thatProbETAoutperforms state-of-the-art deterministic and probabilistic baselines, with Mean Absolute Percentage Error decreasing by over 12.60%. Moreover, the learned link representations align with the physical network geometry, potentially making them applicable for other tasks.

Multivariate time series (MTS) forecasting has a wide range of applications in both industry and academia. Recently, spatial-temporal graph neural networks (STGNNs) have gained popularity as MTS forecasting methods. However, current STGNNs can only use the finite length of MTS input data due to the computational complexity. Moreover, they lack the ability to identify similar patterns throughout the entire dataset and struggle with data that exhibit sparsely and discontinuously distributed correlations among variables over an extensive historical period, resulting in only marginal improvements. In this article, we introduce a simple yet effective k-nearest neighbor MTS forecasting (kNN-MTS) framework, which forecasts with a nearest neighbor retrieval mechanism over a large datastore of cached series, using representations from the MTS model for similarity search. This approach requires no additional training and scales to give the MTS model direct access to the whole dataset at test time, resulting in a highly expressive model that consistently improves performance, and has the ability to extract sparse distributed but similar patterns span over multivariables from the entire dataset. Furthermore, a hybrid spatial-temporal encoder (HSTEncoder) is designed for kNN-MTS which can capture both long-term temporal and short-term spatial-temporal dependencies and is shown to provide accurate representation for kNN-MTS for better forecasting. Experimental results on several real-world datasets show a significant improvement in the forecasting performance of kNN-MTS. The quantitative analysis also illustrates the interpretability and efficiency of kNN-MTS, showing better application prospects and opening up a new path for efficiently using the large dataset in MTS models.

Deep probabilistic time series forecasting has gained attention for its ability to provide nonlinear approximation and valuable uncertainty quantification for decision-making. However, existing models often oversimplify the problem by assuming a time-independent error process and overlooking serial correlation. To overcome this limitation, we propose an innovative training method that incorporates error autocorrelation to enhance probabilistic forecasting accuracy. Our method constructs a mini-batch as a collection of D consecutive time series segments for model training. It explicitly learns a time-varying covariance matrix over each mini-batch, encoding error correlation among adjacent time steps. The learned covariance matrix can be used to improve prediction accuracy and enhance uncertainty quantification. We evaluate our method on two different neural forecasting models and multiple public datasets. Experimental results confirm the effectiveness of the proposed approach in improving the performance of both models across a range of datasets, resulting in notable improvements in predictive accuracy.

Learning and understanding car-following (CF) behaviors are crucial for microscopic traffic simulation. Traditional CF models, though simple, often lack generalization capabilities, while many data-driven methods, despite their robustness, operate as "black boxes" with limited interpretability. To bridge this gap, this work introduces a Bayesian Matrix Normal Mixture Regression (MNMR) model that simultaneously captures feature correlations and temporal dynamics inherent in CF behaviors. This approach is distinguished by its separate learning of row and column covariance matrices within the model framework, offering an insightful perspective into the human driver decision-making processes. Through extensive experiments, we assess the model’s performance across various historical steps of inputs, predictive steps of outputs, and model complexities. The results consistently demonstrate our model’s adeptness in effectively capturing the intricate correlations and temporal dynamics present during CF. A focused case study further illustrates the model’s outperforming interpretability of identifying distinct operational conditions through the learned mean and covariance matrices. This not only underlines our model’s effectiveness in understanding complex human driving behaviors in CF scenarios but also highlights its potential as a tool for enhancing the interpretability of CF behaviors in traffic simulations and autonomous driving systems.

Car-following models are essential for microscopic traffic simulation. While conventional models rely on parsimonious formulas with simplified assumptions, recent studies have focused on developing data-driven models with the help of high-resolution trajectory data. This paper presents a data-driven model based on a Bayesian Gaussian mixture model (GMM) for probabilistic forecasting of human car-following behaviors. By incorporating past and future information, our model captures the temporal dynamics of human car-following behaviors, providing accurate predictions of the following vehicle’s behavior and quantifying the forecast uncertainty. We demonstrate the interpretability of the Bayesian GMM in modeling car-following behaviors, providing valuable insights into the heterogeneity and uncertainty of driver behaviors. Additionally, we show that the proposed model can make probabilistic multi-vehicle simulations that reproduce natural traffic phenomena. Our results suggest that the proposed Bayesian GMM is a promising approach for modeling and forecasting car-following behaviors in various driving scenarios, contributing to the development of safer and more efficient transportation systems.

