用偏斜拉普拉斯分布建模生存时间，实现精准个体化预测。
Learning Survival Distributions with the Asymmetric Laplace Distribution
- 基于偏斜拉普拉斯分布构建参数化生存分析模型
- 在真实与合成数据上优于传统参数与非参数方法
- 可直接输出均值、中位数等关键统计量，适合医疗预测场景
概率生存分析旨在根据协变量估计事件未来发生时间的分布。近年来，这类模型多采用非参数形式，避免通过离散化直接估计生存分布，而是通过监督学习在固定时间点估计事件发生概率，或在固定概率下估计事件时间（分位数）。受分位数回归启发，本文提出一种基于偏斜拉普拉斯分布（Asymmetric Laplace Distribution, ALD）的参数化生存分析方法。该分布支持均值、中位数、众数、方差及分位数等常用事件统计量的闭式计算。模型通过最大似然法优化，学习个体层面的ALD分布参数（位置、尺度、偏度）。在合成与真实世界数据上的大量实验表明，该方法在准确性、区分度和校准性方面均优于参数与非参数方法。
原文摘要 · Abstract (English)
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.
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