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Approximate Bayesian computation (ABC) methods provide an elaborate approach to Bayesian inference on complex models, including model choice. Both theoretical arguments and simulation experiments indicate, however, that model posterior…

We consider statistical inference in the density estimation model using a tree-based Bayesian approach, with Optional P\'olya trees as prior distribution. We derive near-optimal convergence rates for corresponding posterior distributions…

Statistics Theory · Mathematics 2021-10-12 Ismaël Castillo , Thibault Randrianarisoa

In Bayesian theory, calculating a posterior probability distribution is highly important but usually difficult. Therefore, some methods have been put forward to deal with such problem, among which, the most popular one is the asymptotic…

Methodology · Statistics 2012-07-20 Zai-Ying Zhou

Decision tree learning is increasingly being used for pointwise inference. Important applications include causal heterogenous treatment effects and dynamic policy decisions, as well as conditional quantile regression and design of…

Machine Learning · Statistics 2024-02-08 Matias D. Cattaneo , Jason M. Klusowski , Peter M. Tian

Rooted trees with probabilities are convenient to represent a class of random processes with memory. They allow to describe and analyze variable length codes for data compression and distribution matching. In this work, the Leaf-Average…

Information Theory · Computer Science 2013-02-05 Georg Böcherer

Since their inception in the 1980's, regression trees have been one of the more widely used non-parametric prediction methods. Tree-structured methods yield a histogram reconstruction of the regression surface, where the bins correspond to…

Statistics Theory · Mathematics 2019-06-17 Veronika Rockova , Stephanie van der Pas

A compositional tree refers to a tree structure on a set of random variables where each random variable is a node and composition occurs at each non-leaf node of the tree. As a generalization of compositional data, compositional trees…

Methodology · Statistics 2021-04-20 Bingkai Wang , Brian S. Caffo , Xi Luo , Chin-Fu Liu , Andreia V. Faria , Michael I. Miller , Yi Zhao

We analyze variational inference for highly symmetric graphical models such as those arising from first-order probabilistic models. We first show that for these graphical models, the tree-reweighted variational objective lends itself to a…

Artificial Intelligence · Computer Science 2014-06-23 Hung Hai Bui , Tuyen N. Huynh , David Sontag

In this paper we present decomposable priors, a family of priors over structure and parameters of tree belief nets for which Bayesian learning with complete observations is tractable, in the sense that the posterior is also decomposable and…

Machine Learning · Computer Science 2013-01-18 Marina Meila , Tommi S. Jaakkola

Many machine learning tools for regression are based on recursive partitioning of the covariate space into smaller regions, where the regression function can be estimated locally. Among these, regression trees and their ensembles have…

Statistics Theory · Mathematics 2017-11-30 Stephanie van der Pas , Veronika Rockova

We introduce Joint Probability Trees (JPT), a novel approach that makes learning of and reasoning about joint probability distributions tractable for practical applications. JPTs support both symbolic and subsymbolic variables in a single…

Machine Learning · Computer Science 2023-02-15 Daniel Nyga , Mareike Picklum , Tom Schierenbeck , Michael Beetz

We study the convergence of the predictive surface of regression trees and forests. To support our analysis we introduce a notion of adaptive concentration for regression trees. This approach breaks tree training into a model selection…

Statistics Theory · Mathematics 2016-05-03 Stefan Wager , Guenther Walther

Probabilistic Regression Trees (PRTrees) generalize traditional decision trees by incorporating probability functions that associate each data point with different regions of the tree, providing smooth decisions and continuous responses.…

Methodology · Statistics 2025-10-07 Taiane Schaedler Prass , Alisson Silva Neimaier , Guilherme Pumi

Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…

Methodology · Statistics 2025-12-01 Maria Alejandra Valdez Cabrera , Amy D Willis , Armeen Taeb

We study the influence of the seed in random trees grown according to the uniform attachment model, also known as uniform random recursive trees. We show that different seeds lead to different distributions of limiting trees from a total…

Probability · Mathematics 2014-10-22 Sébastien Bubeck , Ronen Eldan , Elchanan Mossel , Miklós Z. Rácz

We introduce some natural families of distributions on rooted binary ranked plane trees with a view toward unifying ideas from various fields, including macroevolution, epidemiology, computational group theory, search algorithms and other…

Combinatorics · Mathematics 2017-08-22 Sean Cleary , Mareike Fischer , Robert C. Griffiths , Raazesh Sainudiin

A uniform recursive tree on $n$ vertices is a random tree where each possible $(n-1)!$ labeled recursive rooted tree is selected with equal probability. In this paper we introduce and study weighted trees, a non-uniform recursive tree model…

Probability · Mathematics 2017-12-12 Ella Hiesmayr , Ümit Işlak

We propose Partition Tree, a novel tree-based framework for conditional density estimation over general outcome spaces that supports both continuous and categorical variables within a unified formulation. Our approach models conditional…

Machine Learning · Computer Science 2026-05-13 Felipe Angelim , Alessandro Leite

In many domains, we are interested in analyzing the structure of the underlying distribution, e.g., whether one variable is a direct parent of the other. Bayesian model-selection attempts to find the MAP model and use its structure to…

Machine Learning · Computer Science 2013-01-18 Nir Friedman , Daphne Koller

Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…

Information Theory · Computer Science 2023-09-19 Amirmohammad Farzaneh , Mihai-Alin Badiu , Justin P. Coon