Bayesian Temporal Factorization for Multidimensional Time Series Prediction

TL;DR

This paper introduces a Bayesian temporal factorization framework that models large-scale multidimensional time series data with missing values, enabling accurate predictions and uncertainty quantification without data imputation.

Contribution

It integrates low-rank tensor factorization and VAR processes into a probabilistic model for improved spatiotemporal data prediction with missing values.

Findings

Outperforms existing methods in real-world datasets

Provides effective uncertainty estimates

Handles large-scale, high-dimensional data efficiently

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.