Latent Space Score-based Diffusion Model for Probabilistic Multivariate Time Series Imputation

TL;DR

The Latent Space Score-Based Diffusion Model (LSSDM) is proposed, which not only possesses the power to identify the latent distribution but also seamlessly integrates the diffusion model to obtain the high-fidelity imputed values and assess the uncertainty of the dataset.

Abstract

Accurate imputation is essential for the reliability and success of downstream tasks. Recently, diffusion models have attracted great attention in this field. However, these models neglect the latent distribution in a lower-dimensional space derived from the observed data, which limits the generative capacity of the diffusion model. Additionally, dealing with the original missing data without labels becomes particularly problematic. To address these issues, we propose the Latent Space Score-Based Diffusion Model (LSSDM) for probabilistic multivariate time series imputation. Observed values are projected onto low-dimensional latent space and coarse values of the missing data are reconstructed without knowing their ground truth values by this unsupervised learning approach. Finally, the reconstructed values are fed into a conditional diffusion model to obtain the precise imputed values of the time series. In this way, LSSDM not only possesses the power to identify the latent distribution but also seamlessly integrates the diffusion model to obtain the high-fidelity imputed values and assess the uncertainty of the dataset. Experimental results demonstrate that LSSDM achieves superior imputation performance while also providing a better explanation and uncertainty analysis of the imputation mechanism. The website of the code is \textit{https://github.com/gorgen2020/LSSDM\_imputation}.

Figures (3)

• Figure 1: The framework of LSSDM.
• Figure 2: MAE at different missing rates on different datasets.
• Figure 3: The latent distribution of different input on P12.