Evolving Features vs Evolving Entire Trees with GP for Interpretable Survival Analysis

Peter A.N. Bosman; Tanja Alderliesten; Thalea Schlender

arxiv: 2605.30119 · v2 · pith:N7OOUPSTnew · submitted 2026-05-28 · 💻 cs.LG · cs.AI· cs.NE

Evolving Features vs Evolving Entire Trees with GP for Interpretable Survival Analysis

Thalea Schlender , Peter A.N. Bosman , Tanja Alderliesten This is my paper

Pith reviewed 2026-06-29 08:46 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.NE

keywords survival analysisgenetic programmingsurvival treesfeature constructioncensored dataevolutionary algorithmsinterpretable models

0 comments

The pith

Evolutionary feature construction improves predictive performance of survival trees on two real-world datasets.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tests genetic programming to build feature sets or full survival trees for predicting time to an event when data is censored. It finds that evolved features raise accuracy for multiple tree-building methods at two depths on two datasets. Jointly evolving tree structure and split rules is presented as fast and flexible. This matters for medical applications where models must stay understandable while handling incomplete observations.

Core claim

Multi-objective genetic programming evolves inspectable higher-order feature combinations that improve survival tree accuracy across induction strategies on two real-world datasets and two tree depths, while the joint evolution of tree structure and non-linear split logic offers speed and flexible presentation advantages.

What carries the argument

Multi-objective genetic programming applied to evolve feature sets or entire survival tree structures and split logic.

If this is right

Evolutionary feature construction raises predictive performance for different survival tree induction strategies.
Shallow survival trees reach competitive accuracy when paired with evolved higher-order features.
Joint evolution of tree structure and splits provides a faster alternative with flexible output format.
The evolved models capture complex relationships while remaining inspectable.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same evolutionary approach could be tested on additional censored-data problems outside medicine.
Comparing run times and final tree sizes directly between feature evolution and full-tree evolution would clarify trade-offs.
The method might allow smaller trees overall, reducing the need for post-hoc simplification steps.

Load-bearing premise

That observed performance gains come from the evolutionary process itself rather than other setup differences, and that the resulting models stay human-inspectable after introducing complex feature combinations or jointly optimized splits.

What would settle it

Re-running the exact experiments on the same two datasets and depths with standard non-evolved features and finding no accuracy difference would falsify the claimed improvement from evolutionary construction.

Figures

Figures reproduced from arXiv: 2605.30119 by Peter A.N. Bosman, Tanja Alderliesten, Thalea Schlender.

**Figure 2.** Figure 2: Top performing survival trees of depth 3 for GBSG. Subfigure 2a shows a greedy ST on the original input features, achieving a mean IBS of 0.124, whereas Subfigure 2b shows the GFC greedy ST of depth 3 that achieves the lowest mean IBS of 0.115. Subfigure 2c shows the evolutionary ST of depth 3, in which both features and tree structure are evolved jointly, which achieves the lowest mean IBS of 0.116. Note … view at source ↗

**Figure 3.** Figure 3: IBS performances on the GBSG use case The bootstrapped mean IBS and its 95% confidence interval over 1000 bootstraps on the external cohort. All dots are survival tree models derived via multiple-feature multi-objective construction, whereas the lines represent baselines made on the original input features. 0.17 0.18 0.19 0.20 IBS 1 5 10 15 20 25 30 35 40 45 Complexity a Greedy Numeric Ops 0.17 0.18 0.19 0… view at source ↗

**Figure 4.** Figure 4: IBS performances on the METABRIC use case. Bootstrapped mean IBS and 95% confidence interval over 1000 bootstraps on the external cohort. Dots are ST models derived via multiple-feature multi-objective construction, whereas lines represent baselines made using original input features [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗

**Figure 5.** Figure 5: IBS performances and achieved hypervolume across different configurations for the evolutionary STs of depth 2 and 3. A Ablation study of the improvements for the evolutionary ST In this section, the enhancements designed to enhance the evolutionary ST are briefly investigated. For this, we use the GBSG use case and run 6 different configurations: with and without tree swapping, combined with three budgets… view at source ↗

**Figure 6.** Figure 6: 50% Attainment surfaces for the different evolutionary ST configuration Figure 6a shows the 50% attainment surface on different configurations of the evolutionary ST depth of 2, whereas Figure 6b shows the 50% attainment surface on different configurations of the evolutionary ST depth of 3 [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗

read the original abstract

Survival analysis concerns the task of predicting the time until an event occurs. Often used in the medical field, survival analysis deals with incomplete (i.e., censored) data, for instance, from patients who did not experience the event during the duration of the study. For practical use, both accuracy and interpretability are important. Survival trees are easy-to-follow survival models that split the patient cohort recursively into discrete patient groups. Whilst survival trees can capture complex relationships, they typically need to grow large, threatening interpretability. Moreover, survival trees are often built using greedy approaches that may overlook globally optimal split combinations, limiting predictive performance. Shallow survival trees require expressive, higher-order feature combinations to achieve competitive accuracy. We therefore use genetic programming to multi-objectively evolve inherently inspectable feature sets and study how they interact with different tree induction strategies. We further introduce an evolutionary approach that jointly optimises the survival tree structure and the non-linear split logic. Our findings demonstrate that evolutionary feature construction improves predictive performance across different tree induction strategies on two real-world datasets and two different survival tree depths. Given its speed and flexible presentation, the multi-objective evolution of entire trees likely holds the most future promise.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

GP feature evolution lifts survival tree performance on two datasets but gains may trace to uneven tuning rather than the method itself.

read the letter

The main takeaway is that multi-objective GP for constructing inspectable features improves survival tree accuracy across induction strategies on two real medical datasets at two depths, while jointly evolving the full tree structure and splits looks faster and more flexible for future use. The direct head-to-head comparison of feature-set evolution versus joint tree evolution is the genuinely new element; prior GP survival work exists but this framing of their interaction with different tree strategies is not standard.

The paper handles the medical motivation cleanly: survival trees need to stay shallow for interpretability yet still capture interactions, and greedy splits can miss better combinations. Using GP to evolve higher-order features while keeping them human-readable is a practical response, and testing the same idea on both feature construction and full-tree evolution gives a useful contrast. The multi-objective setup to trade off accuracy against complexity fits the interpretability goal.

The soft spots are mostly around attribution and reporting. The abstract claims improvements without metrics, intervals, or tests, and the stress-test concern holds: nothing indicates that the non-GP baselines received the same hyperparameter search budget, cross-validation scheme, or preprocessing as the evolutionary variants. If the GP runs simply got more optimization effort, the performance edge cannot be credited to the evolutionary component. For the joint-tree version the risk is higher because the larger search space can produce more complex models even if the paper calls the output flexible. Censoring handling is also left undescribed.

This is for people working on evolutionary computation applied to survival or interpretable medical models. A reader already following GP tree methods will pick up the comparison and the joint-evolution idea, but the narrow scope (two datasets, two depths) limits broader takeaway. The thinking is clear and engaged with the literature, with no obvious internal contradictions.

Send it to peer review. The empirical angle is worth referee time, but expect requests for matched tuning budgets, full metrics, and statistical checks before the claims can be taken at face value.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes multi-objective genetic programming to evolve interpretable feature sets for survival trees, comparing this to standard greedy tree induction, and introduces a joint evolutionary approach that optimizes both tree structure and non-linear split rules. It claims that evolutionary feature construction improves predictive performance across tree induction strategies on two real-world datasets at two survival tree depths, while the joint tree evolution is highlighted for its speed and flexible presentation.