Humans are experts at making decisions for challenging driving tasks with uncertainties. Many efforts have been made to model the decision-making process of human drivers at the behavior level. However, limited studies explain how human drivers actively make trustworthy sequential decisions to complete interactive driving tasks in an uncertain environment. This paper argues that human drivers intently search for actions to reduce the uncertainty of their perception of the environment, i.e., perceptual uncertainty, to a low level that allows them to make a trustworthy decision easily. This paper provides a proof-of-concept framework to empirically reveal that human drivers’ perceptual uncertainty decreases when executing interactive tasks with uncertainties. We first introduce an explainable-artificial intelligence approach (i.e., SHapley Additive exPlanation, SHAP) to determine the salient features on which human drivers base decisions. Then, we use entropy-based measures to quantify the drivers’ perceptual changes in these ranked salient features across the decision-making process, reflecting the changes in uncertainties. The validation and verification of our proposed method are conducted in the highway on-ramp merging scenario with congested traffic using the INTERACTION dataset. Experimental results support that human drivers intentionally seek information to reduce their perceptual uncertainties in the number and rank of salient features of their perception of environments to make a trustworthy decision.

Accurate calibration of car-following models is essential for understanding human driving behaviors and implementing high-fidelity microscopic simulations. This work proposes a memory-augmented Bayesian calibration technique to capture both uncertainty in the model parameters and the temporally correlated behavior discrepancy between model predictions and observed data. Specifically, we characterize the parameter uncertainty using a hierarchical Bayesian framework and model the temporally correlated errors using Gaussian processes. We apply the Bayesian calibration technique to the intelligent driver model (IDM) and develop a novel stochastic car-following model named memory-augmented IDM (MA-IDM). To evaluate the effectiveness of MA-IDM, we compare the proposed MA-IDM with Bayesian IDM in which errors are assumed to be i.i.d., and our simulation results based on the HighD dataset show that MA-IDM can generate more realistic driving behaviors and provide better uncertainty quantification than Bayesian IDM. By analyzing the lengthscale parameter of the Gaussian process, we also show that taking the driving actions from the past five seconds into account can be helpful in modeling and simulating the human driver’s car-following behaviors.

Driving style is usually used to characterize driving behavior for a driverora group of drivers. However, it remains unclear how one individual’s driving style shares certain common grounds with other drivers. Our insight is that driving behavior is a sequence of responses to the weighted mixture of latent driving styles that are shareablewithinandbetweenindividuals. To this end, this paper develops a hierarchical latent model to learn the relationship between driving behavior and driving styles. We first propose a fragment-based approach to represent complex sequential driving behavior in a low-dimension feature space. Then, we provide an analytical formulation for the interaction of driving behavior and shareable driving styles through a hierarchical latent model. This model successfully extracts latent driving styles from extensive driving behavior data without the need for manual labeling, offering an interpretable statistical structure. Through real-world testing involving 100 drivers, our developed model is validated, demonstrating a subjective-objective consistency exceeding 90%, outperforming the benchmark method. Experimental results reveal that individuals share driving styles within and between them. We also found that individuals inclined towards aggressiveness only exhibit a higher proportion of such behavior rather than persisting consistently to be aggressive.

Spatiotemporal traffic data imputation is of great significance in intelligent transportation systems and data-driven decision-making processes. To perform efficient learning and accurate reconstruction from partially observed traffic data, we assert the importance of characterizing both global and local trends in time series. In the literature, substantial works have demonstrated the effectiveness of utilizing the low-rank property of traffic data by matrix/tensor completion models. In this study, we first introduce a Laplacian kernel to temporal regularization for characterizing local trends in traffic time series, which can be formulated as a circular convolution. Then, we develop a low-rank Laplacian convolutional representation (LCR) model by putting the circulant matrix nuclear norm and the Laplacian kernelized temporal regularization together, which is proved to meet a unified framework that has a fast Fourier transform (FFT) solution in log-linear time complexity. Through extensive experiments on several traffic datasets, we demonstrate the superiority of LCR over several baseline models for imputing traffic time series of various time series behaviors (e.g., data noises and strong/weak periodicity) and reconstructing sparse speed fields of vehicular traffic flow. The proposed LCR model is also an efficient solution to large-scale traffic data imputation over the existing imputation models.

