# Interpretable Non-linear Survival Analysis with Evolutionary Symbolic Regression

arXiv: https://arxiv.org/abs/2504.05756 · HTML: https://mlsanity.com/paper/2504.05756/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 91 references that are in the map.
- First posted on arXiv 8 Apr 2025.

## Builds on (most cited first, 16 of 16)

- [DeepSurv: Personalized Treatment Recommender System Using A Cox Proportional Hazards Deep Neural Network](https://mlsanity.com/paper/1606.00931/) (2016)
- [Coordinate Descent Algorithms](https://mlsanity.com/paper/1502.04759/) (2015)
- [Explanations can be manipulated and geometry is to blame](https://mlsanity.com/paper/1906.07983/) (2019)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [Integration of Neural Network-Based Symbolic Regression in Deep Learning for Scientific Discovery](https://mlsanity.com/paper/1912.04825/) (2019)
- [Deep Learning for Survival Analysis: A Review](https://mlsanity.com/paper/2305.14961/) (2023)
- [Symbolic Regression is NP-hard](https://mlsanity.com/paper/2207.01018/) (2022)
- [SymFormer: End-to-end symbolic regression using transformer-based architecture](https://mlsanity.com/paper/2205.15764/) (2022)
- [Deep Cox Mixtures for Survival Regression](https://mlsanity.com/paper/2101.06536/) (2021)
- [Deep Learning and Symbolic Regression for Discovering Parametric Equations](https://mlsanity.com/paper/2207.00529/) (2022)
- [The Doctor Just Won't Accept That!](https://mlsanity.com/paper/1711.08037/) (2017)
- [Model Learning with Personalized Interpretability Estimation (ML-PIE)](https://mlsanity.com/paper/2104.06060/) (2021)
- [FPBoost: Fully Parametric Gradient Boosting for Survival Analysis](https://mlsanity.com/paper/2409.13363/) (2024)
- [Computing the Hazard Ratios Associated with Explanatory Variables Using Machine Learning Models of Survival Data](https://mlsanity.com/paper/2102.00637/) (2021)
- [Evolvability Degeneration in Multi-Objective Genetic Programming for Symbolic Regression](https://mlsanity.com/paper/2202.06983/) (2022)

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

- [Adaptive Protection for Evolutionary Feature Construction in Symbolic Regression with Application to Credit Classification](https://mlsanity.com/paper/2608.14209/) (2026)

## Abstract (arXiv)

Survival Regression (SuR) is a key technique for modeling time to event in important applications such as clinical trials and semiconductor manufacturing. Currently, SuR algorithms belong to one of three classes: non-linear black-box -- allowing adaptability to many datasets but offering limited interpretability (e.g., tree ensembles); linear glass-box -- being easier to interpret but limited to modeling only linear interactions (e.g., Cox proportional hazards); and non-linear glass-box -- allowing adaptability and interpretability, but empirically found to have several limitations (e.g., explainable boosting machines, survival trees). In this work, we investigate whether Symbolic Regression (SR), i.e., the automated search of mathematical expressions from data, can lead to non-linear glass-box survival models that are interpretable and accurate. We propose an evolutionary, multi-objective, and multi-expression implementation of SR adapted to SuR. Our empirical results on five real-world datasets show that SR consistently outperforms traditional glass-box methods for SuR in terms of accuracy per number of dimensions in the model, while exhibiting comparable accuracy with black-box methods. Furthermore, we offer qualitative examples to assess the interpretability potential of SR models for SuR. Code at: https://github.com/lurovi/SurvivalMultiTree-pyNSGP.