Bayesian Temporal Factorization for Multidimensional Time Series Prediction

Abstract

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.

15 pages, 9 figures, 3 tables

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Cited by in corpus (16)

• A Nonconvex Low-Rank Tensor Completion Model for Spatiotemporal Traffic Data Imputation
• Low-Rank Autoregressive Tensor Completion for Spatiotemporal Traffic Data Imputation
• Dynamic Spatiotemporal Graph Convolutional Neural Networks for Traffic Data Imputation with Complex Missing Patterns
• ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputation
• Scalable Low-Rank Tensor Learning for Spatiotemporal Traffic Data Imputation
• Truncated tensor Schatten p-norm based approach for spatiotemporal traffic data imputation with complicated missing patterns
• Laplacian Convolutional Representation for Traffic Time Series Imputation
• Stacked Bidirectional and Unidirectional LSTM Recurrent Neural Network for Forecasting Network-wide Traffic State with Missing Values
• Spatial-temporal Conv-sequence Learning with Accident Encoding for Traffic Flow Prediction
• Low-Rank Autoregressive Tensor Completion for Multivariate Time Series Forecasting
• Anti-circulant dynamic mode decomposition with sparsity-promoting for highway traffic dynamics analysis
• Road Network Guided Fine-Grained Urban Traffic Flow Inference
• A Biased Deep Tensor Factorization Network For Tensor Completion
• Deep Markov Spatio-Temporal Factorization
• Incremental Bayesian tensor learning for structural monitoring data imputation and response forecasting
• Block Hankel Tensor ARIMA for Multiple Short Time Series Forecasting