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Although regression trees were originally designed for large datasets, they can profitably be used on small datasets as well, including those from replicated or unreplicated complete factorial experiments. We show that in the latter…

Statistics Theory · Mathematics 2007-06-13 Wei-Yin Loh

Imputing missing values is an important preprocessing step in data analysis, but the literature offers little guidance on how to choose between different imputation models. This letter suggests adopting the imputation model that generates a…

Methodology · Statistics 2021-07-13 Moritz Marbach

Researchers now routinely use AI or other machine learning methods to estimate latent variables of economic interest, then plug-in the estimates as covariates in a regression. We show both theoretically and empirically that naively treating…

Econometrics · Economics 2025-05-01 Laura Battaglia , Timothy Christensen , Stephen Hansen , Szymon Sacher

We present convincing empirical evidence for an effective and general strategy for building accurate small models. Such models are attractive for interpretability and also find use in resource-constrained environments. The strategy is to…

Machine Learning · Computer Science 2024-04-30 Abhishek Ghose

Class imbalance in real-world data poses a common bottleneck for machine learning tasks, since achieving good generalization on under-represented examples is often challenging. Mitigation strategies, such as under or oversampling the data…

Disordered Systems and Neural Networks · Physics 2025-02-03 Emanuele Loffredo , Mauro Pastore , Simona Cocco , Rémi Monasson

Multiple imputation has become one of the standard methods in drawing inferences in many incomplete data applications. Applications of multiple imputation in relatively more complex settings, such as high-dimensional clustered data, require…

Methodology · Statistics 2025-04-08 Qiushuang Li , Recai Yucel

Modern data acquisition based on high-throughput technology is often facing the problem of missing data. Algorithms commonly used in the analysis of such large-scale data often depend on a complete set. Missing value imputation offers a…

Applications · Statistics 2014-06-03 Daniel J. Stekhoven , Peter Bühlmann

Tree-based learning methods such as Random Forest and XGBoost are still the gold-standard prediction methods for tabular data. Feature importance measures are usually considered for feature selection as well as to assess the effect of…

Applications · Statistics 2024-12-19 Jakob Schwerter , Andrés Romero , Florian Dumpert , Markus Pauly

The paper considers linear regression problems where the number of predictor variables is possibly larger than the sample size. The basic motivation of the study is to combine the points of view of model selection and functional regression…

Statistics Theory · Mathematics 2012-02-24 Alois Kneip , Pascal Sarda

We propose and study a method for learning interpretable representations for the task of regression. Features are represented as networks of multi-type expression trees comprised of activation functions common in neural networks in addition…

Neural and Evolutionary Computing · Computer Science 2019-03-26 William La Cava , Tilak Raj Singh , James Taggart , Srinivas Suri , Jason H. Moore

Model-assisted regression estimation is fundamental in survey sampling for incorporating auxiliary information. However, when the auxiliary dimension grows with the sample size, the standard Generalized regression (GREG) estimator can…

Methodology · Statistics 2026-04-10 Yonghyun Kwon , Shu Yang , Jae Kwang Kim

In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…

Machine Learning · Computer Science 2013-12-30 N. Denizcan Vanli , Suleyman S. Kozat

Random forests are widely used in regression. However, the decision trees used as base learners are poor approximators of linear relationships. To address this limitation we propose RaFFLE (Random Forest Featuring Linear Extensions), a…

Machine Learning · Computer Science 2025-02-17 Jakob Raymaekers , Peter J. Rousseeuw , Thomas Servotte , Tim Verdonck , Ruicong Yao

In certain situations that shall be undoubtedly more and more common in the Big Data era, the datasets available are so massive that computing statistics over the full sample is hardly feasible, if not unfeasible. A natural approach in this…

Machine Learning · Statistics 2015-01-12 Stéphan Clémençon , Patrice Bertail , Emilie Chautru , Guillaume Papa

This paper shows that decision trees constructed with Classification and Regression Trees (CART) and C4.5 methodology are consistent for regression and classification tasks, even when the number of predictor variables grows…

Machine Learning · Statistics 2023-11-15 Jason M. Klusowski , Peter M. Tian

Decision trees are popular Classification and Regression tools and, when small-sized, easy to interpret. Traditionally, a greedy approach has been used to build the trees, yielding a very fast training process; however, controlling sparsity…

Optimization and Control · Mathematics 2020-02-24 Rafael Blanquero , Emilio Carrizosa , Cristina Molero-Río , Dolores Romero Morales

Random forest (RF) methodology is one of the most popular machine learning techniques for prediction problems. In this article, we discuss some cases where random forests may suffer and propose a novel generalized RF method, namely…

Machine Learning · Statistics 2019-04-24 Haozhe Zhang , Dan Nettleton , Zhengyuan Zhu

Often machine learning methods are applied and results reported in cases where there is little to no information concerning accuracy of the output. Simply because a computer program returns a result does not insure its validity. If…

Machine Learning · Statistics 2022-05-25 Jerome H. Friedman

Urban Building Energy Models (UBEM) are vital for enhancing energy efficiency and sustainability in urban planning. However, data scarcity often challenges their validation, particularly the lack of hourly measured data and the variety of…

Applications · Statistics 2025-04-30 Chunxiao Wang , Bruno Duplessis , Eric Peirano , Pascal Schetelat , Peter Riederer

Tree-structured models are a powerful alternative to parametric regression models if non-linear effects and interactions are present in the data. Yet, classical tree-structured models might not be appropriate if data comes in clusters of…

Methodology · Statistics 2025-01-23 Nikolai Spuck , Matthias Schmid , Moritz Berger