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Predictive Distribution Modeling Using Transformation Forests


Hothorn, Torsten; Zeileis, Achim (2021). Predictive Distribution Modeling Using Transformation Forests. Journal of Computational and Graphical Statistics, 30(4):1181-1196.

Abstract

Regression models for supervised learning problems with a continuous response are commonly understood as models for the conditional mean of the response given predictors. This notion is simple and therefore appealing for interpretation and visualization. Information about the whole underlying conditional distribution is, however, not available from these models. A more general understanding of regression models as models for conditional distributions allows much broader inference, for example, the computation of prediction intervals or probabilistic predictions for exceeding certain thresholds. Several random forest-type algorithms aim at estimating conditional distributions, most prominently quantile regression forests. We propose a novel approach based on a parametric family of distributions characterized by their transformation function. A dedicated novel “transformation tree” algorithm able to detect distributional changes is developed. Based on these transformation trees, we introduce “transformation forests” as an adaptive local likelihood estimator of conditional distribution functions. The resulting predictive distributions are fully parametric yet very general and allow inference procedures, such as likelihood-based variable importances, to be applied in a straightforward way. Supplemental files for this article are available online.

Abstract

Regression models for supervised learning problems with a continuous response are commonly understood as models for the conditional mean of the response given predictors. This notion is simple and therefore appealing for interpretation and visualization. Information about the whole underlying conditional distribution is, however, not available from these models. A more general understanding of regression models as models for conditional distributions allows much broader inference, for example, the computation of prediction intervals or probabilistic predictions for exceeding certain thresholds. Several random forest-type algorithms aim at estimating conditional distributions, most prominently quantile regression forests. We propose a novel approach based on a parametric family of distributions characterized by their transformation function. A dedicated novel “transformation tree” algorithm able to detect distributional changes is developed. Based on these transformation trees, we introduce “transformation forests” as an adaptive local likelihood estimator of conditional distribution functions. The resulting predictive distributions are fully parametric yet very general and allow inference procedures, such as likelihood-based variable importances, to be applied in a straightforward way. Supplemental files for this article are available online.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:04 Faculty of Medicine > Epidemiology, Biostatistics and Prevention Institute (EBPI)
Dewey Decimal Classification:610 Medicine & health
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Statistics, Probability and Uncertainty
Physical Sciences > Discrete Mathematics and Combinatorics
Uncontrolled Keywords:Statistics, Probability and Uncertainty, Discrete Mathematics and Combinatorics, Statistics and Probability
Language:English
Date:2 October 2021
Deposited On:15 Mar 2022 10:48
Last Modified:26 Jun 2024 01:50
Publisher:American Statistical Association
ISSN:1061-8600
OA Status:Hybrid
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1080/10618600.2021.1872581
Project Information:
  • : FunderSchweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
  • : Grant ID
  • : Project Title
  • : FunderSNSF
  • : Grant IDIZSEZ0_177091
  • : Project TitleA Party for Model-based Forest Inference
  • : FunderSNSF
  • : Grant ID200021_184603
  • : Project TitleA Lego System for Transformation Inference
  • Content: Published Version
  • Licence: Creative Commons: Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)