Deep generative models have demonstrated their effectiveness in learning latent representation and modeling complex dependencies of time series. In this article, we present a smoothness-inducing sequential variational auto-encoder (VAE) (SISVAE) model for the robust estimation and anomaly detection of multidimensional time series. Our model is based on VAE, and its backbone is fulfilled by a recurrent neural network to capture latent temporal structures of time series for both the generative model and the inference model. Specifically, our model parameterizes mean and variance for each time-stamp with flexible neural networks, resulting in a nonstationary model that can work without the assumption of constant noise as commonly made by existing Markov models. However, such flexibility may cause the model fragile to anomalies. To achieve robust density estimation which can also benefit detection tasks, we propose a smoothness-inducing prior over possible estimations. The proposed prior works as a regularizer that places penalty at nonsmooth reconstructions. Our model is learned efficiently with a novel stochastic gradient variational Bayes estimator. In particular, we study two decision criteria for anomaly detection: reconstruction probability and reconstruction error. We show the effectiveness of our model on both synthetic data sets and public real-world benchmarks.

Jidong Tian, Yitian Li, Wenqing Chen, Liqiang Xiao, Hao He, Yaohui Jin. Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing. 2021.

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 “when→what→where”, a.k.a. “time→activity→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.