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Neural Networks for Censored Expectile Regression Based on Data Augmentation

Wei Cao, Shanshan Wang

TL;DR

This work addresses censored data in expectile regression by introducing DAERNN, a data augmentation framework that imputes censored outcomes and iteratively updates ERNNs to estimate the $ au$-th conditional expectile $e_{ au}(Y|\boldsymbol{X})$ without requiring a parametric survival model. The method unifies right-, left-, and interval-censoring through a three-stage loop (data augmentation, model updating, prediction) and uses an MLP to model $m_{\tau}(\cdot)$ with MBGD optimization. Across simulations and two real datasets (WHAS and YVR), DAERNN consistently outperforms existing censored ERNNs (e.g., WERNN, DALinear) and achieves predictive performance close to full-data or oracle models, while maintaining reasonable computation time. This approach expands the applicability of censored ERNNs in risk, survival, and environmental contexts, though interpretability and high-dimensional scalability remain avenues for future work, including semiparametric hybrids and feature screening. The core ideas rely on seamlessly integrating data augmentation with neural expectile estimation to robustly handle censoring without explicit survival function specification, thereby delivering accurate, flexible modeling of heterogeneous distributions under censoring.

Abstract

Expectile regression neural networks (ERNNs) are powerful tools for capturing heterogeneity and complex nonlinear structures in data. However, most existing research has primarily focused on fully observed data, with limited attention paid to scenarios involving censored observations. In this paper, we propose a data augmentation based ERNNs algorithm, termed DAERNN, for modeling heterogeneous censored data. The proposed DAERNN is fully data driven, requires minimal assumptions, and offers substantial flexibility. Simulation studies and real data applications demonstrate that DAERNN outperforms existing censored ERNNs methods and achieves predictive performance comparable to models trained on fully observed data. Moreover, the algorithm provides a unified framework for handling various censoring mechanisms without requiring explicit parametric model specification, thereby enhancing its applicability to practical censored data analysis.

Neural Networks for Censored Expectile Regression Based on Data Augmentation

TL;DR

This work addresses censored data in expectile regression by introducing DAERNN, a data augmentation framework that imputes censored outcomes and iteratively updates ERNNs to estimate the -th conditional expectile without requiring a parametric survival model. The method unifies right-, left-, and interval-censoring through a three-stage loop (data augmentation, model updating, prediction) and uses an MLP to model with MBGD optimization. Across simulations and two real datasets (WHAS and YVR), DAERNN consistently outperforms existing censored ERNNs (e.g., WERNN, DALinear) and achieves predictive performance close to full-data or oracle models, while maintaining reasonable computation time. This approach expands the applicability of censored ERNNs in risk, survival, and environmental contexts, though interpretability and high-dimensional scalability remain avenues for future work, including semiparametric hybrids and feature screening. The core ideas rely on seamlessly integrating data augmentation with neural expectile estimation to robustly handle censoring without explicit survival function specification, thereby delivering accurate, flexible modeling of heterogeneous distributions under censoring.

Abstract

Expectile regression neural networks (ERNNs) are powerful tools for capturing heterogeneity and complex nonlinear structures in data. However, most existing research has primarily focused on fully observed data, with limited attention paid to scenarios involving censored observations. In this paper, we propose a data augmentation based ERNNs algorithm, termed DAERNN, for modeling heterogeneous censored data. The proposed DAERNN is fully data driven, requires minimal assumptions, and offers substantial flexibility. Simulation studies and real data applications demonstrate that DAERNN outperforms existing censored ERNNs methods and achieves predictive performance comparable to models trained on fully observed data. Moreover, the algorithm provides a unified framework for handling various censoring mechanisms without requiring explicit parametric model specification, thereby enhancing its applicability to practical censored data analysis.
Paper Structure (16 sections, 8 equations, 5 figures, 9 tables, 1 algorithm)

This paper contains 16 sections, 8 equations, 5 figures, 9 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methodology
  3. Model setup
  4. Data-Augmented Expectile Regression Neural Networks for Censored Data: DAERNN
  5. General framework of DAERNN
  6. Estimation of ERNNs model
  7. Simulation Studies
  8. Data generation
  9. Performance results
  10. Results for right-censoring case
  11. Results for other censoring types
  12. Computational cost
  13. Empirical study
  14. WHAS dataset
  15. YVR dataset
  16. ...and 1 more sections

Figures (5)

  • Figure 1: Flowchart of DAERNN Algorithm
  • Figure 2: Expectile Losses of predicted responses for different methods and settings at $\tau = 0.1, 0.3, 0.5, 0.7,$ and $0.9$, under right censoring with different censoring rate.
  • Figure 3: The boxplots of the predicted responses at $\tau = 0.1, 0.3, 0.5, 0.7, 0.9$ from the Oracle models and the $\textsf{DAERNN}$ under Model 1, across different error distributions and censoring rates.
  • Figure 4: The boxplots of the predicted responses at $\tau = 0.1, 0.3, 0.5, 0.7, 0.9$ from the Oracle models and the $\textsf{DAERNN}$ under Model 2, across different error distributions and censoring rates.
  • Figure 5: The expectile loss ($\text{EL}$) of Oracle,DALinear and DAERNN method for left-censoring case top panel and interval- censoring scenario bottom panle, with 25% and 50% censor rates.