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Counterfactual explanation of machine learning survival models

Kovalev, M.; Utkin, L.; Coolen, F.; Konstantinov, A.

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M. Kovalev

L. Utkin

A. Konstantinov


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 wellknown Particle Swarm Optimization algorithm. Numerical experiments with real and synthetic data demonstrate the proposed method.


Kovalev, M., Utkin, L., Coolen, F., & Konstantinov, A. (2022). Counterfactual explanation of machine learning survival models. Informatica: An International Journal, 32(4), 817-847.

Journal Article Type Article
Acceptance Date Dec 2, 2021
Online Publication Date Dec 9, 2021
Publication Date 2022
Deposit Date Dec 4, 2021
Publicly Available Date Dec 6, 2021
Journal Informatica
Print ISSN 0868-4952
Electronic ISSN 1822-8844
Publisher Vilnius University
Peer Reviewed Peer Reviewed
Volume 32
Issue 4
Pages 817-847
Keywords interpretable model; explainable AI; survival analysis; censored data; convex optimization; counterfactual explanation; Cox model; Particle Swarm Optimization;


Accepted Journal Article (5.8 Mb)

Copyright Statement
Accepted Manuscript: © [Maxim Kovalev, Lev Utkin, Frank Coolen, Andrei Konstantinov, 2021]. The definitive, peer reviewed and edited version of this article is published in [Informatica, 32, 4, 817-847, 2021, DOI 10.15388/21-INFOR468].

Version of Record: © Vilnius University. This article is Open Access under a Creative Commons Attribution (CC BY) licence

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