用数学构造的神经网络自动学习病人特征与时间对生存风险的影响。
KAPLAN: Kolmogorov-Arnold Prognostic Learnable Activation Networks for Survival Analysis
- 基于柯尔莫哥洛夫-阿诺德定理设计可解释的神经网络，自动捕捉变量与时间的复杂关系。
- 在6个临床数据集上预测性能优于或媲美传统统计模型和深度学习方法。
- 适合需要高可解释性且处理多维临床数据的医疗预测场景。
生存分析旨在建模协变量与时间共同作用下事件发生时间的分布，面对右删失数据。经典方法如Cox模型和广义加性模型（GAMs）需手动指定交互项和时变效应，在丰富的临床数据下日益不切实际。我们提出KAPLAN-HR，一种基于B样条的柯尔莫哥洛夫-阿诺德网络（KAN），用于非参数估计条件风险函数，该函数是协变量与时间的联合函数。单层KAPLAN-HR模型可恢复GAM结构，更深架构通过组合捕捉交互作用和时变效应。我们建立了非参数KAN风险估计器的收敛速率，其仅依赖于底层KAN表示的光滑性，而非协变量维度，从而缓解了对可被KAN表示目标的维数灾难问题。在六个临床基准数据集上的评估显示，KAPLAN-HR的预测性能匹配或超过现有统计与深度学习生存分析方法。
原文摘要 · Abstract (English)
Survival analysis aims to model how covariates and time jointly shape the time-to-event distribution under right censoring. Classical methods such as the Cox model and generalised additive models (GAMs) require interactions and time-varying effects to be manually specified, which is increasingly impractical on rich clinical datasets. We introduce KAPLAN-HR, a B-spline Kolmogorov-Arnold Network (KAN) for nonparametric estimation of the conditional hazard as a joint function of covariates and time. A single-layer KAPLAN-HR model recovers a GAM, while deeper architectures capture interactions and time-varying effects through composition. We establish a convergence rate for the nonparametric KAN hazard estimator that depends only on the smoothness of the underlying KAN representation and not on the covariate dimension, thereby mitigating the curse of dimensionality for KAN-representable targets. In evaluations over six clinical benchmark datasets, KAPLAN-HR matches or exceeds the predictive performance of established statistical and deep learning survival methods.
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