# Functional Decomposition and Shapley Interactions for Interpreting Survival Models

arXiv: https://arxiv.org/abs/2602.16505 · HTML: https://mlsanity.com/paper/2602.16505/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 68 references that are in the map.
- First posted on arXiv 18 Feb 2026.

## Builds on (most cited first, 23 of 23)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Attention-based Deep Multiple Instance Learning](https://mlsanity.com/paper/1802.04712/) (2018)
- [All Models are Wrong, but Many are Useful: Learning a Variable's Importance by Studying an Entire Class of Prediction Models Simultaneously](https://mlsanity.com/paper/1801.01489/) (2018)
- [Time-to-Event Prediction with Neural Networks and Cox Regression](https://mlsanity.com/paper/1907.00825/) (2019)
- [The Shapley Taylor Interaction Index](https://mlsanity.com/paper/1902.05622/) (2019)
- [True to the Model or True to the Data?](https://mlsanity.com/paper/2006.16234/) (2020)
- [Towards Human-centered Explainable AI: A Survey of User Studies for Model Explanations](https://mlsanity.com/paper/2210.11584/) (2022)
- [Deep Learning for Survival Analysis: A Review](https://mlsanity.com/paper/2305.14961/) (2023)
- [Faith-Shap: The Faithful Shapley Interaction Index](https://mlsanity.com/paper/2203.00870/) (2022)
- [From Shapley Values to Generalized Additive Models and back](https://mlsanity.com/paper/2209.04012/) (2022)
- [SHAP-IQ: Unified Approximation of any-order Shapley Interactions](https://mlsanity.com/paper/2303.01179/) (2023)
- [Survival regression with accelerated failure time model in XGBoost](https://mlsanity.com/paper/2006.04920/) (2020)
- [SurvLIME: A method for explaining machine learning survival models](https://mlsanity.com/paper/2003.08371/) (2020)
- [SurvSHAP(t): Time-dependent explanations of machine learning survival models](https://mlsanity.com/paper/2208.11080/) (2022)
- [KernelSHAP-IQ: Weighted Least-Square Optimization for Shapley Interactions](https://mlsanity.com/paper/2405.10852/) (2024)
- [Using Shapley Values and Variational Autoencoders to Explain Predictive Models with Dependent Mixed Features](https://mlsanity.com/paper/2111.13507/) (2021)
- [Regression-adjusted Monte Carlo Estimators for Shapley Values and Probabilistic Values](https://mlsanity.com/paper/2506.11849/) (2025)
- [SurvSet: An open-source time-to-event dataset repository](https://mlsanity.com/paper/2203.03094/) (2022)
- [SVARM-IQ: Efficient Approximation of Any-order Shapley Interactions through Stratification](https://mlsanity.com/paper/2401.13371/) (2024)
- [Unifying Feature-Based Explanations with Functional ANOVA and Cooperative Game Theory](https://mlsanity.com/paper/2412.17152/) (2024)
- [Interpretable machine learning for time-to-event prediction in medicine and healthcare](https://mlsanity.com/paper/2303.09817/) (2023)
- [Explaining Similarity in Vision-Language Encoders with Weighted Banzhaf Interactions](https://mlsanity.com/paper/2508.05430/) (2025)
- [Gradient-based Explanations for Deep Learning Survival Models](https://mlsanity.com/paper/2502.04970/) (2025)

## Built on by (most cited first, 1 of 1)

- [A Hilbert-Valued Functional Decomposition Framework for Explaining Time-Dependent Outputs](https://mlsanity.com/paper/2609.11295/) (2026)

## Abstract (arXiv)

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.