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Sequence representations supporting queries $access$, $select$ and $rank$ are at the core of many data structures. There is a considerable gap between the various upper bounds and the few lower bounds known for such representations, and how…
Constraint programming (CP) has been used with great success to tackle a wide variety of constraint satisfaction problems which are computationally intractable in general. Global constraints are one of the important factors behind the…
Determinant maximization provides an elegant generalization of problems in many areas, including convex geometry, statistics, machine learning, fair allocation of goods, and network design. In an instance of the determinant maximization…
Hypergraphs, increasingly utilised to model complex and diverse relationships in modern networks, have gained significant attention for representing intricate higher-order interactions. Among various challenges, cohesive subgraph discovery…
A coreset is a point set containing information about geometric properties of a larger point set. A series of previous works show that in many machine learning problems, especially in clustering problems, coreset could be very useful to…
The paper develops a general framework for constrained clustering which is based on the close connection of geometric clustering and diagrams. Various new structural and algorithmic results are proved (and known results generalized and…
Designing small-sized \emph{coresets}, which approximately preserve the costs of the solutions for large datasets, has been an important research direction for the past decade. We consider coreset construction for a variety of general…
To cope with the high level of ambiguity faced in domains such as Computer Vision or Natural Language processing, robust prediction methods often search for a diverse set of high-quality candidate solutions or proposals. In structured…
The problem of clustering noisy and incompletely observed high-dimensional data points into a union of low-dimensional subspaces and a set of outliers is considered. The number of subspaces, their dimensions, and their orientations are…
In this note we give an example application of a recently presented predictive learning method called Rule Ensembles. The application we present is the search for super-symmetric particles at the Large Hadron Collider. In particular, we…
Ensembles of artificial neural networks show improved generalization capabilities that outperform those of single networks. However, for aggregation to be effective, the individual networks must be as accurate and diverse as possible. An…
Tensor networks provide a powerful framework for compressing multi-dimensional data. The optimal tensor network structure for a given data tensor depends on both data characteristics and specific optimality criteria, making tensor network…
Structured pruning is an effective approach for compressing large pre-trained neural networks without significantly affecting their performance. However, most current structured pruning methods do not provide any performance guarantees, and…
In 'An asymptotic result on compressed sensing matrices', a new construction for compressed sensing matrices using combinatorial design theory was introduced. In this paper, we use deterministic and probabilistic methods to analyse the…
High-throughput computational materials design promises to greatly accelerate the process of discovering new materials and compounds, and of optimizing their properties. The large databases of structures and properties that result from…
We investigate two new optimization problems -- minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint…
In this paper, we study a number of well-known combinatorial optimization problems that fit in the following paradigm: the input is a collection of (potentially inconsistent) local relationships between the elements of a ground set (e.g.,…
The best subset selection (or "best subsets") estimator is a classic tool for sparse regression, and developments in mathematical optimization over the past decade have made it more computationally tractable than ever. Notwithstanding its…
Feature importance ranking has become a powerful tool for explainable AI. However, its nature of combinatorial optimization poses a great challenge for deep learning. In this paper, we propose a novel dual-net architecture consisting of…
The area of constrained clustering has been extensively explored by researchers and used by practitioners. Constrained clustering formulations exist for popular algorithms such as k-means, mixture models, and spectral clustering but have…