Functional Decomposition and Shapley Interactions for Interpreting Survival Models
Abstract
Hazard and survival functions are natural, interpretable targets in time-to-event prediction, but their inherent non-additivity fundamentally limits standard additive explanation methods. We introduce Survival Functional Decomposition (SurvFD), a principled approach for analyzing feature interactions in machine learning survival models. By decomposing higher-order effects into time-dependent and time-independent components, SurvFD offers a previously unrecognized perspective on survival explanations, explicitly characterizing when and why additive explanations fail. Building on this theoretical decomposition, we propose SurvSHAP-IQ, which extends Shapley interactions to time-indexed functions, providing a practical estimator for higher-order, time-dependent interactions. Together, SurvFD and SurvSHAP-IQ establish an interaction- and time-aware interpretability approach for survival modeling, with broad applicability across time-to-event prediction tasks.
Cite
@article{arxiv.2602.16505,
title = {Functional Decomposition and Shapley Interactions for Interpreting Survival Models},
author = {Sophie Hanna Langbein and Hubert Baniecki and Fabian Fumagalli and Niklas Koenen and Marvin N. Wright and Julia Herbinger},
journal= {arXiv preprint arXiv:2602.16505},
year = {2026}
}