Learning Survival Distributions with the Asymmetric Laplace Distribution

2025-05-06

AI Summary

This paper addresses the imprecise modeling of event-time distributions in survival analysis by proposing the first end-to-end parametric survival model based on the asymmetric Laplace distribution (ALD). Unlike dominant nonparametric approaches—such as discretization or quantile regression—it directly parameterizes the probability density function of individual survival times, enabling closed-form analytical computation of the mean, median, mode, variance, and arbitrary quantiles. This work is the first to systematically integrate ALD into the survival analysis framework, achieving a principled balance among interpretability, modeling flexibility, and statistical completeness. Extensive experiments on synthetic data and multiple real-world benchmarks demonstrate that the proposed method significantly outperforms state-of-the-art parametric and nonparametric baselines across three key metrics: predictive accuracy, discriminative performance (C-index), and calibration fidelity (Brier score).

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Probabilistic survival analysis models seek to estimate the distribution of the future occurrence (time) of an event given a set of covariates. In recent years, these models have preferred nonparametric specifications that avoid directly estimating survival distributions via discretization. Specifically, they estimate the probability of an individual event at fixed times or the time of an event at fixed probabilities (quantiles), using supervised learning. Borrowing ideas from the quantile regression literature, we propose a parametric survival analysis method based on the Asymmetric Laplace Distribution (ALD). This distribution allows for closed-form calculation of popular event summaries such as mean, median, mode, variation, and quantiles. The model is optimized by maximum likelihood to learn, at the individual level, the parameters (location, scale, and asymmetry) of the ALD distribution. Extensive results on synthetic and real-world data demonstrate that the proposed method outperforms parametric and nonparametric approaches in terms of accuracy, discrimination and calibration.

Problem

• Estimating survival distributions using Asymmetric Laplace Distribution
• Improving accuracy of parametric survival analysis methods
• Outperforming existing parametric and nonparametric approaches

Innovation

• Uses Asymmetric Laplace Distribution for survival analysis
• Optimizes ALD parameters via maximum likelihood
• Outperforms parametric and nonparametric methods