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Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…

This paper investigates convex quadratic optimization problems involving $n$ indicator variables, each associated with a continuous variable, particularly focusing on scenarios where the matrix $Q$ defining the quadratic term is positive…

Decision tree learning is a widely used approach in machine learning, favoured in applications that require concise and interpretable models. Heuristic methods are traditionally used to quickly produce models with reasonably high accuracy.…

Prediction+optimization is a common real-world paradigm where we have to predict problem parameters before solving the optimization problem. However, the criteria by which the prediction model is trained are often inconsistent with the goal…

The tree metric theorem provides a combinatorial four point condition that characterizes dissimilarity maps derived from pairwise compatible split systems. A similar (but weaker) four point condition characterizes dissimilarity maps derived…

This paper proposes an efficient hypergraph partitioning framework based on a novel multi-objective non-convex constrained relaxation model. A modified accelerated proximal gradient algorithm is employed to generate diverse $k$-dimensional…

This article describes a novel optimization solution framework, called alternating gradient descent (GD) and minimization (AltGDmin), that is useful for many problems for which alternating minimization (AltMin) is a popular solution. AltMin…

The aim of this paper is to develop a method for proving almost sure convergence in Gromov-Hausodorff-Prokhorov topology for a class of models of growing random graphs that generalises R\'emy's algorithm for binary trees. We describe the…

Interpretability is crucial for doctors, hospitals, pharmaceutical companies and biotechnology corporations to analyze and make decisions for high stakes problems that involve human health. Tree-based methods have been widely adopted for…

While normalizing flows for continuous data have been extensively researched, flows for discrete data have only recently been explored. These prior models, however, suffer from limitations that are distinct from those of continuous flows.…

Efficient and automated design of optimizers plays a crucial role in full-stack AutoML systems. However, prior methods in optimizer search are often limited by their scalability, generability, or sample efficiency. With the goal of…

We consider a general class of two-stage distributionally robust optimization (DRO) problems where the ambiguity set is constrained by fixed marginal probability laws that are not necessarily discrete. We derive primal and dual formulations…

In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…

Modern machine learning algorithms usually involve tuning multiple (from one to thousands) hyperparameters which play a pivotal role in terms of model generalizability. Black-box optimization and gradient-based algorithms are two dominant…

This monograph develops a comprehensive statistical learning framework that is robust to (distributional) perturbations in the data using Distributionally Robust Optimization (DRO) under the Wasserstein metric. Beginning with fundamental…

We introduce a variational algorithm to simulate quantum many-body states based on a tree tensor network ansatz which releases the isometry constraint usually imposed by the real-space renormalization coarse-graining: This additional…

Phylogenetic trees are leaf-labelled trees used to model the evolution of species. Here we explore the practical impact of kernelization (i.e. data reduction) on the NP-hard problem of computing the TBR distance between two unrooted binary…

Graph mining for structural patterns is a fundamental task in many applications. Compilation-based graph mining systems, represented by AutoMine, generate specialized algorithms for the provided patterns and substantially outperform other…

This paper introduces a new algorithm for trajectory optimization, Decoupled Reduced-space and Adaptive Feasibility-repair Trajectory Optimization (DRAFTO). It first constructs a constrained objective that accounts for smoothness, safety,…

The Gromov-Wasserstein (GW) distances define a family of metrics, based on ideas from optimal transport, which enable comparisons between probability measures defined on distinct metric spaces. They are particularly useful in areas such as…