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We develop conformal prediction methods for constructing valid predictive confidence sets in multiclass and multilabel problems without assumptions on the data generating distribution. A challenge here is that typical conformal prediction…
Due to their accuracies, methods based on ensembles of regression trees are a popular approach for making predictions. Some common examples include Bayesian additive regression trees, boosting and random forests. This paper focuses on…
To improve the uncertainty quantification of variance networks, we propose a novel tree-structured local neural network model that partitions the feature space into multiple regions based on uncertainty heterogeneity. A tree is built upon…
The tree-structured varying coefficient model (TSVC) is a flexible regression approach that allows the effects of covariates to vary with the values of the effect modifiers. Relevant effect modifiers are identified inherently using…
A variety of problems in computational physics and engineering require the convolution of the heat kernel (a Gaussian) with either discrete sources, densities supported on boundaries, or continuous volume distributions. We present a unified…
Contour trees offer an abstract representation of the level set topology in scalar fields and are widely used in topological data analysis and visualization. However, applying contour trees to large-scale scientific datasets remains…
Decision trees are renowned for their ability to achieve high predictive performance while remaining interpretable, especially on tabular data. Traditionally, they are constructed through recursive algorithms, where they partition the data…
We derive the exact partition function for a discrete model of random trees embedded in a one-dimensional space. These trees have vertices labeled by integers representing their position in the target space, with the SOS constraint that…
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…
We introduce an extension of the P\'olya tree approach for constructing distributions on the space of probability measures. By using optional stopping and optional choice of splitting variables, the construction gives rise to random…
We develop a general statistical framework for the analysis and inference of large tree-structured data, with a focus on developing asymptotic goodness-of-fit tests. We first propose a consistent statistical model for binary trees, from…
Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…
Decision trees and models that use them as primitives are workhorses of machine learning in Euclidean spaces. Recent work has further extended these models to the Lorentz model of hyperbolic space by replacing axis-parallel hyperplanes with…
Recursive decision trees are widely used to estimate heterogeneous causal treatment effects in experimental and observational studies. These methods are typically implemented using CART-type recursive partitioning and are often viewed as…
A simple and computationally efficient scheme for tree-structured vector quantization is presented. Unlike previous methods, its quantization error depends only on the intrinsic dimension of the data distribution, rather than the apparent…
Regression trees are becoming increasingly popular as omnibus predicting tools and as the basis of numerous modern statistical learning ensembles. Part of their popularity is their ability to create a regression prediction without ever…
This paper revisits a fundamental problem in statistical inference from a non-asymptotic theoretical viewpoint $\unicode{x2013}$ the construction of confidence sets. We establish a finite-sample bound for the estimator, characterizing its…
The curse of dimensionality has remained a challenge for a wide variety of algorithms in data mining, clustering, classification and privacy. Recently, it was shown that an increasing dimensionality makes the data resistant to effective…
Tree methods (recursive partitioning) are a popular class of nonparametric methods for analyzing data. One extension of the basic tree methodology is the survival tree, which applies recursive partitioning to censored survival data. There…
Spatio temporal data are more ubiquitous and richer than even before and the availability of such data poses great challenges in data analytics. Ecological facilitation, the positive effect of density of individuals on the individual's…