# Counterfactual explanation of machine learning survival models

arXiv: https://arxiv.org/abs/2006.16793 · HTML: https://mlsanity.com/paper/2006.16793/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jun 2020.

## Built on by (most cited first, 8 of 8)

- [If Only We Had Better Counterfactual Explanations: Five Key Deficits to Rectify in the Evaluation of Counterfactual XAI Techniques](https://mlsanity.com/paper/2103.01035/) (2021)
- [A Survey on Graph Counterfactual Explanations: Definitions, Methods, Evaluation, and Research Challenges](https://mlsanity.com/paper/2210.12089/) (2022)
- [SurvSHAP(t): Time-dependent explanations of machine learning survival models](https://mlsanity.com/paper/2208.11080/) (2022)
- [Interpretable Machine Learning for Survival Analysis](https://mlsanity.com/paper/2403.10250/) (2024)
- [survex: an R package for explaining machine learning survival models](https://mlsanity.com/paper/2308.16113/) (2023)
- [CoxSE: Exploring the Potential of Self-Explaining Neural Networks with Cox Proportional Hazards Model for Survival Analysis](https://mlsanity.com/paper/2407.13849/) (2024)
- [SurvBeNIM: The Beran-Based Neural Importance Model for Explaining the Survival Models](https://mlsanity.com/paper/2312.06638/) (2023)
- [SurvCF(t): Counterfactual Explanations for Survival Analysis in Predictive Maintenance Multivariate Time Series Data](https://mlsanity.com/paper/2607.16969/) (2026)

## Abstract (arXiv)

A method for counterfactual explanation of machine learning survival models is proposed. One of the difficulties of solving the counterfactual explanation problem is that the classes of examples are implicitly defined through outcomes of a machine learning survival model in the form of survival functions. A condition that establishes the difference between survival functions of the original example and the counterfactual is introduced. This condition is based on using a distance between mean times to event. It is shown that the counterfactual explanation problem can be reduced to a standard convex optimization problem with linear constraints when the explained black-box model is the Cox model. For other black-box models, it is proposed to apply the well-known Particle Swarm Optimization algorithm. A lot of numerical experiments with real and synthetic data demonstrate the proposed method.