arXiv:2607.16802cs.LGcs.CV2026-07被引 1

提出新损失函数,让模型训练时损失值直接反映预测准确性。

Value-Monotonicity Matters: A Concordance Loss for Deep Survival Prediction

论文配图:Value-Monotonicity Matters: A Concordance Loss for Deep Survival Prediction
图 1 · 摘自论文原文
  • 设计值单调的SCL损失,使损失下降时排名性能持续提升。
  • 在18个数据集上,C-index与标准方法相当,且损失与指标相关性高达0.99。
  • 适合小样本、高删失的癌症数据端到端训练,可替代耗时的C-index评估。

深度生存模型通常用协和指数(C-index)评估,但训练时多采用似然损失(如Cox部分似然、离散时间负对数似然等)。这种不匹配在验证阶段可接受,但在小样本、高删失的肿瘤学队列中,频繁计算C-index代价高昂。本文发现似然损失不可靠:某些方向上损失下降而C-index不变,导致损失值与性能脱钩。为此提出符号函数协和损失(SCL),其值近似为1减去温度调整后的C-index,确保优化过程中损失越低,排名性能越高。SCL与架构无关,线性模型下退化为凸生存排序支持向量机。在四个模态的18个数据集上,统一五折交叉验证,SCL达到与标准似然损失相当的判别能力,且在17个数据集中排名第一或在1个标准差内。相比似然损失-0.03至0.53的相关性,SCL在训练中保持0.96至0.99的强相关性。校准性(集成Brier分数)也相当。SCL提供可靠的值单调优化目标,可作为昂贵验证过程的替代信号。

原文摘要 · Abstract (English)

Deep survival models are evaluated almost exclusively by the concordance index (C-index), yet they are commonly trained using likelihood objectives such as the Cox partial likelihood, discrete-time negative log-likelihood, and DeepHit likelihood. This mismatch is usually considered acceptable because the C-index can be recomputed on validation data during training. However, for end-to-end training of high-capacity encoders on small, heavily censored oncology cohorts, frequent C-index evaluation is computationally expensive, making the loss value itself an important signal for monitoring, early stopping, and model selection. We show that likelihood losses are unreliable for this purpose and propose a value-monotone concordance loss. We prove that every strictly proper survival likelihood admits directions where the loss decreases while the C-index remains unchanged, causing the loss value to decouple from ranking performance. We then study a sigmoid concordance loss (SCL), whose value approximates one minus the C-index up to a temperature term, ensuring that lower loss corresponds to higher C-index during optimization. The loss is architecture agnostic and reduces to a convex survival ranking support vector machine for linear models. Across eighteen datasets from four modalities using a unified five-fold cross-validation protocol, SCL achieves discrimination comparable to standard likelihood losses and is the best or within one standard deviation of the best C-index. Unlike likelihood losses, SCL maintains a strong correlation between loss value and C-index during training, with rank correlations of 0.96 to 0.99 compared with -0.03 to 0.53 for likelihood losses. Calibration measured by the integrated Brier score is comparable. SCL provides a value-monotone optimization objective whose value can serve as a reliable surrogate for the C-index during expensive end-to-end training.

生存分析损失函数医学AIC-index

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