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Incorporating domain-specific constraints into machine learning models is essential for generating predictions that are both accurate and feasible in real-world applications. This paper introduces new methods for training Output-Constrained…
Global optimization of decision trees is a long-standing challenge in combinatorial optimization, yet such models play an important role in interpretable machine learning. Although the problem has been investigated for several decades, only…
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…
Several recent publications report advances in training optimal decision trees (ODT) using mixed-integer programs (MIP), due to algorithmic advances in integer programming and a growing interest in addressing the inherent suboptimality of…
This paper proposes a new mixed-integer programming (MIP) formulation to optimize split rule selection in the decision tree induction process, and develops an efficient search algorithm that is able to solve practical instances of the MIP…
In recent years, there has been growing attention to interpretable machine learning models which can give explanatory insights on their behaviour. Thanks to their interpretability, decision trees have been intensively studied for…
We study computational aspects of a key problem in robust statistics -- the penalized least trimmed squares (LTS) regression problem, a robust estimator that mitigates the influence of outliers in data by capping residuals with large…
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.…
Nonconvex optimization refers to the process of solving problems whose objective or constraints are nonconvex. Historically, this type of problems have been very difficult to solve to global optimality, with traditional solvers often…
Decision trees are a popular machine learning model which are traditionally trained by heuristic methods. Massive improvements in computing power and optimisation techniques has led to renewed interest in learning globally optimal decision…
Decision trees are a popular choice of explainable model, but just like neural networks, they suffer from adversarial examples. Existing algorithms for fitting decision trees robust against adversarial examples are greedy heuristics and…
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…
The global optimization of classification trees has demonstrated considerable promise, notably in enhancing accuracy, optimizing size, and thereby improving human comprehensibility. While existing optimal classification trees substantially…
We consider the problem of learning classification trees that are robust to distribution shifts between training and testing/deployment data. This problem arises frequently in high stakes settings such as public health and social work where…
Decision trees are one of the most useful and popular methods in the machine learning toolbox. In this paper, we consider the problem of learning optimal decision trees, a combinatorial optimization problem that is challenging to solve at…
The Binary Space Partitioning-Tree~(BSP-Tree) process was recently proposed as an efficient strategy for space partitioning tasks. Because it uses more than one dimension to partition the space, the BSP-Tree Process is more efficient and…
Multivariate decision trees are powerful machine learning tools for classification and regression that attract many researchers and industry professionals. An optimal binary tree has two types of vertices, (i) branching vertices which have…
Combinatorial optimisation problems framed as mixed integer linear programmes (MILPs) are ubiquitous across a range of real-world applications. The canonical branch-and-bound algorithm seeks to exactly solve MILPs by constructing a search…
Decision trees are among the most popular machine learning models and are used routinely in applications ranging from revenue management and medicine to bioinformatics. In this paper, we consider the problem of learning optimal binary…
In this paper, we present Batch Informed Trees (BIT*), a planning algorithm based on unifying graph- and sampling-based planning techniques. By recognizing that a set of samples describes an implicit random geometric graph (RGG), we are…