Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Generative Conditional Missing Imputation Networks

George Sun, Yi-Hui Zhou

TL;DR

This work tackles missing data imputation by introducing Generative Conditional Missing Imputation Networks (GCMI), a framework that learns the conditional distribution $p(x_j|X_{(-j)})$ through an ensemble of generators and discriminators. By integrating a multiple-imputation strategy via chained equations, GCMI enhances stability and accuracy across MCAR, MAR, and MNAR settings, and is validated on synthetic data and real ICU datasets (MIMIC-III and eICU). Theoretical analysis shows the approach aligns generator outputs with the true conditionals, minimizing a Pearson chi-squared divergence, while practical experiments demonstrate superior imputation performance relative to state-of-the-art methods. The results suggest GCMI is a robust tool for high-quality imputation in complex, high-m sparsity domains, with an open-source implementation planned.

Abstract

In this study, we introduce a sophisticated generative conditional strategy designed to impute missing values within datasets, an area of considerable importance in statistical analysis. Specifically, we initially elucidate the theoretical underpinnings of the Generative Conditional Missing Imputation Networks (GCMI), demonstrating its robust properties in the context of the Missing Completely at Random (MCAR) and the Missing at Random (MAR) mechanisms. Subsequently, we enhance the robustness and accuracy of GCMI by integrating a multiple imputation framework using a chained equations approach. This innovation serves to bolster model stability and improve imputation performance significantly. Finally, through a series of meticulous simulations and empirical assessments utilizing benchmark datasets, we establish the superior efficacy of our proposed methods when juxtaposed with other leading imputation techniques currently available. This comprehensive evaluation not only underscores the practicality of GCMI but also affirms its potential as a leading-edge tool in the field of statistical data analysis.

Generative Conditional Missing Imputation Networks

TL;DR

This work tackles missing data imputation by introducing Generative Conditional Missing Imputation Networks (GCMI), a framework that learns the conditional distribution through an ensemble of generators and discriminators. By integrating a multiple-imputation strategy via chained equations, GCMI enhances stability and accuracy across MCAR, MAR, and MNAR settings, and is validated on synthetic data and real ICU datasets (MIMIC-III and eICU). Theoretical analysis shows the approach aligns generator outputs with the true conditionals, minimizing a Pearson chi-squared divergence, while practical experiments demonstrate superior imputation performance relative to state-of-the-art methods. The results suggest GCMI is a robust tool for high-quality imputation in complex, high-m sparsity domains, with an open-source implementation planned.

Abstract

In this study, we introduce a sophisticated generative conditional strategy designed to impute missing values within datasets, an area of considerable importance in statistical analysis. Specifically, we initially elucidate the theoretical underpinnings of the Generative Conditional Missing Imputation Networks (GCMI), demonstrating its robust properties in the context of the Missing Completely at Random (MCAR) and the Missing at Random (MAR) mechanisms. Subsequently, we enhance the robustness and accuracy of GCMI by integrating a multiple imputation framework using a chained equations approach. This innovation serves to bolster model stability and improve imputation performance significantly. Finally, through a series of meticulous simulations and empirical assessments utilizing benchmark datasets, we establish the superior efficacy of our proposed methods when juxtaposed with other leading imputation techniques currently available. This comprehensive evaluation not only underscores the practicality of GCMI but also affirms its potential as a leading-edge tool in the field of statistical data analysis.
Paper Structure (20 sections, 10 equations, 5 figures, 2 tables)

This paper contains 20 sections, 10 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Generative Conditional Networks for Missing Imputation (GCMI)
  4. Theoretical Properties of GCMI
  5. Algorithm
  6. Experiments
  7. Synthetic data
  8. Real-data
  9. MIMIC-III Laboratory Data
  10. eICU Collaborative Research Database
  11. Experiment Setup
  12. Results
  13. Synthetic data imputation
  14. Imputation Performance on Real ICU Datasets
  15. MIMIC-III Critical Care Data
  16. ...and 5 more sections

Figures (5)

  • Figure 1: GCIN: $G$ takes a random noise vector $z$ as input, conditioned on the given condition $X_{(-j)}$, and produces the imputed value for $X_{(j)}$ as output. $D$ aims to evaluate input data samples and differentiate between real and imputed values, considering the given condition $X_{(-j)}$. The ReLU activation function is incorporated within the generator to introduce non-linearity and enhance the model's expressive capacity.
  • Figure 2: GCMI: Perform initial imputation for missing values in X using a chosen method and sort variables based on missing proportions. Iterate through each column $j$ and fit a generative conditional imputation neural network (GCIN) on $\mathbf{x}_{j}^{obs} \sim G_{j} ( \mathbf{X}_{(-j)}^{obs}, \: \mathbf{z} )$. Once the GCIN algorithm converges, update $\mathbf{X}$ with $\mathbf{x}_{j}^{mis} \leftarrow G_{j} ( \mathbf{X}_{(-j)}^{mis}, \: \mathbf{z} )$ and check convergence for imputation.
  • Figure 3: Missing Proportions of the 36 Common Laboratory Tests in MIMIC-III.
  • Figure 4: Covariate matrix missing imputation error measured by RMSE under three missing mechanisms and a range of different missing rates
  • Figure :