GP-VAE: Deep Probabilistic Time Series Imputation

2019/07/09 by Vincent Fortuin, Fortuin, Vincent, Dmitry Baranchuk +5 · 30 citations
Computer Science · Mathematics · #Artificial intelligence #Computer science #Curse of dimensionality #Data mining #Deep learning #Dimensionality reduction #FOS: Computer and information sciences #Gaussian #Gaussian Processes and Bayesian Inference #Gaussian process #Generative Adversarial Networks and Image Synthesis #Imputation (statistics) #Interpretability #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning in Healthcare #Machine learning #Missing data #Multivariate statistics #Pattern recognition (psychology) #Probabilistic logic #Time series #cs.LG #stat.ML

paper · pdf · doi:10.48550/arxiv.1907.04155

published in arXiv (Cornell University) 108, 1651-1661 (Cornell University) · Accepted for publication at the 23rd International Conference on Artificial Intelligence and Statistics (AISTATS 2020)

openalex publication_date 2019/07/09 · arxiv created 2020/02/20 · arxiv updated 2020/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Auto-Encoding Variational Bayes
• Gradient-based learning applied to document recognition
• EDDI: Efficient Dynamic Discovery of High-Value Information with Partial VAE
• Variational Inference: A Review for Statisticians

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