arXiv subjects

Jacobus G. M. van der Linden

Publications and source records attributed to Jacobus G. M. van der Linden.

6 recordsLinked to original sources

arXiv2026

Optimal or Greedy Decision Trees? Revisiting their Objectives, Tuning, and Performance

Recently there has been a surge of interest in optimal decision tree (ODT) methods that globally optimize accuracy directly, in contrast to traditional approaches that locally optimize an impurity or information metric. However, the literature shows conflicting evidence on the value of ODTs, with some demonstrating superior out-of-sample performance of ODTs over greedy approaches, while others show the opposite. The value and performance of ODTs therefore remains one of several open question regarding ODTs, most of which could not be answered before due to lack of scalability. With our experimental study---the largest to this date---we examine five such open questions. Our results show (i) that a major advantage of ODTs over greedy approaches is that they can optimize the target objective directly (e.g., accuracy rather than a proxy such as Gini impurity); (ii) that hyperparameter tuning of ODTs is essential; and reaffirm (iii) that optimal methods, on average, obtain smaller and more accurate trees than greedy approaches. Our results also refute two previously posited hypotheses: (iv) that the difference between optimal and greedy approaches diminish with more data, and (v) that optimal methods are more sensitive to overfitting. Finally, our work provides insights on the value of ODTs, clear recommendations for researchers and practitioners on the usage of greedy and optimal methods, and code for future comparisons.

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arXiv2026

Search Strategies for Optimal Classification and Regression Trees

Optimal decision trees (ODTs) are compact, interpretable machine learning models that globally optimize a given objective, but their scalability remains challenging. While recent work has proposed a variety of search strategies to improve scalability, the precise contribution of each strategy remains unclear. To address this gap, we introduce a general algorithmic framework for ODTs that instantiates previously used search strategies and enables the definition of new ones. This provides a common lens through which to understand and compare different strategies, which we use to empirically investigate the effect of 18 search strategies. Compared to the state of the art, the best strategy in our evaluation achieves significantly better anytime performance for classification, and improves runtime by more than an order of magnitude for regression.

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arXiv2025

SORTeD Rashomon Sets of Sparse Decision Trees: Anytime Enumeration

Sparse decision tree learning provides accurate and interpretable predictive models that are ideal for high-stakes applications by finding the single most accurate tree within a (soft) size limit. Rather than relying on a single "best" tree, Rashomon sets-trees with similar performance but varying structures-can be used to enhance variable importance analysis, enrich explanations, and enable users to choose simpler trees or those that satisfy stakeholder preferences (e.g., fairness) without hard-coding such criteria into the objective function. However, because finding the optimal tree is NP-hard, enumerating the Rashomon set is inherently challenging. Therefore, we introduce SORTD, a novel framework that improves scalability and enumerates trees in the Rashomon set in order of the objective value, thus offering anytime behavior. Our experiments show that SORTD reduces runtime by up to two orders of magnitude compared with the state of the art. Moreover, SORTD can compute Rashomon sets for any separable and totally ordered objective and supports post-evaluating the set using other separable (and partially ordered) objectives. Together, these advances make exploring Rashomon sets more practical in real-world applications.

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arXiv2025

Necessary and Sufficient Conditions for Optimal Decision Trees using Dynamic Programming

Global optimization of decision trees has shown to be promising in terms of accuracy, size, and consequently human comprehensibility. However, many of the methods used rely on general-purpose solvers for which scalability remains an issue. Dynamic programming methods have been shown to scale much better because they exploit the tree structure by solving subtrees as independent subproblems. However, this only works when an objective can be optimized separately for subtrees. We explore this relationship in detail and show the necessary and sufficient conditions for such separability and generalize previous dynamic programming approaches into a framework that can optimize any combination of separable objectives and constraints. Experiments on five application domains show the general applicability of this framework, while outperforming the scalability of general-purpose solvers by a large margin.

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arXiv2025

Optimal Classification Trees for Continuous Feature Data Using Dynamic Programming with Branch-and-Bound

Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three. Therefore, most methods rely on a coarse binarization of continuous features to maintain scalability. We propose a novel algorithm that optimizes trees directly on the continuous feature data using dynamic programming with branch-and-bound. We develop new pruning techniques that eliminate many sub-optimal splits in the search when similar to previously computed splits and we provide an efficient subroutine for computing optimal depth-two trees. Our experiments demonstrate that these techniques improve runtime by one or more orders of magnitude over state-of-the-art optimal methods and improve test accuracy by 5% over greedy heuristics.

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arXiv2024

Optimal Survival Trees: A Dynamic Programming Approach

Survival analysis studies and predicts the time of death, or other singular unrepeated events, based on historical data, while the true time of death for some instances is unknown. Survival trees enable the discovery of complex nonlinear relations in a compact human comprehensible model, by recursively splitting the population and predicting a distinct survival distribution in each leaf node. We use dynamic programming to provide the first survival tree method with optimality guarantees, enabling the assessment of the optimality gap of heuristics. We improve the scalability of our method through a special algorithm for computing trees up to depth two. The experiments show that our method's run time even outperforms some heuristics for realistic cases while obtaining similar out-of-sample performance with the state-of-the-art.

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