Related papers: Tight Mixed-Integer Optimization Formulations for …

In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…

Clustered data, which arise when observations are nested within groups, are incredibly common in clinical, education, and social science research. Traditionally, a linear mixed model, which includes random effects to account for…

An important problem in optimization is the construction of mixed-integer programming (MIP) formulations of disjunctive constraints that are both strong and small. Motivated by lower bounds on the number of integer variables that are…

Based on decision trees, many fields have arguably made tremendous progress in recent years. In simple words, decision trees use the strategy of "divide-and-conquer" to divide the complex problem on the dependency between input features and…

Fixed effects models are very flexible because they do not make assumptions on the distribution of effects and can also be used if the heterogeneity component is correlated with explanatory variables. A disadvantage is the large number of…

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…

In this paper, we show that conditional inference trees and ensembles are suitable methods for modeling linguistic variation. As against earlier linguistic applications, however, we claim that their suitability is strongly increased if we…

Mixed-integer programming (MIP) has emerged as a powerful framework for learning optimal decision trees. Yet, existing MIP approaches for regression tasks are either limited to purely binary features or become computationally intractable…

We present a class of linear programming approximations for constrained optimization problems. In the case of mixed-integer polynomial optimization problems, if the intersection graph of the constraints has bounded tree-width our…

We proposed the tensor-input tree (TT) method for scalar-on-tensor and tensor-on-tensor regression problems. We first address scalar-on-tensor problem by proposing scalar-output regression tree models whose input variable are tensors (i.e.,…

Chance constrained optimization problems allow to model problems where constraints involving stochastic components should only be violated with a small probability. Evolutionary algorithms have been applied to this scenario and shown to…

We introduce Hyper-Trees as a novel framework for modeling time series data using gradient boosted trees. Unlike conventional tree-based approaches that forecast time series directly, Hyper-Trees learn the parameters of a target time series…

Recent studies have demonstrated advantages of information fusion based on sparsity models for multimodal classification. Among several sparsity models, tree-structured sparsity provides a flexible framework for extraction of…

This paper introduces Weighted Optimal Classification Forests (WOCFs), a new family of classifiers that takes advantage of an optimal ensemble of decision trees to derive accurate and interpretable classifiers. We propose a novel…

Generalized linear and additive models are very efficient regression tools but the selection of relevant terms becomes difficult if higher order interactions are needed. In contrast, tree-based methods also known as recursive partitioning…

Within machine learning, the supervised learning field aims at modeling the input-output relationship of a system, from past observations of its behavior. Decision trees characterize the input-output relationship through a series of nested…

Extended formulations are an important tool in polyhedral combinatorics. Many combinatorial optimization problems require an exponential number of inequalities when modeled as a linear program in the natural space of variables. However, by…

Bringing together nonlinear optimization with polyhedral and integrality constraints enables versatile modeling, but poses significant computational challenges. We investigate a method to address these problems based on sequential…

This paper is concerned with the approximation of high-dimensional functions in a statistical learning setting, by empirical risk minimization over model classes of functions in tree-based tensor format. These are particular classes of…

We present an integrated prediction-optimization (PredOpt) framework to efficiently solve sequential decision-making problems by predicting the values of binary decision variables in an optimal solution. We address the key issues of…