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In this paper we propose and study a version of the Dyadic Classification and Regression Trees (DCART) estimator from Donoho (1997) for (fixed design) quantile regression in general dimensions. We refer to this proposed estimator as the…
Decision trees with binary splits are popularly constructed using Classification and Regression Trees (CART) methodology. For binary classification and regression models, this approach recursively divides the data into two near-homogenous…
By revisiting the end-cut preference (ECP) phenomenon associated with a single CART (Breiman et al. (1984)), we introduce MinimaxSplit decision trees, a robust alternative to CART that selects splits by minimizing the worst-case child risk…
Classification and Regression Trees (CARTs) are off-the-shelf techniques in modern Statistics and Machine Learning. CARTs are traditionally built by means of a greedy procedure, sequentially deciding the splitting predictor variable(s) and…
We consider the framework of non-stationary stochastic optimization [Besbes et al, 2015] with squared error losses and noisy gradient feedback where the dynamic regret of an online learner against a time varying comparator sequence is…
Decision trees are powerful machine learning algorithms, widely used in fields such as economics and medicine for their simplicity and interpretability. However, decision trees such as CART are prone to overfitting, especially when grown…
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…
Decision trees are one of the most widely used nonparametric methods for regression and classification. In existing literature, decision tree-based methods have been used for estimating continuous functions or piecewise-constant functions.…
Undirected graphical models encode in a graph $G$ the dependency structure of a random vector $Y$. In many applications, it is of interest to model $Y$ given another random vector $X$ as input. We refer to the problem of estimating the…
Although it is an extremely effective, easy-to-use, and increasingly popular tool for nonparametric regression, the Bayesian Additive Regression Trees (BART) model is limited by the fact that it can only produce discontinuous output.…
Decision trees with binary splits are popularly constructed using Classification and Regression Trees (CART) methodology. For regression models, this approach recursively divides the data into two near-homogenous daughter nodes according to…
We study piece-wise constant signals corrupted by additive Gaussian noise over a $d$-dimensional lattice. Data of this form naturally arise in a host of applications, and the tasks of signal detection or testing, de-noising and estimation…
Decision trees partition the feature space using hard binary thresholds, assigning identical confidence to instances far from a decision boundary and to those directly on it. We introduce ternary decision trees, which augment each split…
We consider the recently introduced application of the Deck of Cards Method (DCM) to ordinal regression proposing two extensions related to two main research trends in Multiple Criteria Decision Aiding, namely scaling and ordinal regression…
Classification and Regression Tree (CART), Random Forest (RF) and Gradient Boosting Tree (GBT) are probably the most popular set of statistical learning methods. However, their statistical consistency can only be proved under very…
Current implementations of Bayesian Additive Regression Trees (BART) are based on axis-aligned decision rules that recursively partition the feature space using a single feature at a time. Several authors have demonstrated that oblique…
In supervised learning, decision trees are valued for their interpretability and performance. While greedy decision tree algorithms like CART remain widely used due to their computational efficiency, they often produce sub-optimal solutions…
As a flexible nonparametric learning tool, the random forests algorithm has been widely applied to various real applications with appealing empirical performance, even in the presence of high-dimensional feature space. Unveiling the…
This paper develops a performant Bayesian approach to conditional average treatment effect (CATE) estimation in regression discontinuity designs (RDD), an increasingly prevalent form of quasi-experiment that facilitates causal inference.…
Bayesian Additive Regression Trees(BART) is a Bayesian nonparametric approach which has been shown to be competitive with the best modern predictive methods such as random forest and Gradient Boosting Decision Tree.The sum of trees…