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Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…

Statistics Theory · Mathematics 2007-06-13 Marcus Hutter

Variational inference is a popular technique to approximate a possibly intractable Bayesian posterior with a more tractable one. Recently, boosting variational inference has been proposed as a new paradigm to approximate the posterior by a…

Machine Learning · Computer Science 2018-03-08 Francesco Locatello , Rajiv Khanna , Joydeep Ghosh , Gunnar Rätsch

Additive models, such as produced by gradient boosting, and full interaction models, such as classification and regression trees (CART), are widely used algorithms that have been investigated largely in isolation. We show that these models…

The Distributional Random Forest (DRF) is a recently introduced Random Forest algorithm to estimate multivariate conditional distributions. Due to its general estimation procedure, it can be employed to estimate a wide range of targets such…

Statistics Theory · Mathematics 2023-12-20 Jeffrey Näf , Corinne Emmenegger , Peter Bühlmann , Nicolai Meinshausen

We present nonparametric algorithms for estimating optimal individualized treatment rules. The proposed algorithms are based on the XGBoost algorithm, which is known as one of the most powerful algorithms in the machine learning literature.…

Machine Learning · Statistics 2020-02-04 Duzhe Wang , Haoda Fu , Po-Ling Loh

Missing data is an expected issue when large amounts of data is collected, and several imputation techniques have been proposed to tackle this problem. Beneath classical approaches such as MICE, the application of Machine Learning…

Machine Learning · Statistics 2017-12-01 Burim Ramosaj , Markus Pauly

Traditional statistical and machine learning methods typically assume that the training and test data follow the same distribution. However, this assumption is frequently violated in real-world applications, where the training data in the…

Methodology · Statistics 2025-07-08 Hanxuan Ye , Hongzhe Li

We propose and study a multi-scale approach to vector quantization. We develop an algorithm, dubbed reconstruction trees, inspired by decision trees. Here the objective is parsimonious reconstruction of unsupervised data, rather than…

Machine Learning · Computer Science 2019-09-05 Enrico Cecini , Ernesto De Vito , Lorenzo Rosasco

Modern machine learning methods and the availability of large-scale data have significantly advanced our ability to predict target quantities from large sets of covariates. However, these methods often struggle under distributional shifts,…

Machine Learning · Statistics 2025-12-24 Nicola Gnecco , Jonas Peters , Sebastian Engelke , Niklas Pfister

In an era where artificial intelligence and machine learning algorithms increasingly impact human life, it is crucial to develop models that account for potential discrimination in their predictions. This paper tackles this problem by…

Machine Learning · Statistics 2024-10-10 Anna Gottard , Vanessa Verrina , Sabrina Giordano

Empirical risk minimization often performs poorly when the distribution of the target domain differs from those of source domains. To address such potential distribution shifts, we develop an unsupervised domain adaptation approach that…

Machine Learning · Statistics 2025-03-25 Zhenyu Wang , Peter Bühlmann , Zijian Guo

A core step of every algorithm for learning regression trees is the selection of the best splitting variable from the available covariates and the corresponding split point. Early tree algorithms (e.g., AID, CART) employed greedy search…

Methodology · Statistics 2019-06-26 Lisa Schlosser , Torsten Hothorn , Achim Zeileis

This paper proposes a new method to combine several densities such that each density dominates a separate part of a joint distribution. The method is fully unsupervised, i.e. the parameters in the densities and the thresholds are…

Methodology · Statistics 2009-02-25 Lars Holden , Ola Haug

Given i.i.d. data from an unknown distribution, we consider the problem of predicting future items. An adaptive way to estimate the probability density is to recursively subdivide the domain to an appropriate data-dependent granularity. A…

Probability · Mathematics 2009-12-30 Marcus Hutter

We introduce WildWood (WW), a new ensemble algorithm for supervised learning of Random Forest (RF) type. While standard RF algorithms use bootstrap out-of-bag samples to compute out-of-bag scores, WW uses these samples to produce improved…

Machine Learning · Computer Science 2023-06-14 Stéphane Gaïffas , Ibrahim Merad , Yiyang Yu

In this article, we investigate the use of a probabilistic model for unsupervised clustering in text collections. Unsupervised clustering has become a basic module for many intelligent text processing applications, such as information…

Information Retrieval · Computer Science 2016-08-16 Loïs Rigouste , Olivier Cappé , François Yvon

Despite the rise to dominance of deep learning in unstructured data domains, tree-based methods such as Random Forests (RF) and Gradient Boosted Decision Trees (GBDT) are still the workhorses for handling discriminative tasks on tabular…

Machine Learning · Computer Science 2025-04-21 João Bravo

We propose a robust variant of boosting forest to the various adversarial defense methods, and apply it to enhance the robustness of the deep neural network. We retain the deep network architecture, weights, and middle layer features, then…

Computer Vision and Pattern Recognition · Computer Science 2022-11-01 Jianqiao Wangni

Decision trees and random forest remain highly competitive for classification on medium-sized, standard datasets due to their robustness, minimal preprocessing requirements, and interpretability. However, a single tree suffers from high…

Machine Learning · Statistics 2025-12-02 Cencheng Shen , Yuexiao Dong , Carey E. Priebe

There is a large literature explaining why AdaBoost is a successful classifier. The literature on AdaBoost focuses on classifier margins and boosting's interpretation as the optimization of an exponential likelihood function. These existing…

Machine Learning · Statistics 2017-05-02 Abraham J. Wyner , Matthew Olson , Justin Bleich , David Mease