Significance. If the performance gains are shown to arise specifically from the evolutionary component under controlled conditions, the work could support more accurate shallow survival trees that remain human-inspectable, addressing the tension between complexity and interpretability in medical survival modeling. The use of real-world datasets and explicit multi-objective framing for feature construction are strengths.

major comments (2)

[Experimental results] Experimental results section: the central claim that evolutionary feature construction improves performance requires explicit evidence that all baselines (including standard tree induction) received identical hyperparameter search budgets, the same cross-validation folds, and uniform preprocessing/feature scaling. The abstract supplies no such details, and without them the reported gains cannot be attributed to the GP component rather than unequal optimization effort or data handling differences.
[Methods and results] Methods and results sections: the manuscript must report the concrete performance metrics (e.g., concordance index or integrated Brier score), confidence intervals, statistical tests, and how right-censoring was handled in the evaluation; the abstract asserts improvements but provides none of these quantities, preventing evaluation of the magnitude or reliability of the claimed gains.

minor comments (1)

[Abstract] Abstract: the phrasing 'two different survival tree depths' is ambiguous without specifying the exact depths or the datasets used; adding these details would improve clarity for readers.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on experimental rigor and reporting. We address the major comments point by point below and will revise the manuscript accordingly where needed.

read point-by-point responses

Referee: [Experimental results] Experimental results section: the central claim that evolutionary feature construction improves performance requires explicit evidence that all baselines (including standard tree induction) received identical hyperparameter search budgets, the same cross-validation folds, and uniform preprocessing/feature scaling. The abstract supplies no such details, and without them the reported gains cannot be attributed to the GP component rather than unequal optimization effort or data handling differences.

Authors: We agree that controlled conditions are necessary to isolate the contribution of the evolutionary component. The experimental protocol in the full manuscript applies the same 5-fold cross-validation splits, identical grid-search hyperparameter budgets, and uniform preprocessing (including no scaling, as tree methods are scale-invariant) to all compared approaches. To make this explicit and address the concern, we will add a dedicated paragraph in the revised Experimental Results section confirming these shared settings and referencing the common experimental harness. revision: yes
Referee: [Methods and results] Methods and results sections: the manuscript must report the concrete performance metrics (e.g., concordance index or integrated Brier score), confidence intervals, statistical tests, and how right-censoring was handled in the evaluation; the abstract asserts improvements but provides none of these quantities, preventing evaluation of the magnitude or reliability of the claimed gains.

Authors: The evaluation uses the concordance index with right-censoring handled via the standard Kaplan-Meier-based splitting criterion and evaluation. However, the current manuscript version does not include the requested numerical values, confidence intervals, or statistical tests in the abstract or results summary. We will revise the Methods and Results sections to report mean C-index values with standard deviations across folds, paired statistical tests, and explicit handling of censoring. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical comparison on external data with no self-referential derivations

full rationale

The paper is an empirical study comparing genetic programming variants for feature construction and tree evolution against standard survival tree induction on two real-world datasets. No equations, fitted parameters, or predictions are presented that reduce to the inputs by construction. The central claims rest on performance metrics from held-out data rather than any self-definition, self-citation chain, or renamed known result. The work is self-contained against external benchmarks and does not invoke uniqueness theorems or ansatzes from prior author work as load-bearing justification.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. The approach relies on standard genetic programming operators and multi-objective selection applied to survival-tree induction.

pith-pipeline@v0.9.1-grok · 5753 in / 1190 out tokens · 34401 ms · 2026-06-29T08:46:45.944924+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

27 extracted references · 4 canonical work pages · 1 internal anchor

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Zhang, R., Xin, R., Seltzer, M., Rudin, C.: Optimal sparse survival trees. Proceed- ings of machine learning research238, 352 (2024)

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2002

[1] [1]

Altman, D.G., Royston, P.: What do we mean by validating a prognostic model? Statistics in medicine19(4), 453–473 (2000)

2000

[2] [2]

