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Predicting individual mobility patterns is crucial across various applications. While current methods mainly focus on predicting the next location for personalized services like recommendations, they often fall short in supporting broader applications such as traffic management and epidemic control, which require longer period forecasts of human mobility. This study addresses mid-term mobility prediction, aiming to capture daily travel patterns and forecast trajectories for the upcoming day or week. We propose a novel Multi-scale Spatial-Temporal Decoupled Predictor (MSTDP) designed to efficiently extract spatial and temporal information by decoupling daily trajectories into distinct location-duration chains. Our approach employs a hierarchical encoder to model multi-scale temporal patterns, including daily recurrence and weekly periodicity, and utilizes a transformer-based decoder to globally attend to predicted information in the location or duration chain. Additionally, we introduce a spatial heterogeneous graph learner to capture multi-scale spatial relationships, enhancing semantic-rich representations. Extensive experiments, including statistical physics analysis, are conducted on large-scale mobile phone records in five cities (Boston, Los Angeles, SF Bay Area, Shanghai, and Tokyo), to demonstrate MSTDP's advantages. Applied to epidemic modeling in Boston, MSTDP significantly outperforms the best-performing baseline, achieving a remarkable 62.8% reduction in MAE for cumulative new cases.

Human mobility studies how people move to access their needed resources and plays a significant role in urban planning and location-based services. As a paramount task of human mobility modeling, next location prediction is challenging because of the diversity of users' historical trajectories that gives rise to complex mobility patterns and various contexts. Deep sequential models have been widely used to predict the next location by leveraging the inherent sequentiality of trajectory data. However, they do not fully leverage the relationship between locations and fail to capture users' multi-level preferences. This work constructs a trajectory graph from users' historical traces and proposes a \textbf{Traj}ectory \textbf{G}raph \textbf{E}nhanced \textbf{O}rientation-based \textbf{S}equential network (TrajGEOS) for next-location prediction tasks. TrajGEOS introduces hierarchical graph convolution to capture location and user embeddings. Such embeddings consider not only the contextual feature of locations but also the relation between them, and serve as additional features in downstream modules. In addition, we design an orientation-based module to learn users' mid-term preferences from sequential modeling modules and their recent trajectories. Extensive experiments on three real-world LBSN datasets corroborate the value of graph and orientation-based modules and demonstrate that TrajGEOS outperforms the state-of-the-art methods on the next location prediction task.

In this paper, we study an optimal control problem of a mean-field forward-backward stochastic system with random jumps in progressive structure, where both regular and singular controls are considered in our formula. In virtue of the variational technology, the related stochastic maximum principle (SMP) has been obtained, and it is essentially different from that in the classical predictable structure. Specifically, there are three parts in our SMP, i.e. continuous part, jump part and impulse part, and they are respectively used to characterize the characteristics of the optimal controls at continuous time, jump time and impulse time. This shows that the progressive structure can more accurately describe the characteristics of the optimal control at the jump time. We also give two linear-quadratic (LQ) examples to show the significance of our results.

Modeling human mobility helps to understand how people are accessing resources and physically contacting with each other in cities, and thus contributes to various applications such as urban planning, epidemic control, and location-based advertisement. Next location prediction is one decisive task in individual human mobility modeling and is usually viewed as sequence modeling, solved with Markov or RNN-based methods. However, the existing models paid little attention to the logic of individual travel decisions and the reproducibility of the collective behavior of population. To this end, we propose a Causal and Spatial-constrained Long and Short-term Learner (CSLSL) for next location prediction. CSLSL utilizes a causal structure based on multi-task learning to explicitly model the "\textit{when$\rightarrow$what$\rightarrow$where}", a.k.a. "\textit{time$\rightarrow$activity$\rightarrow$location}" decision logic. We next propose a spatial-constrained loss function as an auxiliary task, to ensure the consistency between the predicted and actual spatial distribution of travelers' destinations. Moreover, CSLSL adopts modules named Long and Short-term Capturer (LSC) to learn the transition regularities across different time spans. Extensive experiments on three real-world datasets show promising performance improvements of CSLSL over baselines and confirm the effectiveness of introducing the causality and consistency constraints. The implementation is available at https://github.com/urbanmobility/CSLSL., Comment: Updated version (We have corrected the title error in the previous version.)

Anomaly detection plays a crucial role in various real-world applications, including healthcare and finance systems. Owing to the limited number of anomaly labels in these complex systems, unsupervised anomaly detection methods have attracted great attention in recent years. Two major challenges faced by the existing unsupervised methods are: (i) distinguishing between normal and abnormal data in the transition field, where normal and abnormal data are highly mixed together; (ii) defining an effective metric to maximize the gap between normal and abnormal data in a hypothesis space, which is built by a representation learner. To that end, this work proposes a novel scoring network with a score-guided regularization to learn and enlarge the anomaly score disparities between normal and abnormal data. With such score-guided strategy, the representation learner can gradually learn more informative representation during the model training stage, especially for the samples in the transition field. We next propose a score-guided autoencoder (SG-AE), incorporating the scoring network into an autoencoder framework for anomaly detection, as well as other three state-of-the-art models, to further demonstrate the effectiveness and transferability of the design. Extensive experiments on both synthetic and real-world datasets demonstrate the state-of-the-art performance of these score-guided models (SGMs)., Comment: Final version in TNNLS