The problem of discovering interpretable dynamic patterns from spatiotemporal data is studied in this paper. For that purpose, we develop a time-varying reduced-rank vector autoregression (VAR) model whose coefficient matrices are parameterized by low-rank tensor factorization. Benefiting from the tensor factorization structure, the proposed model can simultaneously achieve model compression and pattern discovery. In particular, the proposed model allows one to characterize nonstationarity and time-varying system behaviors underlying spatiotemporal data. To evaluate the proposed model, extensive experiments are conducted on various spatiotemporal datasets representing different nonlinear dynamical systems, including fluid dynamics, sea surface temperature, USA surface temperature, and NYC taxi trips. Experimental results demonstrate the effectiveness of the proposed model for analyzing spatiotemporal data and characterizing spatial/temporal patterns. In the spatial context, the spatial patterns can be automatically extracted and intuitively characterized by the spatial modes. In the temporal context, the complex time-varying system behaviors can be revealed by the temporal modes in the proposed model. Thus, our model lays an insightful foundation for understanding complex spatiotemporal data in real-world dynamical systems. The adapted datasets and Python implementation are publicly available athttps://github.com/xinychen/vars.

Multivariate time series forecasting plays an increasingly critical role in various applications, such as power management, smart cities, finance, and healthcare. Recent advances in temporal graph neural networks (GNNs) have shown promising results in multivariate time series forecasting due to their ability to characterize high-dimensional nonlinear correlations and temporal patterns. However, the vulnerability of deep neural networks (DNNs) constitutes serious concerns about using these models to make decisions in real-world applications. Currently, how to defend multivariate forecasting models, especially temporal GNNs, is overlooked. The existing adversarial defense studies are mostly in static and single-instance classification domains, which cannot apply to forecasting due to the generalization challenge and the contradiction issue. To bridge this gap, we propose an adversarial danger identification method for temporally dynamic graphs to effectively protect GNN-based forecasting models. Our method consists of three steps: 1) a hybrid GNN-based classifier to identify dangerous times; 2) approximate linear error propagation to identify the dangerous variates based on the high-dimensional linearity of DNNs; and 3) a scatter filter controlled by the two identification processes to reform time series with reduced feature erasure. Our experiments, including four adversarial attack methods and four state-of-the-art forecasting models, demonstrate the effectiveness of the proposed method in defending forecasting models against adversarial attacks.

The bus system is a critical component of sustainable urban transportation. However, the operation of a bus fleet is unstable in nature, and bus bunching has become a common phenomenon that undermines the efficiency and reliability of bus systems. Recently research has demonstrated the promising application of multi-agent reinforcement learning (MARL) to achieve efficient vehicle holding control to avoid bus bunching. However, existing studies essentially overlook the robustness issue resulting from perturbations and anomalies in a transit system, which is of utmost importance when transferring the models for real-world deployment/application. In this study, we integrate implicit quantile network and meta-learning to develop a distributional MARL framework—IQNC-M—to learn continuous control. The proposed IQNC-M framework achieves efficient and reliable control decisions through better handling various uncertainties in real-time transit operations. Specifically, we introduce an interpretable meta-learning module to incorporate global information into the distributional MARL framework, which is an effective solution to circumvent the credit assignment issue in the transit system. In addition, we design a specific learning procedure to train each agent within the framework to pursue a robust control policy. We develop simulation environments based on real-world bus services and passenger demand data and evaluate the proposed framework against both traditional holding control models and state-of-the-art MARL models. Our results show that the proposed IQNC-M framework can effectively handle the general perturbations and various extreme events, such as traffic state perturbations and demand surges, thus improving both efficiency and reliability of the transit system.

This paper studies the traffic state estimation (TSE) problem using sparse observations from mobile sensors. Most existing TSE methods either rely on well-defined physical traffic flow models or require large amounts of simulation data as input to train learning algorithms. Different from previous studies, in this paper we propose a purely data-driven and model-free solution. We consider TSE as a spatiotemporal matrix completion/interpolation problem and apply spatiotemporal delay embedding to transform the original incomplete matrix into a fourth-order Hankel structured tensor. By imposing a low-rank assumption on this tensor structure, we can approximate and characterize both global patterns and local patterns in a data-driven manner. We use a truncated nuclear norm of a balanced spatiotemporal unfolding to approximate the tensor rank and develop an efficient algorithm based on the Alternating Direction Method of Multipliers (ADMM) to solve the problem. The proposed framework only involves two hyperparameters, spatial and temporal window lengths, which are easy to set given the degree of data sparsity. To validate the effectiveness of our proposed method, we conducted numerical experiments on real-world high-resolution trajectory data, which demonstrated its superiority in some challenging scenarios. The proposed method shows great potential for solving the TSE problem using sparse observations from mobile sensors and can be applied in various traffic applications.

