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We consider conducting inference on the output of the Classification and Regression Tree (CART) [Breiman et al., 1984] algorithm. A naive approach to inference that does not account for the fact that the tree was estimated from the data…

Fixed effects models are very flexible because they do not make assumptions on the distribution of effects and can also be used if the heterogeneity component is correlated with explanatory variables. A disadvantage is the large number of…

This paper introduces a new methodology for constructing a network of companies called a dynamic asset graph. This is similar to the dynamic asset tree studied recently, as both are based on correlations between asset returns. However, the…

Tree-based models have proven to be an effective solution for web ranking as well as other problems in diverse domains. This paper focuses on optimizing the runtime performance of applying such models to make predictions, given an…

Large language models achieve strong reasoning performance, yet existing decoding strategies either explore blindly (random sampling) or redundantly (independent multi-sampling). We propose Entropy-Tree, a tree-based decoding method that…

Regression methods for interval-valued data have been increasingly studied in recent years. As most of the existing works focus on linear models, it is important to note that many problems in practice are nonlinear in nature and therefore…

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…

Classification of functional data where observations are curves or trajectories poses unique challenges, particularly under severe class imbalance. Traditional Random Forest algorithms, while robust for tabular data, often fail to capture…

We seek decision rules for prediction-time cost reduction, where complete data is available for training, but during prediction-time, each feature can only be acquired for an additional cost. We propose a novel random forest algorithm to…

A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density…

The spectacular success of deep generative models calls for quantitative tools to measure their statistical performance. Divergence frontiers have recently been proposed as an evaluation framework for generative models, due to their ability…

We present an axiomatic framework for analyzing the algorithmic properties of decision trees. This framework supports the classification of decision tree problems through structural and ancestral constraints within a rigorous mathematical…

Object Oriented Data Analysis is a new area in statistics that studies populations of general data objects. In this article we consider populations of tree-structured objects as our focus of interest. We develop improved analysis tools for…

This paper presents an augmented deep factor model that generates latent factors for cross-sectional asset pricing. The conventional security sorting on firm characteristics for constructing long-short factor portfolio weights is nonlinear…

Recent studies have demonstrated advantages of information fusion based on sparsity models for multimodal classification. Among several sparsity models, tree-structured sparsity provides a flexible framework for extraction of…

Techniques to reduce the energy burden of an industrial ecosystem often require solving a multiobjective optimization problem. However, collecting experimental data can often be either expensive or time-consuming. In such cases, statistical…

Few problems in statistics are as perplexing as variable selection in the presence of very many redundant covariates. The variable selection problem is most familiar in parametric environments such as the linear model or additive variants…

We present a detailed analysis of the class of regression decision tree algorithms which employ a regulized piecewise-linear node-splitting criterion and have regularized linear models at the leaves. From a theoretic standpoint, based on…

Extreme value applications commonly employ regression techniques to capture cross-sectional heterogeneity or time-variation in the data. Estimation of the parameters of an extreme value regression model is notoriously challenging due to the…

We explore a decomposition in which returns on a large class of portfolios relative to the market depend on a smooth non-negative drift and changes in the asset price distribution. This decomposition is obtained using general continuous…