Consistency of Honest Decision Trees and Random Forests

• URL: http://arxiv.org/abs/2601.14991v1
• Date: Wed, 21 Jan 2026 13:40:36 GMT
• Title: Consistency of Honest Decision Trees and Random Forests
• Authors: Martin Bladt, Rasmus Frigaard Lemvig,
• Abstract summary: We study various types of consistency of honest decision trees and random forests in the regression setting.<n>We establish weak and almost sure convergence of honest trees and honest forest averages to the true regression function.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study various types of consistency of honest decision trees and random forests in the regression setting. In contrast to related literature, our proofs are elementary and follow the classical arguments used for smoothing methods. Under mild regularity conditions on the regression function and data distribution, we establish weak and almost sure convergence of honest trees and honest forest averages to the true regression function, and moreover we obtain uniform convergence over compact covariate domains. The framework naturally accommodates ensemble variants based on subsampling and also a two-stage bootstrap sampling scheme. Our treatment synthesizes and simplifies existing analyses, in particular recovering several results as special cases. The elementary nature of the arguments clarifies the close relationship between data-adaptive partitioning and kernel-type methods, providing an accessible approach to understanding the asymptotic behavior of tree-based methods.

Related papers

• Random Forests as Statistical Procedures: Design, Variance, and Dependence [0.0]
  We develop a finite-sample, design-based formulation of random forests in which each tree is an explicit randomized conditional regression function.<n>This perspective yields an exact variance identity for the forest predictor that separates finite-aggregation variability from a structural dependence term.<n>The resulting framework clarifies how resampling, feature-level randomization, and split selection govern resolution, tree variability, and dependence.
  arXiv  Detail & Related papers  (2026-02-13T17:08:43Z)
• Partition Trees: Conditional Density Estimation over General Outcome Spaces [46.1988967916659]
  We propose Partition Trees, a tree-based framework for conditional density estimation over general outcome spaces.<n>Our approach models conditional distributions as piecewise-constant densities on data adaptive partitions and learns trees by directly minimizing conditional negative log-likelihood.
  arXiv  Detail & Related papers  (2026-02-03T22:12:30Z)
• Learning Discrete Bayesian Networks with Hierarchical Dirichlet Shrinkage [52.914168158222765]
  We detail a comprehensive Bayesian framework for learning DBNs.<n>We give a novel Markov chain Monte Carlo (MCMC) algorithm utilizing parallel Langevin proposals to generate exact posterior samples.<n>We apply our methodology to uncover prognostic network structure from primary breast cancer samples.
  arXiv  Detail & Related papers  (2025-09-16T17:24:35Z)
• Ensembles of Probabilistic Regression Trees [46.53457774230618]
  Tree-based ensemble methods have been successfully used for regression problems in many applications and research studies. We study ensemble versions of probabilisticregression trees that provide smooth approximations of the objective function by assigningeach observation to each region with respect to a probability distribution.
  arXiv  Detail & Related papers  (2024-06-20T06:51:51Z)
• Collaborative Heterogeneous Causal Inference Beyond Meta-analysis [68.4474531911361]
  We propose a collaborative inverse propensity score estimator for causal inference with heterogeneous data. Our method shows significant improvements over the methods based on meta-analysis when heterogeneity increases.
  arXiv  Detail & Related papers  (2024-04-24T09:04:36Z)
• On the Pointwise Behavior of Recursive Partitioning and Its Implications for Heterogeneous Causal Effect Estimation [8.394633341978007]
  Decision tree learning is increasingly being used for pointwise inference. We show that adaptive decision trees can fail to achieve convergence rates of convergence in the norm with non-vanishing probability. We show that random forests can remedy the situation, turning poor performing trees into nearly optimal procedures.
  arXiv  Detail & Related papers  (2022-11-19T21:28:30Z)
• Distributional Adaptive Soft Regression Trees [0.0]
  This article proposes a new type of a distributional regression tree using a multivariate soft split rule. One great advantage of the soft split is that smooth high-dimensional functions can be estimated with only one tree. We show by means of extensive simulation studies that the algorithm has excellent properties and outperforms various benchmark methods.
  arXiv  Detail & Related papers  (2022-10-19T08:59:02Z)
• Random Forest Weighted Local Fréchet Regression with Random Objects [18.128663071848923]
  We propose a novel random forest weighted local Fr'echet regression paradigm.<n>Our first method uses these weights as the local average to solve the conditional Fr'echet mean.<n>Second method performs local linear Fr'echet regression, both significantly improving existing Fr'echet regression methods.
  arXiv  Detail & Related papers  (2022-02-10T09:10:59Z)
• Stochastic Optimization Forests [60.523606291705214]
  We show how to train forest decision policies by growing trees that choose splits to directly optimize the downstream decision quality, rather than splitting to improve prediction accuracy as in the standard random forest algorithm. We show that our approximate splitting criteria can reduce running time hundredfold, while achieving performance close to forest algorithms that exactly re-optimize for every candidate split.
  arXiv  Detail & Related papers  (2020-08-17T16:56:06Z)
• Random extrapolation for primal-dual coordinate descent [61.55967255151027]
  We introduce a randomly extrapolated primal-dual coordinate descent method that adapts to sparsity of the data matrix and the favorable structures of the objective function. We show almost sure convergence of the sequence and optimal sublinear convergence rates for the primal-dual gap and objective values, in the general convex-concave case.
  arXiv  Detail & Related papers  (2020-07-13T17:39:35Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.