Learning Survival Distributions with Individually Calibrated Asymmetric Laplace Distribution

Survival analysis plays a critical role in modeling time-to-event outcomes across various domains. Although recent advances have focused on improving predictive accuracy and concordance, fine-grained calibration remains comparatively underexplored. In this paper, we propose a survival modeling framework based on the Individually Calibrated Asymmetric Laplace Distribution (ICALD), which unifies parametric and nonparametric approaches based on the ALD. We begin by revisiting the probabilistic foundation of the widely used pinball loss in quantile regression and its reparameterization as the asymmetry form of the ALD. This reparameterization enables a principled shift to parametric modeling while preserving the flexibility of nonparametric methods. Furthermore, we show theoretically that ICALD, with the quantile regression loss is probably approximately individually calibrated. Then we design an extended ICALD framework that supports both pre-calibration and post-calibration strategies. Extensive experiments on 14 synthetic and 7 real-world datasets demonstrate that our method achieves competitive performance in terms of predictive accuracy, concordance, and calibration, while outperforming 12 existing baselines including recent pre-calibration and post-calibration methods.