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Machine learning is increasingly used to guide branch-and-cut (B&C) for mixed-integer linear programming by learning score-based policies for selecting branching variables and cutting planes. Many approaches train on local signals from…

Eliciting preferences from human judgements is inherently imprecise, yet most decision analysis methods force a single priority vector from pairwise comparisons, discarding the information embedded in inconsistencies. We instead leverage…

We investigate active learning by pairwise similarity over the leaves of trees originating from hierarchical clustering procedures. In the realizable setting, we provide a full characterization of the number of queries needed to achieve…

A number of recent works have employed decision trees for the construction of explainable partitions that aim to minimize the $k$-means cost function. These works, however, largely ignore metrics related to the depths of the leaves in the…

We introduce canonical correlation forests (CCFs), a new decision tree ensemble method for classification and regression. Individual canonical correlation trees are binary decision trees with hyperplane splits based on local canonical…

Decision trees are renowned for their ability to achieve high predictive performance while remaining interpretable, especially on tabular data. Traditionally, they are constructed through recursive algorithms, where they partition the data…

In binary classification tasks, accurate representation of probabilistic predictions is essential for various real-world applications such as predicting payment defaults or assessing medical risks. The model must then be well-calibrated to…

Tree ensembles are non-parametric methods widely recognized for their accuracy and ability to capture complex interactions. While these models excel at prediction, they are difficult to interpret and may fail to uncover useful relationships…

Standard supervised learning procedures are validated against a test set that is assumed to have come from the same distribution as the training data. However, in many problems, the test data may have come from a different distribution. We…

Clustering serves as a vital tool for uncovering latent data structures, and achieving both high accuracy and interpretability is essential. To this end, existing methods typically construct binary decision trees by solving mixed-integer…

Many machine learning tools for regression are based on recursive partitioning of the covariate space into smaller regions, where the regression function can be estimated locally. Among these, regression trees and their ensembles have…

Top-down induction of decision trees has been observed to suffer from the inadequate functioning of the pruning phase. In particular, it is known that the size of the resulting tree grows linearly with the sample size, even though the…

One-class Classification (OCC) is an area of machine learning which addresses prediction based on unbalanced datasets. Basically, OCC algorithms achieve training by means of a single class sample, with potentially some additional…

While globally optimal empirical risk minimization (ERM) decision trees have become computationally feasible and empirically successful, rigorous theoretical guarantees for their statistical performance remain limited. In this work, we…

The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…

This paper studies simultaneous feature selection and extraction in supervised and unsupervised learning. We propose and investigate selective reduced rank regression for constructing optimal explanatory factors from a parsimonious subset…

Feature subsampling is a core component of random forests and other ensemble methods. While recent theory suggests that this randomization acts solely as a variance reduction mechanism analogous to ridge regularization, these results…

Pairwise ordered tree alignment are combinatorial objects that appear in RNA secondary structure comparison. However, the usual representation of tree alignments as supertrees is ambiguous, i.e. two distinct supertrees may induce identical…

We consider the problem of learning decision rules for prediction with feature budget constraint. In particular, we are interested in pruning an ensemble of decision trees to reduce expected feature cost while maintaining high prediction…

When introducing physics-constrained deep learning solutions to the volumetric super-resolution of scientific data, the training is challenging to converge and always time-consuming. We propose a new hierarchical sampling method based on…