arXiv:2606.06393cs.LG2026-06

提出一套适用于右删失生存数据的合理评分框架,解决传统方法失效问题。

Proper Scoring Rules for Right-Censored Survival Data

  • 先映射预测分布至删失机制,再应用原始评分
  • 在多种删失条件下仍能正确排序最优预测
  • 适合生存分析、医疗预测等需处理删失数据的研究

合理评分规则为概率预测的训练与评估提供了严格的理论基础。然而,在存在右删失的情况下,事件时间仅部分可观测,使得标准评分规则无法直接使用。本文提出一种基于简单思想的右删失生存结果评分框架:首先将预测分布通过删失机制映射,然后在诱导的观测数据分布上应用基础的合理评分。该方法得到固定删失时间下的局部评分,以及删失时间随机或部分观测时的边际评分。由此构造的评分框架统一了已知的右删失似然和IPCW型准则,并推导出右删失版的CRPS、分位数损失、Brier评分与能量评分。我们证明,在条件独立删失假设下,边际评分是合理的,且在可识别区域严格合理。相同原则还导出了删失回归(censored engression),一种用于多元右删失生存建模的样本学习目标。实验表明,在多种删失情形下,本方法能正确排序最优预测,而依赖预测的插值加权评分会出现排名反转;删失回归也显著优于对删失结果的朴素训练。

原文摘要 · Abstract (English)

Proper scoring rules provide a rigorous theoretical basis for the training and evaluation of probabilistic forecasts. However, in the presence of right censoring, the event time is only partially observed, rendering conventional scoring rules inapplicable in their standard form. We propose a framework for proper scoring of right-censored survival outcomes based on a simple idea: first, map the predictive distribution through the censoring mechanism, then apply the underlying proper score on the induced observed-data law. This yields localized scores for fixed censoring times and marginalized scores when the censoring time is random or only partially observed. The resulting construction recovers familiar right-censored likelihood and IPCW-type criteria within a coherent framework, while also yielding right-censored versions of the CRPS, pinball loss, Brier score, and energy score. We show that the marginalized score is proper under conditional independent censoring and strictly proper on the identifiable region. The same principle also leads to censored engression, a sample-based learning objective for multivariate right-censored survival modeling. In experiments, our scores correctly rank the oracle forecast across several censoring regimes, whereas forecast-dependent plug-in weighted scores can exhibit ranking reversals. Censored engression likewise substantially improves over naive training on censored outcomes.

生存分析删失数据评分规则概率预测

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