Journal of the Royal Statistical So- ciety: Series B (Methodological)34(2), 187–202 (1972)

Cox, D.R.: Regression models and life-tables. Journal of the Royal Statistical So- ciety: Series B (Methodological)34(2), 187–202 (1972)

1972

[3] [3]

Nature 486(7403), 346–352 (2012)

Curtis, C., Shah, S.P., Chin, S.F., Turashvili, G., Rueda, O.M., Dunning, M.J., Speed, D., Lynch, A.G., Samarajiwa, S., Yuan, Y., et al.: The genomic and tran- scriptomic architecture of 2,000 breast tumours reveals novel subgroups. Nature 486(7403), 346–352 (2012)

2012

[4] [4]

Cancer research60(3), 636–643 (2000)

Foekens,J.A.,Peters,H.A.,Look,M.P.,Portengen,H.,Schmitt,M.,Kramer,M.D., Brünner, N., Jänicke, F., Gelder, M.E.M.v., Henzen-Logmans, S.C., et al.: The urokinase system of plasminogen activation and prognosis in 2780 breast cancer patients. Cancer research60(3), 636–643 (2000)

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In: International conference on parallel problem solving from nature

Fonseca, C.M., Fleming, P.J.: On the performance assessment and comparison of stochastic multiobjective optimizers. In: International conference on parallel problem solving from nature. pp. 584–593. Springer (1996)

1996

[6] [6]

Statistics in medicine18(17- 18), 2529–2545 (1999)

Graf, E., Schmoor, C., Sauerbrei, W., Schumacher, M.: Assessment and comparison of prognostic classification schemes for survival data. Statistics in medicine18(17- 18), 2529–2545 (1999)

1999

[7] [7]

Statistics in medicine15(4), 361–387 (1996)

Harrell Jr, F.E., Lee, K.L., Mark, D.B.: Multivariable prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors. Statistics in medicine15(4), 361–387 (1996)

1996

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arXiv preprint arXiv:2505.01262 (2025)

Harrison, J., Bosman, P.A., Alderliesten, T.: Thinking outside the template with modular gp-gomea. arXiv preprint arXiv:2505.01262 (2025)

work page arXiv 2025

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In: Proceedings of the AAAI Conference on Artifi- cial Intelligence

Huisman, T., van der Linden, J.G., Demirović, E.: Optimal survival trees: A dy- namic programming approach. In: Proceedings of the AAAI Conference on Artifi- cial Intelligence. vol. 38, pp. 12680–12688 (2024)

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Ishwaran, H., Kogalur, U.B., Blackstone, E.H., Lauer, M.S.: Random survival forests (2008)

2008

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Journal of the American statistical association53(282), 457–481 (1958)

Kaplan, E.L., Meier, P.: Nonparametric estimation from incomplete observations. Journal of the American statistical association53(282), 457–481 (1958)

1958

[12] [12]

BMC medical research methodology18, 1–12 (2018)

Katzman, J.L., Shaham, U., Cloninger, A., Bates, J., Jiang, T., Kluger, Y.: Deep- surv:personalizedtreatmentrecommendersystemusingacoxproportionalhazards deep neural network. BMC medical research methodology18, 1–12 (2018)

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Bioinformatics p

Knottenbelt, W., McGough, W., Wray, R., Zhang, W.Z., Liu, J., Machado, I.P., Gao, Z., Crispin-Ortuzar, M.: Coxkan: Kolmogorov-arnold networks for inter- pretable, high-performance survival analysis. Bioinformatics p. btaf413 (2025)

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Jour- nal of the American Statistical Association88(422), 457–467 (1993), http://www.jstor.org/stable/2290325 16 T.Schlender et al

LeBlanc, M., Crowley, J.: Survival trees by goodness of split. Jour- nal of the American Statistical Association88(422), 457–467 (1993), http://www.jstor.org/stable/2290325 16 T.Schlender et al

work page arXiv 1993

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KAN: Kolmogorov-Arnold Networks

