# BayOTIDE: Bayesian Online Multivariate Time series Imputation with functional decomposition

arXiv: https://arxiv.org/abs/2308.14906 · HTML: https://mlsanity.com/paper/2308.14906/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 50 references that are in the map.
- First posted on arXiv 28 Aug 2023.

## Builds on (most cited first, 22 of 22)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Expectation Propagation for approximate Bayesian inference](https://mlsanity.com/paper/1301.2294/) (2013)
- [GP-VAE: Deep Probabilistic Time Series Imputation](https://mlsanity.com/paper/1907.04155/) (2019)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [CoST: Contrastive Learning of Disentangled Seasonal-Trend Representations for Time Series Forecasting](https://mlsanity.com/paper/2202.01575/) (2022)
- [Learning Temporally Causal Latent Processes from General Temporal Data](https://mlsanity.com/paper/2110.05428/) (2021)
- [Temporally Disentangled Representation Learning](https://mlsanity.com/paper/2210.13647/) (2022)
- [NAOMI: Non-Autoregressive Multiresolution Sequence Imputation](https://mlsanity.com/paper/1901.10946/) (2019)
- [RobustSTL: A Robust Seasonal-Trend Decomposition Algorithm for Long Time Series](https://mlsanity.com/paper/1812.01767/) (2018)
- [Time Series Data Imputation: A Survey on Deep Learning Approaches](https://mlsanity.com/paper/2011.11347/) (2020)
- [Uncertainty-Aware Variational-Recurrent Imputation Network for Clinical Time Series](https://mlsanity.com/paper/2003.00662/) (2020)
- [Provably Convergent Schr"odinger Bridge with Applications to Probabilistic Time Series Imputation](https://mlsanity.com/paper/2305.07247/) (2023)
- [SaDI: A Self-adaptive Decomposed Interpretable Framework for Electric Load Forecasting under Extreme Events](https://mlsanity.com/paper/2306.08299/) (2023)
- [Multivariate Bayesian Structural Time Series Model](https://mlsanity.com/paper/1801.03222/) (2018)
- [Conditional Expectation Propagation](https://mlsanity.com/paper/1910.12360/) (2019)

## Built on by (most cited first, 10 of 10)

- [Sports-Traj: A Unified Trajectory Generation Model for Multi-Agent Movement in Sports](https://mlsanity.com/paper/2405.17680/) (2024)
- [Zero-shot Imputation with Foundation Inference Models for Dynamical Systems](https://mlsanity.com/paper/2402.07594/) (2024)
- [Task-oriented Time Series Imputation Evaluation via Generalized Representers](https://mlsanity.com/paper/2410.06652/) (2024)
- [Continuous Representation Methods, Theories, and Applications: An Overview and Perspectives](https://mlsanity.com/paper/2505.15222/) (2025)
- [Causal View of Time Series Imputation: Some Identification Results on Missing Mechanism](https://mlsanity.com/paper/2505.07180/) (2025)
- [Rating Quality of Diverse Time Series Data by Meta-learning from LLM Judgment](https://mlsanity.com/paper/2506.01290/) (2025)
- [Lightweight Time Series Data Valuation on Time Series Foundation Models via In-Context Finetuning](https://mlsanity.com/paper/2511.11648/) (2025)
- [tBayes-MICE: A Bayesian Approach to Multiple Imputation for Time Series Data](https://mlsanity.com/paper/2603.27142/) (2026)
- [EVIL: Evolving Interpretable Algorithms for Zero-Shot Inference on Event Sequences and Time Series with LLMs](https://mlsanity.com/paper/2604.15787/) (2026)
- [QiYao-I: A Manifold Based Foundation Model for Irregular Multivariate Time Series Forecasting](https://mlsanity.com/paper/2610.06936/) (2026)

## Abstract (arXiv)

In real-world scenarios like traffic and energy, massive time-series data with missing values and noises are widely observed, even sampled irregularly. While many imputation methods have been proposed, most of them work with a local horizon, which means models are trained by splitting the long sequence into batches of fit-sized patches. This local horizon can make models ignore global trends or periodic patterns. More importantly, almost all methods assume the observations are sampled at regular time stamps, and fail to handle complex irregular sampled time series arising from different applications. Thirdly, most existing methods are learned in an offline manner. Thus, it is not suitable for many applications with fast-arriving streaming data. To overcome these limitations, we propose BayOTIDE: Bayesian Online Multivariate Time series Imputation with functional decomposition. We treat the multivariate time series as the weighted combination of groups of low-rank temporal factors with different patterns. We apply a group of Gaussian Processes (GPs) with different kernels as functional priors to fit the factors. For computational efficiency, we further convert the GPs into a state-space prior by constructing an equivalent stochastic differential equation (SDE), and developing a scalable algorithm for online inference. The proposed method can not only handle imputation over arbitrary time stamps, but also offer uncertainty quantification and interpretability for the downstream application. We evaluate our method on both synthetic and real-world datasets.We release the code at {https://github.com/xuangu-fang/BayOTIDE}