CoChat
Sign Up
Cited by 4,021Statistical Methods and InferenceData Mining Algorithms and ApplicationsStatistical Methods and Applications

The DOI matches its Crossref record; 62 of the 62 references it cites were found in a registry or an index.

Unbiased Recursive Partitioning: A Conditional Inference Framework

Open access
Hothorn, Torsten, Hornik, Kurt, Zeileis, Achim·2006·Journal of Computational and Graphical Statistics
DOI 10.1198/106186006x133933
Open this paper in CoChat — free account

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.

Overview

Integrity signals

Registry

Crossref · 10.1198/106186006x133933

Cites

62 of 62 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Verification

Claims the paper makes

The text we found for this paper looks like another document, so its claims and self-check weren’t run. The registry and citation checks still apply.

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The text we found for this paper looks like another document, so the self-check wasn’t run.

Citations

Cites

Show all 57 references

Research works printed but not linked: 9

  1. De'ath G., 2002, Ecology, 83, 1105
  2. Dobra A., 2001, Proceedings of the Eighteenth International Conference on Machine Learning, San Francisco: Morgan Kaufmann, pp., 90
  3. Frank E., 1998, Proceedings of the Fifteenth International Conference on Machine Learning, San Francisco: Morgan Kaufmann, pp., 152
  4. Loh W.-Y., 2002, Statistica Sinica, 12, 361
  5. Loh W.-Y., 1997, Statistica Sinica, 7, 815
  6. Mingers J., 1987, Journal of the Operations Research Society, 38, 39
  7. Peters A., 2002, R News, 2, 33
  8. Schumacher M., 2001, J. Crowley, New York, Basel: Marcel Dekker, pp., 321
  9. White A. P., 1994, Machine Learning, 15, 321

Cited by

Sorted by citations

Items 1,001–1,011 of 1,011

Related

See all

Metadata

Authors
Hothorn, T., Hornik, K., & Zeileis, A.
Affiliations
Vienna University of Economics and Business (AT)
ORCID
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
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

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review