Learning Survival Distributions with Individually Calibrated Asymmetric Laplace Distribution

Abstract

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.