Liu, Z., Wang, Y., Vaidya, S., Ruehle, F., Halverson, J., Soljačić, M., Hou, T.Y., Tegmark, M.: Kan: Kolmogorov-arnold networks. arXiv preprint arXiv:2404.19756 (2024)

work page internal anchor Pith review Pith/arXiv arXiv 2024

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Mantel, N., et al.: Evaluation of survival data and two new rank order statistics arising in its consideration. Cancer Chemother Rep50(3), 163–170 (1966)

1966

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Korean Journal of Radiology 22(10), 1697 (2021)

Park, S.Y., Park, J.E., Kim, H., Park, S.H.: Review of statistical methods for evaluating the performance of survival or other time-to-event prediction models (from conventional to deep learning approaches). Korean Journal of Radiology 22(10), 1697 (2021)

2021

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Journal of Machine Learning Research21(212), 1–6 (2020), http://jmlr.org/papers/v21/20-729.html

Pölsterl, S.: scikit-survival: A library for time-to-event analysis built on top of scikit-learn. Journal of Machine Learning Research21(212), 1–6 (2020), http://jmlr.org/papers/v21/20-729.html

2020

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In: Proceedings of the Genetic and Evolu- tionary Computation Conference

Schlender, T., Malafaia, M., Alderliesten, T., Bosman, P.: Improving the efficiency of gp-gomea for higher-arity operators. In: Proceedings of the Genetic and Evolu- tionary Computation Conference. pp. 971–979 (2024)

2024

[21] [21]

arXiv preprint arXiv:2509.22673 (2025)

Schlender,T.,Romme,C.J.,vanderLinden,Y.M.,vanLonkhuijzen,L.R.,Bosman, P.A., Alderliesten, T.: Pisa: An ai pipeline for interpretable-by-design survival analysis providing multiple complexity-accuracy trade-off models. arXiv preprint arXiv:2509.22673 (2025)

work page arXiv 2025

[22] [22]

german breast cancer study group

Schumacher,M.,Bastert,G.,Bojar,H.,Hübner,K.,Olschewski,M.,Sauerbrei,W., Schmoor, C., Beyerle, C., Neumann, R., Rauschecker, H.: Randomized 2 x 2 trial evaluating hormonal treatment and the duration of chemotherapy in node-positive breast cancer patients. german breast cancer study group. Journal of Clinical On- cology12(10), 2086–2093 (1994)

2086

[23] [23]

In: Pro- ceedings of the Genetic and Evolutionary Computation Conference

Sijben, E., Alderliesten, T., Bosman, P.A.: Multi-modal multi-objective model- based genetic programming to find multiple diverse high-quality models. In: Pro- ceedings of the Genetic and Evolutionary Computation Conference. pp. 440–448 (2022)

2022

[24] [24]

Swarm and Evolutionary Computa- tion53, 100640 (2020)

Virgolin, M., Alderliesten, T., Bosman, P.A.: On explaining machine learning mod- els by evolving crucial and compact features. Swarm and Evolutionary Computa- tion53, 100640 (2020)

2020

[25] [25]

Journal of statistical software77, 1–17 (2017)

Wright, M.N., Ziegler, A.: ranger: A fast implementation of random forests for high dimensional data in c++ and r. Journal of statistical software77, 1–17 (2017)

2017

[26] [26]

Proceed- ings of machine learning research238, 352 (2024)

Zhang, R., Xin, R., Seltzer, M., Rudin, C.: Optimal sparse survival trees. Proceed- ings of machine learning research238, 352 (2024)

2024

[27] [27]

Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE transactions on Evolutionary Com- putation3(4), 257–271 (2002) GP for Interpretable Survival Analysis 17 (a) (b) (c) (d) Fig.5:IBS performances and achieved hypervolume across different configurations for the evolutionary STs of...

2002