# GP-VAE: Deep Probabilistic Time Series Imputation

arXiv: https://arxiv.org/abs/1907.04155 · HTML: https://mlsanity.com/paper/1907.04155/

## Key facts

- Cited by 172 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2019.

## Built on by (most cited first, 30 of 172)

- [Diffusion Models: A Comprehensive Survey of Methods and Applications](https://mlsanity.com/paper/2209.00796/) (2022)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglement](https://mlsanity.com/paper/2301.03028/) (2023)
- [DFA-NeRF: Personalized Talking Head Generation via Disentangled Face Attributes Neural Rendering](https://mlsanity.com/paper/2201.00791/) (2022)
- [Time-MMD: Multi-Domain Multimodal Dataset for Time Series Analysis](https://mlsanity.com/paper/2406.08627/) (2024)
- [Diffusion Models for Time Series Applications: A Survey](https://mlsanity.com/paper/2305.00624/) (2023)
- [PriSTI: A Conditional Diffusion Framework for Spatiotemporal Imputation](https://mlsanity.com/paper/2302.09746/) (2023)
- [Deep Learning for Multivariate Time Series Imputation: A Survey](https://mlsanity.com/paper/2402.04059/) (2024)
- [Neural Diffusion Processes](https://mlsanity.com/paper/2206.03992/) (2022)
- [Uncovering the Missing Pattern: Unified Framework Towards Trajectory Imputation and Prediction](https://mlsanity.com/paper/2303.16005/) (2023)
- [Utilizing Image Transforms and Diffusion Models for Generative Modeling of Short and Long Time Series](https://mlsanity.com/paper/2410.19538/) (2024)
- [Deep Latent State Space Models for Time-Series Generation](https://mlsanity.com/paper/2212.12749/) (2022)
- [GATGPT: A Pre-trained Large Language Model with Graph Attention Network for Spatiotemporal Imputation](https://mlsanity.com/paper/2311.14332/) (2023)
- [Missing Value Imputation on Multidimensional Time Series](https://mlsanity.com/paper/2103.01600/) (2021)
- [Autoregressive Conditional Neural Processes](https://mlsanity.com/paper/2303.14468/) (2023)
- [TSI-Bench: Benchmarking Time Series Imputation](https://mlsanity.com/paper/2406.12747/) (2024)
- [Networked Time Series Imputation via Position-aware Graph Enhanced Variational Autoencoders](https://mlsanity.com/paper/2305.18612/) (2023)
- [On the Challenges and Opportunities in Generative AI](https://mlsanity.com/paper/2403.00025/) (2024)
- [Deep Imputation of Missing Values in Time Series Health Data: A Review with Benchmarking](https://mlsanity.com/paper/2302.10902/) (2023)
- [Provably Convergent Schr"odinger Bridge with Applications to Probabilistic Time Series Imputation](https://mlsanity.com/paper/2305.07247/) (2023)
- [Promptable Game Models: Text-Guided Game Simulation via Masked Diffusion Models](https://mlsanity.com/paper/2303.13472/) (2023)
- [Probabilistic Imputation for Time-series Classification with Missing Data](https://mlsanity.com/paper/2308.06738/) (2023)
- [GinAR: An End-To-End Multivariate Time Series Forecasting Model Suitable for Variable Missing](https://mlsanity.com/paper/2405.11333/) (2024)
- [TSGM: A Flexible Framework for Generative Modeling of Synthetic Time Series](https://mlsanity.com/paper/2305.11567/) (2023)
- [SSD-TS: Exploring the Potential of Linear State Space Models for Diffusion Models in Time Series Imputation](https://mlsanity.com/paper/2410.13338/) (2024)
- [Decoupling Local and Global Representations of Time Series](https://mlsanity.com/paper/2202.02262/) (2022)
- [Retrieval Based Time Series Forecasting](https://mlsanity.com/paper/2209.13525/) (2022)

## Abstract (arXiv)

Multivariate time series with missing values are common in areas such as healthcare and finance, and have grown in number and complexity over the years. This raises the question whether deep learning methodologies can outperform classical data imputation methods in this domain. However, naive applications of deep learning fall short in giving reliable confidence estimates and lack interpretability. We propose a new deep sequential latent variable model for dimensionality reduction and data imputation. Our modeling assumption is simple and interpretable: the high dimensional time series has a lower-dimensional representation which evolves smoothly in time according to a Gaussian process. The non-linear dimensionality reduction in the presence of missing data is achieved using a VAE approach with a novel structured variational approximation. We demonstrate that our approach outperforms several classical and deep learning-based data imputation methods on high-dimensional data from the domains of computer vision and healthcare, while additionally improving the smoothness of the imputations and providing interpretable uncertainty estimates.