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We present an algorithm for learning decision trees using stochastic gradient information as the source of supervision. In contrast to previous approaches to gradient-based tree learning, our method operates in the incremental learning…

Machine Learning · Statistics 2019-09-25 Henry Gouk , Bernhard Pfahringer , Eibe Frank

The concept of trustworthy AI has gained widespread attention lately. One of the aspects relevant to trustworthy AI is robustness of ML models. In this study, we show how to probabilistically quantify robustness against naturally occurring…

Machine Learning · Computer Science 2022-11-30 Christoph Schweimer , Sebastian Scher

We analyze the finite sample mean squared error (MSE) performance of regression trees and forests in the high dimensional regime with binary features, under a sparsity constraint. We prove that if only $r$ of the $d$ features are relevant…

Statistics Theory · Mathematics 2020-10-23 Vasilis Syrgkanis , Manolis Zampetakis

Decision tree and random forest classification and regression are some of the most widely used in machine learning approaches. Binary decision tree implementations commonly use conditioning in the form 'feature $\leq$ (or $<$) threshold',…

Machine Learning · Computer Science 2023-12-19 Gábor Timár , György Kovács

Detecting interaction effects (IEs) in meta-regression is challenging, especially when few studies are available and many plausible interactions are considered. In many meta-analyses, interpretability is essential, which limits the use of…

Other Statistics · Statistics 2026-03-09 Jan-Bernd Igelmann , Paula Lorenz , Markus Pauly

Bayesian Additive Regression Trees (BART) are a powerful ensemble learning technique for modeling nonlinear regression functions. Although initially BART was proposed for predicting only continuous and binary response variables, over the…

Statistics Theory · Mathematics 2026-03-24 Enakshi Saha

Ensembles of classification and regression trees remain popular machine learning methods because they define flexible non-parametric models that predict well and are computationally efficient both during training and testing. During…

Machine Learning · Computer Science 2012-06-22 Sebastian Nowozin

We develop early stopping rules for growing regression tree estimators. The fully data-driven stopping rule is based on monitoring the global residual norm. The best-first search and the breadth-first search algorithms together with linear…

Statistics Theory · Mathematics 2025-07-29 Ratmir Miftachov , Markus Reiß

Bayesian Additive Regression Trees (BART) is a flexible machine learning algorithm capable of capturing nonlinearities between an outcome and covariates and interaction among covariates. We extend BART to a semiparametric regression…

Applications · Statistics 2018-06-13 Bret Zeldow , Vincent Lo Re , Jason Roy

Both humans and artificial systems frequently use trial and error methods to problem solving. In order to be effective, this type of strategy implies having high quality control knowledge to guide the quest for the optimal solution.…

Artificial Intelligence · Computer Science 2012-04-24 Patrick Taillandier , Cécile Duchêne , Alexis Drogoul

In order to speed-up classification models when facing a large number of categories, one usual approach consists in organizing the categories in a particular structure, this structure being then used as a way to speed-up the prediction…

Machine Learning · Computer Science 2015-11-26 Aurélia Léon , Ludovic Denoyer

Decision trees are widely used for interpretable machine learning due to their clearly structured reasoning process. However, this structure belies a challenge we refer to as predictive equivalence: a given tree's decision boundary can be…

Machine Learning · Computer Science 2025-10-15 Hayden McTavish , Zachery Boner , Jon Donnelly , Margo Seltzer , Cynthia Rudin

Data analysis and machine learning have become an integrative part of the modern scientific methodology, offering automated procedures for the prediction of a phenomenon based on past observations, unraveling underlying patterns in data and…

Machine Learning · Statistics 2015-06-04 Gilles Louppe

Learning a regression function using censored or interval-valued output data is an important problem in fields such as genomics and medicine. The goal is to learn a real-valued prediction function, and the training output labels indicate an…

Machine Learning · Statistics 2017-10-30 Alexandre Drouin , Toby Dylan Hocking , François Laviolette

Decision trees are a popular technique in statistical data classification. They recursively partition the feature space into disjoint sub-regions until each sub-region becomes homogeneous with respect to a particular class. The basic…

Machine Learning · Statistics 2015-04-15 D. C. Wickramarachchi , B. L. Robertson , M. Reale , C. J. Price , J. Brown

We study the problem of formally verifying individual fairness of decision tree ensembles, as well as training tree models which maximize both accuracy and individual fairness. In our approach, fairness verification and fairness-aware…

Machine Learning · Computer Science 2021-01-05 Francesco Ranzato , Caterina Urban , Marco Zanella

Regression models for supervised learning problems with a continuous target are commonly understood as models for the conditional mean of the target given predictors. This notion is simple and therefore appealing for interpretation and…

Methodology · Statistics 2018-01-09 Torsten Hothorn , Achim Zeileis

Threshold Autoregressive (TAR) models have been widely used by statisticians for non-linear time series forecasting during the past few decades, due to their simplicity and mathematical properties. On the other hand, in the forecasting…

Machine Learning · Computer Science 2022-11-17 Rakshitha Godahewa , Geoffrey I. Webb , Daniel Schmidt , Christoph Bergmeir

Bayesian additive regression trees (BART) is a semi-parametric regression model offering state-of-the-art performance on out-of-sample prediction. Despite this success, standard implementations of BART typically provide inaccurate…

Methodology · Statistics 2023-02-27 Meijiang Wang , Jingyu He , P. Richard Hahn

In the fight against hard-to-treat diseases such as cancer, it is often difficult to discover new treatments that benefit all subjects. For regulatory agency approval, it is more practical to identify subgroups of subjects for whom the…

Methodology · Statistics 2014-10-09 Wei-Yin Loh , Xu He , Michael Man