Related papers: On the equivalence of the Hermitian eigenvalue pro…
We define geometric matrix midranges for positive definite Hermitian matrices and study the midrange problem from a number of perspectives. Special attention is given to the midrange of two positive definite matrices before considering the…
We consider large non-Hermitian random matrices $X$ with complex, independent, identically distributed centred entries and show that the linear statistics of their eigenvalues are asymptotically Gaussian for test functions having…
A dominating induced matching, also called an efficient edge domination, of a graph $G=(V,E)$ with $n=|V|$ vertices and $m=|E|$ edges is a subset $F \subseteq E$ of edges in the graph such that no two edges in $F$ share a common endpoint…
Max-k-Cut and correlation clustering are fundamental graph partitioning problems. For a graph with G=(V,E) with n vertices, the methods with the best approximation guarantees for Max-k-Cut and the Max-Agree variant of correlation clustering…
For large-scale eigenvalue problems requiring many mutually orthogonal eigenvectors, traditional numerical methods suffer substantial computational and communication costs with limited parallel scalability, primarily due to explicit…
Characterizing precisely the asymptotic generalization error of neural networks using parameters that can be estimated efficiently is a crucial problem in machine learning, which relies heavily on heuristics and practitioners' intuition to…
In this paper, the Riemannian gradient algorithm and the natural gradient algorithm are applied to solve descent direction problems on the manifold of positive definite Hermitian matrices, where the geodesic distance is considered as the…
Graph representation learning is a ubiquitous task in machine learning where the goal is to embed each vertex into a low-dimensional vector space. We consider the bipartite graph and formalize its representation learning problem as a…
We show how the band structure and beam dynamics of non-Hermitian $PT$-symmetric sinusoidal optical lattices can be approached from the point of view of the equivalent Hermitian problem, obtained by an analytic continuation in the…
The matching problem between two adjacency matrices can be formulated as the NP-hard quadratic assignment problem (QAP). Previous work on semidefinite programming (SDP) relaxations to the QAP have produced solutions that are often tight in…
The (non-uniform) sparsest cut problem is the following graph-partitioning problem: given a "supply" graph, and demands on pairs of vertices, delete some subset of supply edges to minimize the ratio of the supply edges cut to the total…
Precision matrix estimation in a multivariate Gaussian model is fundamental to network estimation. Although there exist both Bayesian and frequentist approaches to this, it is difficult to obtain good Bayesian and frequentist properties…
Graph alignment refers to the task of finding the vertex correspondence between two correlated graphs of $n$ vertices. Extensive study has been done on polynomial-time algorithms for the graph alignment problem under the Erd\H{o}s-R\'enyi…
The sparse generalized eigenvalue problem arises in a number of standard and modern statistical learning models, including sparse principal component analysis, sparse Fisher discriminant analysis, and sparse canonical correlation analysis.…
Graph matching---aligning a pair of graphs to minimize their edge disagreements---has received wide-spread attention from both theoretical and applied communities over the past several decades, including combinatorics, computer vision, and…
Scalable algorithms to solve optimization and regression tasks even approximately, are needed to work with large datasets. In this paper we study efficient techniques from matrix sketching to solve a variety of convex constrained regression…
In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…
Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalues, and is of practical interest because of wide range of applications in fields such as structural…
We adapt a symmetric interior penalty discontinuous Galerkin method using a patch reconstructed approximation space to solve elliptic eigenvalue problems, including both second and fourth order problems in 2D and 3D. It is a direct…
The algorithm of Gutwenger et al. to insert an edge $e$ in linear time into a planar graph $G$ with a minimal number of crossings on $e$, is a helpful tool for designing heuristics that minimize edge crossings in drawings of general graphs.…