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In this article, we construct a generalization of the Blum-Fran\c{c}ois Beta-splitting model for evolutionary trees, which was itself inspired by Aldous' Beta-splitting model on cladograms. The novelty of our approach allows for asymmetric…

Probability · Mathematics 2016-07-04 Raazesh Sainudiin , Amandine Veber

In the past several years a wide range of methods for the construction of regression trees and other estimators based on the recursive partitioning of samples have appeared in the statistics literature. Many applications involve data…

Methodology · Statistics 2014-07-07 Daniell Toth , John Eltinge

Learning a Bayesian networks with bounded treewidth is important for reducing the complexity of the inferences. We present a novel anytime algorithm (k-MAX) method for this task, which scales up to thousands of variables. Through extensive…

Artificial Intelligence · Computer Science 2018-02-08 Mauro Scanagatta , Giorgio Corani , Marco Zaffalon , Jaemin Yoo , U Kang

We present methodology for constructing pointwise confidence intervals for the cumulative distribution function and the quantiles of mixing distributions on the unit interval from binomial mixture distribution samples. No assumptions are…

Methodology · Statistics 2023-11-27 Pallavi Basu , Barak Brill , Daniel Yekutieli

Consider a density $f$ on $[0,1]$ that must be estimated from an i.i.d. sample $X_1,...,X_n$ drawn from $f$. In this note, we study binary-tree-based histogram estimates that use recursive splitting of intervals. If the decision to split an…

Statistics Theory · Mathematics 2025-04-24 Luc Devroye , Jad Hamdan

The computational complexity of some depths that satisfy the projection property, such as the halfspace depth or the projection depth, is known to be high, especially for data of higher dimensionality. In such scenarios, the exact depth is…

Statistics Theory · Mathematics 2021-05-28 Stanislav Nagy , Rainer Dyckerhoff , Pavlo Mozharovskyi

The wealth of data being gathered about humans and their surroundings drives new machine learning applications in various fields. Consequently, more and more often, classifiers are trained using not only numerical data but also complex data…

Machine Learning · Computer Science 2022-04-13 Maciej Piernik , Dariusz Brzezinski , Pawel Zawadzki

Nonparametric estimation of the conditional distribution of a response given high-dimensional features is a challenging problem. It is important to allow not only the mean but also the variance and shape of the response density to change…

Machine Learning · Statistics 2013-12-05 Francesca Petralia , Joshua Vogelstein , David B. Dunson

Many data are naturally modeled by an unobserved hierarchical structure. In this paper we propose a flexible nonparametric prior over unknown data hierarchies. The approach uses nested stick-breaking processes to allow for trees of…

Methodology · Statistics 2010-06-08 Ryan Prescott Adams , Zoubin Ghahramani , Michael I. Jordan

Decision trees are popular machine learning models that are simple to build and easy to interpret. Even though algorithms to learn decision trees date back to almost 50 years, key properties affecting their generalization error are still…

Machine Learning · Computer Science 2020-10-16 Jean-Samuel Leboeuf , Frédéric LeBlanc , Mario Marchand

The capabilities of additive manufacturing have facilitated the design and production of mechanical metamaterials with diverse unit cell geometries. Establishing linkages between the vast design space of unit cells and their effective…

Computational Engineering, Finance, and Science · Computer Science 2025-05-05 Hooman Danesh , Maruthi Annamaraju , Tim Brepols , Stefanie Reese , Surya R. Kalidindi

The right ventricular (RV) function deterioration strongly predicts clinical outcomes in numerous circumstances. To boost the clinical deployment of ensemble regression methods that quantify RV volumes using tabular data from the widely…

Tissues and Organs · Quantitative Biology 2024-03-13 Tuan A. Bohoran , Polydoros N. Kampaktsis , Laura McLaughlin , Jay Leb , Gerry P. McCann , Archontis Giannakidis

Multidimensional scaling visualizes dissimilarities among objects and reduces data dimensionality. While many methods address symmetric proximity data, asymmetric and especially three-way proximity data (capturing relationships across…

Methodology · Statistics 2025-11-21 Aleix Alcacer , Rafael Benitez , Vicente J. Bolos , Irene Epifanio

We define the beta diffusion tree, a random tree structure with a set of leaves that defines a collection of overlapping subsets of objects, known as a feature allocation. A generative process for the tree structure is defined in terms of…

Machine Learning · Statistics 2015-04-06 Creighton Heaukulani , David A. Knowles , Zoubin Ghahramani

This paper explores hierarchical clustering in the case where pairs of points have dissimilarity scores (e.g. distances) as a part of the input. The recently introduced objective for points with dissimilarity scores results in every tree…

Machine Learning · Computer Science 2020-09-01 Benjamin Moseley , Yuyan Wang

Stick-breaking (SB) processes are often adopted in Bayesian mixture models for generating mixing weights. When covariates influence the sizes of clusters, SB mixtures are particularly convenient as they can leverage their connection to…

Methodology · Statistics 2024-08-16 Akira Horiguchi , Cliburn Chan , Li Ma

R-trees can be used to store and query sets of point data in two or more dimensions. An easy way to construct and maintain R-trees for two-dimensional points, due to Kamel and Faloutsos, is to keep the points in the order in which they…

Computational Geometry · Computer Science 2017-11-08 Arie Bos , Herman Haverkort

Partitioning trees are efficient data structures for $k$-nearest neighbor search. Machine learning libraries commonly use a special type of partitioning trees called $k$d-trees to perform $k$-nn search. Unfortunately, $k$d-trees can be…

Machine Learning · Computer Science 2023-02-28 Mashaan Alshammari , John Stavrakakis , Adel F. Ahmed , Masahiro Takatsuka

We propose a tree-based algorithm for classification and regression problems in the context of functional data analysis, which allows to leverage representation learning and multiple splitting rules at the node level, reducing…

Machine Learning · Statistics 2020-11-03 Edoardo Belli , Simone Vantini

An important problem in statistics is the construction of confidence regions for unknown parameters. In most cases, asymptotic distribution theory is used to construct confidence regions, so any coverage probability claims only hold…

Statistics Theory · Mathematics 2014-10-28 Ryan Martin