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Unbiased Recursive Partitioning: A Conditional Inference Framework

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Hothorn, Torsten, Hornik, Kurt, Zeileis, Achim·2006·Journal of Computational and Graphical Statistics

DOI 10.1198/106186006x133933

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Abstract

Recursive binary partitioning is a popular tool for regression analysis. Two fundamental problems of exhaustive search procedures usually applied to fit such models have been known for a long time: overfitting and a selection bias towards covariates with many possible splits or missing values. While pruning procedures are able to solve the overfitting problem, the variable selection bias still seriously affects the interpretability of tree-structured regression models. For some special cases unbiased procedures have been suggested, however lacking a common theoretical foundation. We propose a unified framework for recursive partitioning which embeds tree-structured regression models into a well defined theory of conditional inference procedures. Stopping criteria based on multiple test procedures are implemented and it is shown that the predictive performance of the resulting trees is as good as the performance of established exhaustive search procedures. It turns out that the partitions and therefore the models induced by both approaches are structurally different, confirming the need for an unbiased variable selection. Moreover, it is shown that the prediction accuracy of trees with early stopping is equivalent to the prediction accuracy of pruned trees with unbiased variable selection. The methodology presented here is applicable to all kinds of regression problems, including nominal, ordinal, numeric, censored as well as multivariate response variables and arbitrary measurement scales of the covariates. Data from studies on glaucoma classification, node positive breast cancer survival and mammography experience are re-analyzed.

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Authors: Hothorn, T., Hornik, K., & Zeileis, A.
Affiliations: Vienna University of Economics and Business (AT)
ORCID: Hothorn, Torsten
Hornik, Kurt
Zeileis, Achim
Venue: Journal of Computational and Graphical Statistics
Publisher: Informa UK Limited
Published: 2006-09
Volume: 15
Issue: 3
Pages: 651-674
ISSN: 1061-8600 (ISSN-L)
1537-2715
DOI: 10.1198/106186006x133933
OpenAlex: W2123998733
Cited by: 4,021
References: 57
Citations by year: 2026: 171 · 2025: 247 · 2024: 272 · 2023: 310 · 2022: 348 · 2021: 381 · 2020: 332 · 2019: 340 · 2018: 292 · 2017: 258 · 2016: 198 · 2015: 228 · 2014: 171 · 2013: 139 · 2012: 117
FWCI: 27.53
Type: journal article
Language: en
Open access: green
doi.org
Locations: Journal of Computational and Graphical Statistics (publishedVersion)
ePubWU Institutional Repository (Vienna University of Economics and Business) (submittedVersion)
WU Research (submittedVersion)
Zenodo (CERN European Organization for Nuclear Research)
Funders: Deutsche Forschungsgemeinschaft
Linköpings Universitet
Topics: Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
Physical Sciences › Computer Science › Information Systems › Data Mining Algorithms and Applications
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
Keywords: conditional inference, variable selection bias, overfitting, stopping rules, multiple comparisons, early stopping, tree pruning, missing data, prediction accuracy, censored responses, multivariate response

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Unbiased Recursive Partitioning: A Conditional Inference Framework

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