English
Related papers

Related papers: Tight Mixed-Integer Optimization Formulations for …

200 papers

Regression trees and their ensemble methods are popular methods for nonparametric regression: they combine strong predictive performance with interpretable estimators. To improve their utility for locally smooth response surfaces, we study…

Methodology · Statistics 2021-09-13 Sören R. Künzel , Theo F. Saarinen , Edward W. Liu , Jasjeet S. Sekhon

The interpretability of models has become a crucial issue in Machine Learning because of algorithmic decisions' growing impact on real-world applications. Tree ensemble methods, such as Random Forests or XgBoost, are powerful learning tools…

Optimization and Control · Mathematics 2024-01-19 Giulia Di Teodoro , Marta Monaci , Laura Palagi

This paper introduces mixed-integer optimization methods to solve regression problems that incorporate fairness metrics. We propose an exact formulation for training fair regression models. To tackle this computationally hard problem, we…

Machine Learning · Computer Science 2024-12-24 Anna Deza , Andrés Gómez , Alper Atamtürk

The Steiner Forest problem is among the fundamental network design problems. Finding tight linear programming bounds for the problem is the key for both fast Branch-and-Bound algorithms and good primal-dual approximations. On the…

Discrete Mathematics · Computer Science 2017-09-06 Daniel Schmidt , Bernd Zey , François Margot

Given a graph $G=(V,E)$ with a weight $w_v$ associated with each vertex $v\in V$, the maximum weighted induced forest problem (MWIF) consists of encountering a maximum weighted subset $V'\subseteq V$ of the vertices such that $V'$ induces a…

Optimization and Control · Mathematics 2021-12-06 Rafael A. Melo , Celso C. Ribeiro

A decision tree is one of the most popular approaches in machine learning fields. However, it suffers from the problem of overfitting caused by overly deepened trees. Then, a meta-tree is recently proposed. It solves the problem of…

Machine Learning · Statistics 2024-02-12 Ryota Maniwa , Naoki Ichijo , Yuta Nakahara , Toshiyasu Matsushima

Recently, deep neural networks have expanded the state-of-art in various scientific fields and provided solutions to long standing problems across multiple application domains. Nevertheless, they also suffer from weaknesses since their…

Machine Learning · Computer Science 2023-05-03 Felipe Kenji Nakano , Konstantinos Pliakos , Celine Vens

Decision trees and random forest remain highly competitive for classification on medium-sized, standard datasets due to their robustness, minimal preprocessing requirements, and interpretability. However, a single tree suffers from high…

Machine Learning · Statistics 2025-12-02 Cencheng Shen , Yuexiao Dong , Carey E. Priebe

Decision diagrams for classification have some notable advantages over decision trees, as their internal connections can be determined at training time and their width is not bound to grow exponentially with their depth. Accordingly,…

Machine Learning · Computer Science 2022-05-31 Alexandre M. Florio , Pedro Martins , Maximilian Schiffer , Thiago Serra , Thibaut Vidal

Understanding how the optimal value of an optimisation problem changes when its input data is modified is an old question in mathematical optimisation. This paper investigates the computation of the optimal values of a family of (possibly…

Optimization and Control · Mathematics 2026-03-02 Guillaume Derval , Damien Ernst , Quentin Louveaux , Bardhyl Miftari

In order to speed-up classification models when facing a large number of categories, one usual approach consists in organizing the categories in a particular structure, this structure being then used as a way to speed-up the prediction…

Machine Learning · Computer Science 2015-11-26 Aurélia Léon , Ludovic Denoyer

Outcomes of data-driven AI models cannot be assumed to be always correct. To estimate the uncertainty in these outcomes, the uncertainty wrapper framework has been proposed, which considers uncertainties related to model fit, input quality,…

Machine Learning · Computer Science 2022-01-11 Pascal Gerber , Lisa Jöckel , Michael Kläs

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

Many iterative and non-iterative methods have been developed for inverse problems associated with Ising models. Aiming to derive an accurate non-iterative method for the inverse problems, we employ the tree-reweighted approximation. Using…

Machine Learning · Statistics 2018-05-30 Takashi Sano

With the abundance of available data, many enterprises seek to implement data-driven prescriptive analytics to help them make informed decisions. These prescriptive policies need to satisfy operational constraints, and proactively eliminate…

Optimization and Control · Mathematics 2022-07-22 Shivaram Subramanian , Wei Sun , Youssef Drissi , Markus Ettl

In this paper, we propose a novel Mixed-Integer Non-Linear Optimization formulation to construct a risk score, where we optimize the logistic loss with sparsity constraints. Previous approaches are typically designed to handle binary…

Optimization and Control · Mathematics 2025-02-13 Cristina Molero-Río , Claudia D'Ambrosio

Weighted model integration (WMI) extends Weighted model counting (WMC) to the integration of functions over mixed discrete-continuous domains. It has shown tremendous promise for solving inference problems in graphical models and…

Artificial Intelligence · Computer Science 2019-11-21 Zhe Zeng , Guy Van den Broeck

Tree-ensemble algorithms, such as random forest, are effective machine learning methods popular for their flexibility, high performance, and robustness to overfitting. However, since multiple learners are combined, they are not as…

Machine Learning · Computer Science 2023-01-09 Klest Dedja , Felipe Kenji Nakano , Konstantinos Pliakos , Celine Vens

A tight continuous relaxation is a crucial factor in solving mixed integer formulations of many NP-hard combinatorial optimization problems. The (weighted) max $k$-cut problem is a fundamental combinatorial optimization problem with…

Optimization and Control · Mathematics 2023-08-04 Ramin Fakhimi , Hamidreza Validi , Illya V. Hicks , Tamás Terlaky , Luis F. Zuluaga

The use of machine learning algorithms in finance, medicine, and criminal justice can deeply impact human lives. As a consequence, research into interpretable machine learning has rapidly grown in an attempt to better control and fix…

Machine Learning · Computer Science 2021-02-02 Thibaut Vidal , Toni Pacheco , Maximilian Schiffer