# Bayesian Temporal Factorization for Multidimensional Time Series Prediction

arXiv: https://arxiv.org/abs/1910.06366 · HTML: https://mlsanity.com/paper/1910.06366/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Oct 2019.

## Built on by (most cited first, 30 of 47)

- [Deep Time Series Models: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2407.13278/) (2024)
- [PriSTI: A Conditional Diffusion Framework for Spatiotemporal Imputation](https://mlsanity.com/paper/2302.09746/) (2023)
- [ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputation](https://mlsanity.com/paper/2312.01728/) (2023)
- [Low-Rank Autoregressive Tensor Completion for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2104.14936/) (2021)
- [Laplacian Convolutional Representation for Traffic Time Series Imputation](https://mlsanity.com/paper/2212.01529/) (2022)
- [Online Metro Origin-Destination Prediction via Heterogeneous Information Aggregation](https://mlsanity.com/paper/2107.00946/) (2021)
- [PyPOTS: A Python Toolkit for Machine Learning on Partially-Observed Time Series](https://mlsanity.com/paper/2305.18811/) (2023)
- [Truncated tensor Schatten p-norm based approach for spatiotemporal traffic data imputation with complicated missing patterns](https://mlsanity.com/paper/2205.09390/) (2022)
- [Dynamic Spatiotemporal Graph Convolutional Neural Networks for Traffic Data Imputation with Complex Missing Patterns](https://mlsanity.com/paper/2109.08357/) (2021)
- [ST-GIN: An Uncertainty Quantification Approach in Traffic Data Imputation with Spatio-temporal Graph Attention and Bidirectional Recurrent United Neural Networks](https://mlsanity.com/paper/2305.06480/) (2023)
- [Distributional Drift Adaptation with Temporal Conditional Variational Autoencoder for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2209.00654/) (2022)
- [XXLTraffic: Expanding and Extremely Long Traffic forecasting beyond test adaptation](https://mlsanity.com/paper/2406.12693/) (2024)
- [Forecasting Sparse Movement Speed of Urban Road Networks with Nonstationary Temporal Matrix Factorization](https://mlsanity.com/paper/2203.10651/) (2022)
- [Phase-driven Domain Generalizable Learning for Nonstationary Time Series](https://mlsanity.com/paper/2402.05960/) (2024)
- [Mining of Switching Sparse Networks for Missing Value Imputation in Multivariate Time Series](https://mlsanity.com/paper/2409.09930/) (2024)
- [Road Network Guided Fine-Grained Urban Traffic Flow Inference](https://mlsanity.com/paper/2109.14251/) (2021)
- [Bayesian Low-rank Matrix Completion with Dual-graph Embedding: Prior Analysis and Tuning-free Inference](https://mlsanity.com/paper/2203.10044/) (2022)
- [A novel weighted approach for time series forecasting based on visibility graph](https://mlsanity.com/paper/2103.13870/) (2021)
- [Bayesian Complementary Kernelized Learning for Multidimensional Spatiotemporal Data](https://mlsanity.com/paper/2208.09978/) (2022)
- [Spatiotemporal Regularized Tucker Decomposition Approach for Traffic Data Imputation](https://mlsanity.com/paper/2305.06563/) (2023)
- [Guaranteed Multidimensional Time Series Prediction via Deterministic Tensor Completion Theory](https://mlsanity.com/paper/2501.15388/) (2025)
- [STAMImputer: Spatio-Temporal Attention MoE for Traffic Data Imputation](https://mlsanity.com/paper/2506.08054/) (2025)
- [Spatial-temporal Conv-sequence Learning with Accident Encoding for Traffic Flow Prediction](https://mlsanity.com/paper/2105.10478/) (2021)
- [Dynamical Deep Generative Latent Modeling of 3D Skeletal Motion](https://mlsanity.com/paper/2106.10393/) (2021)
- [A Deep Learning Framework for Traffic Data Imputation Considering Spatiotemporal Dependencies](https://mlsanity.com/paper/2304.09182/) (2023)
- [An End-to-End Model for Time Series Classification In the Presence of Missing Values](https://mlsanity.com/paper/2408.05849/) (2024)
- [Low Tensor-Rank Adaptation of Kolmogorov--Arnold Networks](https://mlsanity.com/paper/2502.06153/) (2025)
- [CoIFNet: A Unified Framework for Multivariate Time Series Forecasting with Missing Values](https://mlsanity.com/paper/2506.13064/) (2025)
- [Learning Higher-Order Interactions from Incomplete Spatiotemporal Data with Mixtures of Hypergraph Laplacians](https://mlsanity.com/paper/2605.17316/) (2026)
- [From XXLTraffic to EvoXXLTraffic: Scaling Traffic Forecasting to Sensor-Evolving Networks](https://mlsanity.com/paper/2605.29768/) (2026)

## Abstract (arXiv)

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.