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The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…

Identifying optimal basic feasible solutions to linear programming problems is a critical task for mixed integer programming and other applications. The crossover method, which aims at deriving an optimal extreme point from a suboptimal…

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 new optimization method for the group selection problem in linear regression. In this problem, predictors are assumed to have a natural group structure and the goal is to select a small set of groups that best fits the…

Tree ensembles are powerful models that achieve excellent predictive performances, but can grow to unwieldy sizes. These ensembles are often post-processed (pruned) to reduce memory footprint and improve interpretability. We present…

Improving the precision of heart diseases detection has been investigated by many researchers in the literature. Such improvement induced by the overwhelming health care expenditures and erroneous diagnosis. As a result, various…

Boosting Trees are one of the most successful statistical learning approaches that involve sequentially growing an ensemble of simple regression trees (i.e., "weak learners"). However, gradient boosted trees are not yet available for…

The k-means clustering algorithm is a popular algorithm that partitions data into k clusters. There are many improvements to accelerate the standard algorithm. Most current research employs upper and lower bounds on point-to-cluster…

Structural pruning of neural networks conventionally relies on identifying and discarding less important neurons, a practice often resulting in significant accuracy loss that necessitates subsequent fine-tuning efforts. This paper…

We propose a new optimization-based approach for feature selection in tree ensembles, an important problem in statistics and machine learning. Popular tree ensemble toolkits e.g., Gradient Boosted Trees and Random Forests support feature…

Motivated by two case studies using primary care records from the Clinical Practice Research Datalink, we describe statistical methods that facilitate the analysis of tall data, with very large numbers of observations. Our focus is on…

Sequential model-based optimization sequentially selects a candidate point by constructing a surrogate model with the history of evaluations, to solve a black-box optimization problem. Gaussian process (GP) regression is a popular choice as…

Trust in counterfactual explanations depends critically on whether their recommended changes are truly minimal: suboptimal explanations may vastly overshoot the actual changes needed to alter a decision, and heuristic errors can affect…

Recursive partitioning is the core of several statistical methods including CART, random forest, and boosted trees. Despite the popularity of tree based methods, to date, there did not exist methods for combining multiple trees into a…

Sparse decision tree optimization has been one of the most fundamental problems in AI since its inception and is a challenge at the core of interpretable machine learning. Sparse decision tree optimization is computationally hard, and…

In this paper, we consider the problem of distributed inference in tree based networks. In the framework considered in this paper, distributed nodes make a 1-bit local decision regarding a phenomenon before sending it to the fusion center…

Model customization necessitates high-quality and diverse datasets, but acquiring such data remains time-consuming and labor-intensive. Despite the great potential of large language models (LLMs) for data synthesis, current approaches are…

This dissertation focuses on modern causal inference under uncertainty and data restrictions, with applications to neoadjuvant clinical trials, distributed data networks, and robust individualized decision making. In the first project, we…

High-dimensional design spaces underpin a wide range of physics-based modeling and computational design tasks in science and engineering. These problems are commonly formulated as constrained black-box searches over rugged objective…

Tree ensembles are very popular machine learning models, known for their effectiveness in supervised classification and regression tasks. Their performance derives from aggregating predictions of multiple decision trees, which are renowned…