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Deep End-to-End Survival Analysis with Temporal Consistency

Mariana Vargas Vieyra, Pascal Frossard

TL;DR

This study presents a novel Survival Analysis algorithm designed to efficiently handle large-scale longitudinal data, drawing inspiration from Reinforcement Learning principles, particularly the Deep Q-Network paradigm, extending Temporal Learning concepts to Survival Regression.

Abstract

In this study, we present a novel Survival Analysis algorithm designed to efficiently handle large-scale longitudinal data. Our approach draws inspiration from Reinforcement Learning principles, particularly the Deep Q-Network paradigm, extending Temporal Learning concepts to Survival Regression. A central idea in our method is temporal consistency, a hypothesis that past and future outcomes in the data evolve smoothly over time. Our framework uniquely incorporates temporal consistency into large datasets by providing a stable training signal that captures long-term temporal relationships and ensures reliable updates. Additionally, the method supports arbitrarily complex architectures, enabling the modeling of intricate temporal dependencies, and allows for end-to-end training. Through numerous experiments we provide empirical evidence demonstrating our framework's ability to exploit temporal consistency across datasets of varying sizes. Moreover, our algorithm outperforms benchmarks on datasets with long sequences, demonstrating its ability to capture long-term patterns. Finally, ablation studies show how our method enhances training stability.

Deep End-to-End Survival Analysis with Temporal Consistency

TL;DR

This study presents a novel Survival Analysis algorithm designed to efficiently handle large-scale longitudinal data, drawing inspiration from Reinforcement Learning principles, particularly the Deep Q-Network paradigm, extending Temporal Learning concepts to Survival Regression.

Abstract

In this study, we present a novel Survival Analysis algorithm designed to efficiently handle large-scale longitudinal data. Our approach draws inspiration from Reinforcement Learning principles, particularly the Deep Q-Network paradigm, extending Temporal Learning concepts to Survival Regression. A central idea in our method is temporal consistency, a hypothesis that past and future outcomes in the data evolve smoothly over time. Our framework uniquely incorporates temporal consistency into large datasets by providing a stable training signal that captures long-term temporal relationships and ensures reliable updates. Additionally, the method supports arbitrarily complex architectures, enabling the modeling of intricate temporal dependencies, and allows for end-to-end training. Through numerous experiments we provide empirical evidence demonstrating our framework's ability to exploit temporal consistency across datasets of varying sizes. Moreover, our algorithm outperforms benchmarks on datasets with long sequences, demonstrating its ability to capture long-term patterns. Finally, ablation studies show how our method enhances training stability.

Paper Structure

This paper contains 22 sections, 13 equations, 3 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related work
  3. Preliminaries
  4. Dynamic Survival Analysis
  5. Maximum Likelihood Estimation
  6. Temporal Consistency in Survival Analysis
  7. Proposed Method
  8. Scalable Survival Regression with Temporal Consistency
  9. Pseudo-target and pseudo-weight coefficients.
  10. Training.
  11. Connection to TCSR and DQN
  12. Experiments
  13. Small datasets
  14. Large datasets
  15. Effect of $\tau$ on the variability of the estimates
  16. ...and 7 more sections

Figures (3)

  • Figure 1: Performance of event prediction in small datasets. We present results in terms of the CI (higher is better) and IBS (lower is better). The error bars represent the mean and standard deviation over five random seeds.
  • Figure 2: Variability of estimates for different values of $\tau$ with $\lambda = 0$ for datasets with varying horizons: (a) $H=30$, (b) $H=50$, and (c) $H=100$. The red line indicates the mean value.
  • Figure 3: Concordance Index (left, higher is better) and Integrated Brier Score (right, lower is better) on the test set across five random splits for different values of $\tau$, $\lambda=0$, and dataset horizons: (a) $H=30$, (b) $H=50$, and (c) $H=100$.