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In any given machine learning problem, there may be many models that could explain the data almost equally well. However, most learning algorithms return only one of these models, leaving practitioners with no practical way to explore…

Machine Learning · Computer Science 2022-10-27 Rui Xin , Chudi Zhong , Zhi Chen , Takuya Takagi , Margo Seltzer , Cynthia Rudin

Decision tree optimization is fundamental to interpretable machine learning. The most popular approach is to greedily search for the best feature at every decision point, which is fast but provably suboptimal. Recent approaches find the…

Machine Learning · Computer Science 2025-11-19 Varun Babbar , Hayden McTavish , Cynthia Rudin , Margo Seltzer

Decision forests, including Random Forests and Gradient Boosting Trees, have recently demonstrated state-of-the-art performance in a variety of machine learning settings. Decision forests are typically ensembles of axis-aligned decision…

Decision trees are popular Classification and Regression tools and, when small-sized, easy to interpret. Traditionally, a greedy approach has been used to build the trees, yielding a very fast training process; however, controlling sparsity…

Optimization and Control · Mathematics 2020-02-24 Rafael Blanquero , Emilio Carrizosa , Cristina Molero-Río , Dolores Romero Morales

Today, as increasingly complex predictive models are developed, simple rule sets remain a crucial tool to obtain interpretable predictions and drive high-stakes decision making. However, a single rule set provides a partial representation…

Machine Learning · Computer Science 2024-06-06 Martino Ciaperoni , Han Xiao , Aristides Gionis

Sparse decision trees are one of the most common forms of interpretable models. While recent advances have produced algorithms that fully optimize sparse decision trees for prediction, that work does not address policy design, because the…

Machine Learning · Computer Science 2022-10-27 Ali Behrouz , Mathias Lecuyer , Cynthia Rudin , Margo Seltzer

We introduce an enumeration-free method based on mathematical programming to precisely characterize various properties such as fairness or sparsity within the set of "good models", known as Rashomon set. This approach is generically…

Machine Learning · Computer Science 2025-07-08 Lucas Langlade , Julien Ferry , Gabriel Laberge , Thibaut Vidal

Decision tree optimization is notoriously difficult from a computational perspective but essential for the field of interpretable machine learning. Despite efforts over the past 40 years, only recently have optimization breakthroughs been…

Machine Learning · Computer Science 2022-11-24 Jimmy Lin , Chudi Zhong , Diane Hu , Cynthia Rudin , Margo Seltzer

Sparse decision tree optimization has been one of the most fundamental problems in AI since its inception and is a challenge at the core of interpretable machine learning. Sparse decision tree optimization is computationally hard, and…

Machine Learning · Computer Science 2022-07-07 Hayden McTavish , Chudi Zhong , Reto Achermann , Ilias Karimalis , Jacques Chen , Cynthia Rudin , Margo Seltzer

Interpretable reinforcement learning policies are essential for high-stakes decision-making, yet optimizing decision tree policies in Markov Decision Processes (MDPs) remains challenging. We propose SPOT, a novel method for computing…

Machine Learning · Computer Science 2025-10-23 Xuyuan Xiong , Pedro Chumpitaz-Flores , Kaixun Hua , Cheng Hua

Decision trees are popular in survival analysis for their interpretability and ability to model complex relationships. Survival trees, which predict the timing of singular events using censored historical data, are typically built through…

Machine Learning · Computer Science 2025-11-24 Antonio Consolo , Edoardo Amaldi , Emilio Carrizosa

Given thousands of equally accurate machine learning (ML) models, how can users choose among them? A recent ML technique enables domain experts and data scientists to generate a complete Rashomon set for sparse decision trees--a huge set of…

Human-Computer Interaction · Computer Science 2023-03-02 Zijie J. Wang , Chudi Zhong , Rui Xin , Takuya Takagi , Zhi Chen , Duen Horng Chau , Cynthia Rudin , Margo Seltzer

Functional data analysis (FDA) and ensemble learning can be powerful tools for analyzing complex environmental time series. Recent literature has highlighted the key role of diversity in enhancing accuracy and reducing variance in ensemble…

Machine Learning · Statistics 2024-09-13 Donato Riccio , Fabrizio Maturo , Elvira Romano

Random forests and, more generally, (decision\nobreakdash-)tree ensembles are widely used methods for classification and regression. Recent algorithmic advances allow to compute decision trees that are optimal for various measures such as…

Machine Learning · Computer Science 2024-09-25 Christian Komusiewicz , Pascal Kunz , Frank Sommer , Manuel Sorge

We propose an algorithm named best-scored random forest for binary classification problems. The terminology "best-scored" means to select the one with the best empirical performance out of a certain number of purely random tree candidates…

Machine Learning · Statistics 2019-05-28 Hanyuan Hang , Xiaoyu Liu , Ingo Steinwart

Due to their efficiency and small size, decision trees and random forests are popular machine learning models used for classification on resource-constrained systems. In such systems, the available execution time for inference in a random…

Machine Learning · Computer Science 2026-03-03 Daniel Biebert , Christian Hakert , Kay Heider , Daniel Kuhse , Sebastian Buschjäger , Jian-Jia Chen

Decision trees are widely used for classification and regression tasks in a variety of application fields due to their interpretability and good accuracy. During the past decade, growing attention has been devoted to globally optimized…

Machine Learning · Computer Science 2025-01-28 Antonio Consolo , Edoardo Amaldi , Andrea Manno

Sparse residual tree (SRT) is an adaptive exploration method for multivariate scattered data approximation. It leads to sparse and stable approximations in areas where the data is sufficient or redundant, and points out the possible local…

Numerical Analysis · Mathematics 2019-05-15 Xin Xu , Xiaopeng Luo

We consider the use of decision trees for decision-making problems under the predict-then-optimize framework. That is, we would like to first use a decision tree to predict unknown input parameters of an optimization problem, and then make…

Machine Learning · Computer Science 2020-06-19 Adam N. Elmachtoub , Jason Cheuk Nam Liang , Ryan McNellis

Random forests are an ensemble method relevant for many problems, such as regression or classification. They are popular due to their good predictive performance (compared to, e.g., decision trees) requiring only minimal tuning of…

Methodology · Statistics 2022-10-20 Nikolaus Umlauf , Nadja Klein
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