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The issue of estimating residual variance in regression models has experienced relatively little attention in the machine learning community. However, the estimate is of primary interest in many practical applications, e.g. as a primary…

Statistics Theory · Mathematics 2018-12-18 Burim Ramosaj , Markus Pauly

Classification and Regression Tree (CART), Random Forest (RF) and Gradient Boosting Tree (GBT) are probably the most popular set of statistical learning methods. However, their statistical consistency can only be proved under very…

Statistics Theory · Mathematics 2025-02-17 Haoran Zhan , Yu Liu , Yingcun Xia

Random Forests (RFs) are strong machine learning tools for classification and regression. However, they remain supervised algorithms, and no extension of RFs to the one-class setting has been proposed, except for techniques based on…

Machine Learning · Statistics 2016-11-22 Nicolas Goix , Nicolas Drougard , Romain Brault , Maël Chiapino

We propose a novel ensemble method called Riemann-Lebesgue Forest (RLF) for regression. The core idea in RLF is to mimic the way how a measurable function can be approximated by partitioning its range into a few intervals. With this idea in…

Machine Learning · Statistics 2024-05-13 Tian Qin , Wei-Min Huang

Random Forests (RF) are among the state-of-the-art in many machine learning applications. With the ongoing integration of ML models into everyday life, the deployment and continuous application of models becomes more and more an important…

Machine Learning · Computer Science 2021-10-20 Sebastian Buschjäger , Katharina Morik

Decision Trees (DTs) and Random Forests (RFs) are powerful discriminative learners and tools of central importance to the everyday machine learning practitioner and data scientist. Due to their discriminative nature, however, they lack…

Machine Learning · Computer Science 2020-11-20 Alvaro H. C. Correia , Robert Peharz , Cassio de Campos

We propose generalized random forests, a method for non-parametric statistical estimation based on random forests (Breiman, 2001) that can be used to fit any quantity of interest identified as the solution to a set of local moment…

Methodology · Statistics 2018-04-06 Susan Athey , Julie Tibshirani , Stefan Wager

Random forests is a common non-parametric regression technique which performs well for mixed-type unordered data and irrelevant features, while being robust to monotonic variable transformations. Standard random forests, however, do not…

Computation · Statistics 2019-06-19 Taylor Pospisil , Ann B. Lee

Residual bootstrap is a classical method for statistical inference in regression settings. With massive data sets becoming increasingly common, there is a demand for computationally efficient alternatives to residual bootstrap. We propose a…

Methodology · Statistics 2024-09-30 Indrila Ganguly , Srijan Sengupta , Sujit Ghosh

Random Forests (RF) are among the most powerful and widely used predictive models for centralized tabular data, yet few methods exist to adapt them to the federated learning setting. Unlike most federated learning approaches, the…

Machine Learning · Statistics 2026-05-08 Rémi Khellaf , Erwan Scornet , Aurélien Bellet , Julie Josse

Random Reshuffling (RR) is an algorithm for minimizing finite-sum functions that utilizes iterative gradient descent steps in conjunction with data reshuffling. Often contrasted with its sibling Stochastic Gradient Descent (SGD), RR is…

Optimization and Control · Mathematics 2021-04-06 Konstantin Mishchenko , Ahmed Khaled , Peter Richtárik

Random Reshuffling (RR), which is a variant of Stochastic Gradient Descent (SGD) employing sampling without replacement, is an immensely popular method for training supervised machine learning models via empirical risk minimization. Due to…

Machine Learning · Computer Science 2022-05-11 Grigory Malinovsky , Peter Richtárik

Uncertainty in estimating the log-law parameters is arguably the greatest obstacle to establishing definitive conclusions regarding their numerical values and universality. This challenge is exacerbated by the limited number of studies that…

Fluid Dynamics · Physics 2026-04-15 M. Aguiar Ferreira , B. Ganapathisubramani

Random Forest (Breiman, 2001) is a successful and widely used regression and classification algorithm. Part of its appeal and reason for its versatility is its (implicit) construction of a kernel-type weighting function on training data,…

Machine Learning · Statistics 2022-10-13 Domagoj Ćevid , Loris Michel , Jeffrey Näf , Nicolai Meinshausen , Peter Bühlmann

Recursive least squares (RLS) algorithms were once widely used for training small-scale neural networks, due to their fast convergence. However, previous RLS algorithms are unsuitable for training deep neural networks (DNNs), since they…

Machine Learning · Computer Science 2021-09-08 Chunyuan Zhang , Qi Song , Hui Zhou , Yigui Ou , Hongyao Deng , Laurence Tianruo Yang

Feature subsampling is a core component of random forests and other ensemble methods. While recent theory suggests that this randomization acts solely as a variance reduction mechanism analogous to ridge regularization, these results…

Machine Learning · Statistics 2026-01-06 Xin Chen , Jason M. Klusowski , Yan Shuo Tan , Chang Yu

We consider correlated \emph{factor} regression models (FRM) and analyze the performance of classical ridge interpolators. Utilizing powerful \emph{Random Duality Theory} (RDT) mathematical engine, we obtain \emph{precise} closed form…

Machine Learning · Statistics 2024-06-14 Mihailo Stojnic

This paper extends recursive least squares (RLS) to include time-varying regularization. This extension provides flexibility for updating the least squares regularization term in real time. Existing results with constant regularization…

Signal Processing · Electrical Eng. & Systems 2025-01-09 Brian Lai , Dimitra Panagou , Dennis S. Bernstein

Random Forests (RF) is one of the algorithms of choice in many supervised learning applications, be it classification or regression. The appeal of such tree-ensemble methods comes from a combination of several characteristics: a remarkable…

Machine Learning · Statistics 2020-05-18 Jaouad Mourtada , Stéphane Gaïffas , Erwan Scornet

We propose to prune a random forest (RF) for resource-constrained prediction. We first construct a RF and then prune it to optimize expected feature cost & accuracy. We pose pruning RFs as a novel 0-1 integer program with linear constraints…

Machine Learning · Statistics 2016-06-17 Feng Nan , Joseph Wang , Venkatesh Saligrama