GP-VAE: Deep Probabilistic Time Series Imputation (1907.04155v5)

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.

• The paper presents GP-VAE, a novel model that integrates Variational Autoencoders with Gaussian Processes for efficient time series imputation.
• It employs structured variational inference to capture temporal and cross-channel correlations with linear complexity, overcoming traditional GP limitations.
• Empirical results on synthetic and real-world datasets demonstrate enhanced imputation accuracy and reliable uncertainty estimates, crucial for domains like healthcare.

Deep Probabilistic Time Series Imputation with GP-VAE

The paper "GP-VAE: Deep Probabilistic Time Series Imputation" introduces an innovative approach to the challenge of time series data imputation, particularly in settings characterized by multivariate observations and missing values. This challenge is prevalent in domains such as healthcare and finance, where incomplete data can significantly impair downstream analyses and decision-making processes.

Model Overview

The authors propose a model built on an overview of Variational Autoencoders (VAE) and Gaussian Processes (GP), termed GP-VAE. The foundational assumption of the model is that high-dimensional time series data can be effectively embedded into a lower-dimensional latent space when conforming to Gaussian process dynamics. The GP-VAE leverages a structured variational approximation to facilitate efficient and robust inference, adapting a traditional VAE architecture for sequential data with temporal correlations.

Key Contributions and Methodology

1. Model Design: The model uses a VAE to encode incomplete high-dimensional time series into a latent space, which then follows the smooth dynamics of a Gaussian process. This approach allows it to capture both temporal relations within individual sequences and cross-channel (temporal) correlations in multivariate sequences.
2. Inference Efficiency: A structured variational inference method is employed, modeling posterior correlations in time and reducing the time complexity typically associated with GP inference. The variational distribution captures temporal dependencies with linear complexity concerning the number of time steps, which contrasts with the cubic complexity of naive GP implementations.
3. Multi-Scale Dynamics: The use of a Cauchy kernel for the GP prior permits the model to capture multi-scale temporal dynamics. This is particularly advantageous in medical data settings, wherein various physiological signals may fluctuate at different rates.
4. Empirical Validation: The authors benchmark their model across synthetic and real-world datasets—specifically, Healing MNIST, SPRITES, and Physionet—demonstrating superior performance over various classical and deep learning-based imputation methods. Notably, the GP-VAE achieved improved imputation accuracy and provided credible uncertainty estimates.

Practical and Theoretical Implications

The GP-VAE represents a significant advance in time series imputation by uniting the attributes of VAEs—capability in dimensionality reduction and handling missing data—and the temporal modeling strengths of GPs. This synergy allows for more accurate and interpretable imputations, marking a distinct advantage in domains where understanding uncertainty is crucial, such as healthcare.

Furthermore, the model's ability to provide interpretable posterior uncertainties supports practitioners in making more informed decisions, highlighting areas where predictions may be less certain due to sparse observations. The probabilistic nature of the model facilitates its integration into larger analytical frameworks where downstream tasks not only benefit from accurate imputation but also require quantifiable confidence measures.

Future Directions

The framework opens several pathways for future research, including:

• Expanding the model's applicability to other domains such as financial market analysis, where structured missingness and complex temporal interactions are common.
• Exploring kernel learning methods to potentially adapt the GP-VAE for different types of temporal patterns beyond those captured by the Cauchy kernel.
• Investigating the integration of more sophisticated neural architectures within the VAE framework to capture more intricate dependencies and representation hierarchies.

In conclusion, the GP-VAE model offers a robust new tool for practitioners dealing with incomplete time series data, combining the strengths of neural networks and probabilistic models. Its predictive performance alongside its probabilistic insights make it a notable contribution to the field, with broad applicability across diverse and complex datasets.