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Imputation with Inter-Series Information from Prototypes for Irregular Sampled Time Series

Zhihao Yu, Xu Chu, Liantao Ma, Yasha Wang, Wenwu Zhu

TL;DR

This work tackles imputing irregularly sampled multivariate time series by leveraging inter-series information through learned prototypes. It introduces PRIME, composed of a Prototype Memory, a bidirectional Prototype Gated Recurrent Unit (P-GRU), and a Prototype Refinement module, with dedicated prototype losses to maintain diversity and alignment with series representations. Empirical results on three real-world datasets show PRIME achieving up to $>26\%$ relative improvement in MSE over state-of-the-art methods, and robustness to observation rate and prototype count, while mitigating memorization effects. The approach offers a principled way to exploit cross-series patterns for improved imputation, with potential downstream benefits in healthcare, meteorology, and related domains.

Abstract

Irregularly sampled time series are ubiquitous, presenting significant challenges for analysis due to missing values. Despite existing methods address imputation, they predominantly focus on leveraging intra-series information, neglecting the potential benefits that inter-series information could provide, such as reducing uncertainty and memorization effect. To bridge this gap, we propose PRIME, a Prototype Recurrent Imputation ModEl, which integrates both intra-series and inter-series information for imputing missing values in irregularly sampled time series. Our framework comprises a prototype memory module for learning inter-series information, a bidirectional gated recurrent unit utilizing prototype information for imputation, and an attentive prototypical refinement module for adjusting imputations. We conducted extensive experiments on three datasets, and the results underscore PRIME's superiority over the state-of-the-art models by up to 26% relative improvement on mean square error.

Imputation with Inter-Series Information from Prototypes for Irregular Sampled Time Series

TL;DR

This work tackles imputing irregularly sampled multivariate time series by leveraging inter-series information through learned prototypes. It introduces PRIME, composed of a Prototype Memory, a bidirectional Prototype Gated Recurrent Unit (P-GRU), and a Prototype Refinement module, with dedicated prototype losses to maintain diversity and alignment with series representations. Empirical results on three real-world datasets show PRIME achieving up to relative improvement in MSE over state-of-the-art methods, and robustness to observation rate and prototype count, while mitigating memorization effects. The approach offers a principled way to exploit cross-series patterns for improved imputation, with potential downstream benefits in healthcare, meteorology, and related domains.

Abstract

Irregularly sampled time series are ubiquitous, presenting significant challenges for analysis due to missing values. Despite existing methods address imputation, they predominantly focus on leveraging intra-series information, neglecting the potential benefits that inter-series information could provide, such as reducing uncertainty and memorization effect. To bridge this gap, we propose PRIME, a Prototype Recurrent Imputation ModEl, which integrates both intra-series and inter-series information for imputing missing values in irregularly sampled time series. Our framework comprises a prototype memory module for learning inter-series information, a bidirectional gated recurrent unit utilizing prototype information for imputation, and an attentive prototypical refinement module for adjusting imputations. We conducted extensive experiments on three datasets, and the results underscore PRIME's superiority over the state-of-the-art models by up to 26% relative improvement on mean square error.
Paper Structure (22 sections, 18 equations, 5 figures, 3 tables)

This paper contains 22 sections, 18 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Time Series Imputation
  4. Prototype Learning
  5. Preliminary
  6. Prototype Recurrent Imputation Model
  7. Prototype Memory
  8. Prototype Gated Recurrent Unit
  9. Prototype Refinement
  10. Learning Objective
  11. Experiments
  12. Datasets
  13. Evaluation Settings
  14. Results and Analysis
  15. Ablation Study
  16. ...and 7 more sections

Figures (5)

  • Figure 1: The framework of the PRIME. Prototypes serve as inter-series information to assist in the imputation of time series in the bidirectional P-GRU and Prototype Refinement. The prototypes are updated with the representations from the time series
  • Figure 2: The results of different starting epochs to learn and utilize prototypes. The shadow represents the standard variance. The later the prototype is introduced, the worse the performance
  • Figure 3: Results for different observation rates on the PhysioNet Challenge 2012 dataset
  • Figure 4: Examples of imputation results on the Challenge 2012 dataset with 50% missing observations. For better observation, the values of SSGAN and PRIME are set to the existing observing data if available
  • Figure 5: Results for different numbers of prototypes on the PhysioNet Challenge 2012 dataset