Related papers: Exact Matrix Seriation through Mathematical Optimi…
We propose a novel solution framework for inverse mixed-integer optimization based on analytic center concepts from interior point methods. We characterize the optimality gap of a given solution, provide structural results, and propose…
Hierarchical matrices approximate a given matrix by a decomposition into low-rank submatrices that can be handled efficiently in factorized form. $\mathcal{H}^2$-matrices refine this representation following the ideas of fast multipole…
We show several ways to round a real matrix to an integer one such that the rounding errors in all rows and columns as well as the whole matrix are less than one. This is a classical problem with applications in many fields, in particular,…
Mixture model-based clustering, usually applied to multidimensional data, has become a popular approach in many data analysis problems, both for its good statistical properties and for the simplicity of implementation of the…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
We consider a matrix completion problem that exploits social or item similarity graphs as side information. We develop a universal, parameter-free, and computationally efficient algorithm that starts with hierarchical graph clustering and…
Current state-of-the-art methods for differentially private model training are based on matrix factorization techniques. However, these methods suffer from high computational overhead because they require numerically solving a demanding…
Decision making algorithms are used in a multitude of different applications. Conventional approaches for designing decision algorithms employ principled and simplified modelling, based on which one can determine decisions via tractable…
Metropolitan scale vehicular traffic modeling is used by a variety of private and public sector urban mobility stakeholders to inform the design and operations of road networks. High-resolution stochastic traffic simulators are increasingly…
This paper reviews recent advances in the field of optimization under uncertainty via a modern data lens, highlights key research challenges and promise of data-driven optimization that organically integrates machine learning and…
We consider the problem of solving a large-scale system of linear equations in a distributed or federated manner by a taskmaster and a set of machines, each possessing a subset of the equations. We provide a comprehensive comparison of two…
We introduce a convex optimization modeling framework that transforms a convex optimization problem expressed in a form natural and convenient for the user into an equivalent cone program in a way that preserves fast linear transforms in…
Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…
This paper presents a unified mixed-integer programming framework for training sparse and interpretable neural networks. We develop exact formulations for both fully connected and convolutional architectures by modeling nonlinearities such…
Co-clustering simultaneously clusters rows and columns, revealing more fine-grained groups. However, existing co-clustering methods suffer from poor scalability and cannot handle large-scale data. This paper presents a novel and scalable…
This paper addresses the problem of synchronizing orthogonal matrices over directed graphs. For synchronized transformations (or matrices), composite transformations over loops equal the identity. We formulate the synchronization problem as…
We study the problem of learning similarity by using nonlinear embedding models (e.g., neural networks) from all possible pairs. This problem is well-known for its difficulty of training with the extreme number of pairs. For the special…
Networks analysis has been commonly used to study the interactions between units of complex systems. One problem of particular interest is learning the network's underlying connection pattern given a single and noisy instantiation. While…
Seriation is a problem consisting of seeking the best enumeration order of a set of units whose interrelationship is described by a bipartite graph, that is, a graph whose nodes are partitioned in two sets and arcs only connect nodes in…
Numerical computations involving rational matrices often benefit from preserving underlying matrix structures such as symmetry, Hermitian properties, or sparsity that reflect physical, geometric, or algebraic characteristics of the system.…