Large-scale and multidimensional spatiotemporal data sets are becoming ubiquitous in many real-world applications such as monitoring urban traffic and air quality. Making predictions on these time series has become a critical challenge due to not only the large-scale and high-dimensional nature but also the considerable amount of missing data. In this paper, we propose a Bayesian temporal factorization (BTF) framework for modeling multidimensional time series-in particular spatiotemporal data-in the presence of missing values. By integrating low-rank matrix/tensor factorization and vector autoregressive (VAR) process into a single probabilistic graphical model, this framework can characterize both global and local consistencies in large-scale time series data. The graphical model allows us to effectively perform probabilistic predictions and produce uncertainty estimates without imputing those missing values. We develop efficient Gibbs sampling algorithms for model inference and model updating for real-time prediction and test the proposed BTF framework on several real-world spatiotemporal data sets for both missing data imputation and multi-step rolling prediction tasks. The numerical experiments demonstrate the superiority of the proposed BTF approaches over existing state-of-the-art methods.

Spatiotemporal traffic time series (e.g., traffic volume/speed) collected from sensing systems are often incomplete with considerable corruption and large amounts of missing values, preventing users from harnessing the full power of the data. Missing data imputation has been a long-standing research topic and critical application for real-world intelligent transportation systems. A widely applied imputation method is low-rank matrix/tensor completion; however, the low-rank assumption only preserves the global structure while ignores the strong local consistency in spatiotemporal data. In this paper, we propose a low-rank autoregressive tensor completion (LATC) framework by introducing \textit{temporal variation} as a new regularization term into the completion of a third-order (sensor $\times$ time of day $\times$ day) tensor. The third-order tensor structure allows us to better capture the global consistency of traffic data, such as the inherent seasonality and day-to-day similarity. To achieve local consistency, we design the temporal variation by imposing an AR($p$) model for each time series with coefficients as learnable parameters. Different from previous spatial and temporal regularization schemes, the minimization of temporal variation can better characterize temporal generative mechanisms beyond local smoothness, allowing us to deal with more challenging scenarios such "blackout" missing. To solve the optimization problem in LATC, we introduce an alternating minimization scheme that estimates the low-rank tensor and autoregressive coefficients iteratively. We conduct extensive numerical experiments on several real-world traffic data sets, and our results demonstrate the effectiveness of LATC in diverse missing scenarios.

Missingness and corruption are common problems for real-world traffic data. How to accurately perform imputation and prediction based on incomplete or even sparse traffic data becomes a critical research question in intelligent transportation systems. Low-rank matrix factorization (MF) is a common solution for the general missing value imputation problem. To better characterize and encode the strong spatial and temporal consistency in traffic data, existing work has introduced flexible spatial/temporal Gaussian process (GP) priors to model the latent factors in MF framework, which also allows us to perform kriging for unseen locations and virtual sensors. However, learning the hyperparameters in GP kernels remains a challenging task. In this paper, we present a Bayesian kernelized matrix factorization (BKMF) model with an efficient Markov chain Monte Carlo (MCMC) sampling algorithm for model inference. By learning the kernel hyperparameters from their marginal posteriors through a slice sampling treatment and updating the latent factors alternatively with Gibbs sampling, we achieve a fully Bayesian model for the spatiotemporally kernelized (i.e., GP prior regularized) MF framework. We apply BKMF on both imputation and kriging tasks, and our results demonstrate the superiority of BKMF compared with state-of-the-art spatiotemporal models. In addition, we also explore the effects of different GP kernels in characterizing networked spatiotemporal traffic state data.

Recent studies have demonstrated the great success of graph convolutional networks in short-term traffic forecasting (e.g., 15–30 min ahead) tasks by capturing dependencies in road network structure. Based on these models, long-term forecasting can be achieved by two approaches: (1) recursively generating a one-step-ahead prediction and (2) adapting the models to sequence-to-sequence (seq2seq) learning. However, in practice, these two approaches often show poor performance in long-term forecasting tasks. The recursive approach suffers from the error accumulation problem, as the model is trained based on one-step-ahead loss. On the other hand, seq2seq shows convergence issues that limit its application. To address the issues for long-term forecasting, in this paper, we propose a universal framework that directly transforms any existing state-of-the-art models for one-step-ahead prediction to achieve more accurate long-term forecasting. The proposed framework consists of two components—a base model and a bias block. The base model is assumed to be a well-trained state-of-the-art one-step-ahead forecasting model, and the bias block is constructed by a spatiotemporal graph neural network composed of gated temporal convolution layers and graph convolution layers. The base model and the bias block are residually-connected so that we can substantially reduce the training complexity. Extensive experiments are conducted on existing benchmark datasets. We experiment with several state-of-the-art models in the literature as base models, and our results demonstrate the ability of the proposed universal framework to greatly improve the long-term prediction accuracy for all models.

