KAPLAN: 用于生存分析的Kolmogorov-Arnold可预测可学习激活网络
KAPLAN: Kolmogorov-Arnold Prognostic Learnable Activation Networks for Survival Analysis
AI总结：
提出KAPLAN-HR模型，利用B样条Kolmogorov-Arnold网络非参数估计条件风险函数，通过深层架构自动捕捉交互和时变效应，并证明其收敛速率仅依赖于表示平滑性，从而缓解维度灾难，在六个临床数据集上达到或超越现有方法。
摘要：
生存分析旨在建模协变量和时间如何共同影响右删失下的事件时间分布。经典方法如Cox模型和广义加性模型（GAM）需要手动指定交互和时变效应，这在丰富的临床数据集上越来越不切实际。我们引入了KAPLAN-HR，一种B样条Kolmogorov-Arnold网络（KAN），用于非参数估计条件风险函数作为协变量和时间的联合函数。单层KAPLAN-HR模型恢复GAM，而更深层的架构通过组合捕捉交互和时变效应。我们为非参数KAN风险估计器建立了收敛速率，该速率仅依赖于底层KAN表示的平滑性，而不依赖于协变量维度，从而缓解了KAN可表示目标的维度灾难。在六个临床基准数据集的评估中，KAPLAN-HR匹配或超过了已建立的统计和深度学习生存方法的预测性能。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
