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In the fight against hard-to-treat diseases such as cancer, it is often difficult to discover new treatments that benefit all subjects. For regulatory agency approval, it is more practical to identify subgroups of subjects for whom the…

Methodology · Statistics 2014-10-09 Wei-Yin Loh , Xu He , Michael Man

Recent advancements in Mixed Integer Optimization (MIO) algorithms, paired with hardware enhancements, have led to significant speedups in resolving MIO problems. These strategies have been utilized for optimal subset selection,…

Methodology · Statistics 2024-03-27 Madhav Sankaranarayanan , Intekhab Hossain , Tom Chen

Interpretability is crucial for doctors, hospitals, pharmaceutical companies and biotechnology corporations to analyze and make decisions for high stakes problems that involve human health. Tree-based methods have been widely adopted for…

Machine Learning · Computer Science 2024-05-24 Rui Zhang , Rui Xin , Margo Seltzer , Cynthia Rudin

There has been a surge of interest in learning optimal decision trees using mixed-integer programs (MIP) in recent years, as heuristic-based methods do not guarantee optimality and find it challenging to incorporate constraints that are…

Machine Learning · Computer Science 2023-02-15 Shivaram Subramanian , Wei Sun

Decision trees are interpretable models that are well-suited to non-linear learning problems. Much work has been done on extending decision tree learning algorithms with differential privacy, a system that guarantees the privacy of samples…

Machine Learning · Computer Science 2023-10-13 Daniël Vos , Jelle Vos , Tianyu Li , Zekeriya Erkin , Sicco Verwer

Dynamic treatment regimes (DTRs) are used in medicine to tailor sequential treatment decisions to patients by considering patient heterogeneity. Common methods for learning optimal DTRs, however, have shortcomings: they are typically based…

Machine Learning · Statistics 2023-06-21 Theresa Blümlein , Joel Persson , Stefan Feuerriegel

There are many approaches for training decision trees. This work introduces a novel gradient-based method for constructing decision trees that optimize arbitrary differentiable loss functions, overcoming the limitations of heuristic…

Machine Learning · Computer Science 2025-03-25 Andrei V. Konstantinov , Lev V. Utkin

We propose Causal Interaction Trees for identifying subgroups of participants that have enhanced treatment effects using observational data. We extend the Classification and Regression Tree algorithm by using splitting criteria that focus…

Methodology · Statistics 2021-12-08 Jiabei Yang , Issa J. Dahabreh , Jon A. Steingrimsson

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

Reinforcement learning techniques achieved human-level performance in several tasks in the last decade. However, in recent years, the need for interpretability emerged: we want to be able to understand how a system works and the reasons…

Machine Learning · Computer Science 2023-01-13 Leonardo Lucio Custode , Giovanni Iacca

We address the problem of learning binary decision trees that partition data for some downstream task. We propose to learn discrete parameters (i.e., for tree traversals and node pruning) and continuous parameters (i.e., for tree split…

Machine Learning · Computer Science 2021-06-15 Valentina Zantedeschi , Matt J. Kusner , Vlad Niculae

In traditional machine learning techniques, the degree of closeness between true and predicted values generally measures the quality of predictions. However, these learning algorithms do not consider prescription problems where the…

Machine Learning · Computer Science 2021-01-05 Mehmet Kolcu , Alper E. Murat

Many chemical engineering systems are governed by mechanisms that switch across operating regimes, making the data-driven discovery of regime-dependent governing equations essential for predictive modeling, optimization, and control. We…

Systems and Control · Electrical Eng. & Systems 2026-05-26 Ilias Mitrai , Tongjia Liu , Gabriel E. Sanoja

We propose a prognostic stratum matching framework that addresses the deficiencies of Randomized trial data subgroup analysis and transforms ObservAtional Data to be used as if they were randomized, thus paving the road for precision…

Applications · Statistics 2023-11-06 Dimitris Bertsimas , Angelos G. Koulouras , Georgios Antonios Margonis

For optimization models to be used in practice, it is crucial that users trust the results. A key factor in this aspect is the interpretability of the solution process. A previous framework for inherently interpretable optimization models…

Optimization and Control · Mathematics 2026-02-13 Marc Goerigk , Michael Hartisch , Sebastian Merten , Kartikey Sharma

We consider the problem of learning optimal binary classification trees. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in…

Machine Learning · Statistics 2020-05-14 Sina Aghaei , Andres Gomez , Phebe Vayanos

In recent years, significant progress has been made on algorithms for learning optimal decision trees, primarily in the context of binary features. Extending these methods to continuous features remains substantially more challenging due to…

Machine Learning · Computer Science 2026-01-22 Harold Kiossou , Pierre Schaus , Siegfried Nijssen

Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of $n$ variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the…

Data Structures and Algorithms · Computer Science 2026-05-06 Juha Harviainen , Frank Sommer , Manuel Sorge

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…

Machine Learning · Computer Science 2025-10-24 Xi He , Max A. Little

Random forests are among the most famous algorithms for solving classification problems, in particular for large-scale data sets. Considering a set of labeled points and several decision trees, the method takes the majority vote to classify…

Optimization and Control · Mathematics 2025-01-24 Jan Pablo Burgard , Maria Eduarda Pinheiro , Martin Schmidt