Merging at highway on-ramps while interacting with other human-driven vehicles is challenging for autonomous vehicles (AVs). An efficient route to this challenge requires exploring and exploiting knowledge of the interaction process from demonstrations by humans. However, it is unclear what information (or environmental states) is utilized by the human driver to guide their behavior throughout the whole merging process. This paper provides quantitative analysis and evaluation of the merging behavior at highway on-ramps with congested traffic in a volume of time and space. Two types of social interaction scenarios are considered based on the social preferences of surrounding vehicles:courteousandrude. The significant levels of environmental states for characterizing the interactive merging process are empirically analyzed based on the real-world INTERACTION dataset. Experimental results reveal two fundamental mechanisms in the merging process: 1) Human drivers select different states to make sequential decisions at different moments of task execution; and 2) the social preference of surrounding vehicles can impact variable selection for making decisions. It implies that efficient decision-making design should filter out irrelevant information while considering social preference to achieve comparable human-level performance. These essential findings shed light on developing new decision-making approaches for AVs.

Time series forecasting and spatiotemporal kriging are the two most important tasks in spatiotemporal data analysis. Recent research on graph neural networks has made substantial progress in time series forecasting, while little attention has been paid to the kriging problem---recovering signals for unsampled locations/sensors. Most existing scalable kriging methods (e.g., matrix/tensor completion) are transductive, and thus full retraining is required when we have a new sensor to interpolate. In this paper, we develop an Inductive Graph Neural Network Kriging (IGNNK) model to recover data for unsampled sensors on a network/graph structure. To generalize the effect of distance and reachability, we generate random subgraphs as samples and the corresponding adjacency matrix for each sample. By reconstructing all signals on each sample subgraph, IGNNK can effectively learn the spatial message passing mechanism. Empirical results on several real-world spatiotemporal datasets demonstrate the effectiveness of our model. In addition, we also find that the learned model can be successfully transferred to the same type of kriging tasks on an unseen dataset. Our results show that: 1) GNN is an efficient and effective tool for spatial kriging; 2) inductive GNNs can be trained using dynamic adjacency matrices; 3) a trained model can be transferred to new graph structures and 4) IGNNK can be used to generate virtual sensors.

The bus system is a critical component of sustainable urban transportation. However, due to the significant uncertainties in passenger demand and traffic conditions, bus operation is unstable in nature and bus bunching has become a common phenomenon that undermines the reliability and efficiency of bus services. Despite recent advances in multi-agent reinforcement learning (MARL) on traffic control, little research has focused on bus fleet control due to the tricky asynchronous characteristic---control actions only happen when a bus arrives at a bus stop and thus agents do not act simultaneously. In this study, we formulate route-level bus fleet control as an asynchronous multi-agent reinforcement learning (ASMR) problem and extend the classical actor-critic architecture to handle the asynchronous issue. Specifically, we design a novel critic network to effectively approximate the marginal contribution for other agents, in which graph attention neural network is used to conduct inductive learning for policy evaluation. The critic structure also helps the ego agent optimize its policy more efficiently. We evaluate the proposed framework on real-world bus services and actual passenger demand derived from smart card data. Our results show that the proposed model outperforms both traditional headway-based control methods and existing MARL methods.

Traffic data collected from sensor networks often exhibit strong spatial correlations and recurrent temporal patterns. Learning these patterns and diagnosing anomalies in such spatiotemporal traffic data is critical to improving transportation systems and services. This paper proposes a dynamic framework to model spatiotemporal traffic data, with a particular application on diagnosing anomalies. Within the framework, we focus on characterizing the variation in system dynamics with a time-varying vector autoregressive model. We impose a low-rank tensor structure to model the collection of time-varying system matrices. As the temporal factor matrix captures the principal patterns/signatures across all time-varying system matrices, it is a useful tool to diagnose abnormal generative mechanisms and unexpected temporal patterns. We demonstrate the proposed tensor learning framework’s effectiveness by experimenting with a synthetic data set and real-world spatiotemporal traffic speed data set. The results show the superiority of the proposed model in uncovering anomalous traffic network dynamics.