解决生存树中边界分叉偏好问题，提升模型稳定性和可解释性。
End-Cut Preference in Survival Trees
- 用平滑的S型函数替代硬阈值，缓解分叉倾向
- 理论与实证证明该方法能有效抑制边界偏倚
- 适合关注生存分析建模稳定性的研究者
端点分叉偏好（ECP）问题指在使用贪婪搜索选择最优切分点时，倾向于选择特征取值范围边缘的切分点，这在生存树中同样存在。该问题可能导致极不平衡的分叉、信号弱化，并生成不稳定且难以解释的树结构。本文提出一种平滑的S型代理（SSS）方法，将硬阈值指示函数替换为平滑的S型函数。通过理论分析和数值实验，证明该方法能有效缓解或避免ECP问题。
原文摘要 · Abstract (English)
The end-cut preference (ECP) problem, referring to the tendency to favor split points near the boundaries of a feature's range, is a well-known issue in CART (Breiman et al., 1984). ECP may induce highly imbalanced and biased splits, obscure weak signals, and lead to tree structures that are both unstable and difficult to interpret. For survival trees, we show that ECP also arises when using greedy search to select the optimal cutoff point by maximizing the log-rank test statistic. To address this issue, we propose a smooth sigmoid surrogate (SSS) approach, in which the hard-threshold indicator function is replaced by a smooth sigmoid function. We further demonstrate, both theoretically and through numerical illustrations, that SSS provides an effective remedy for mitigating or avoiding ECP.
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