Related papers: Linear convergence of distributed Dykstra's algori…
We collect some results in combinatorial geometry that follow from an inequality of Langer in algebraic geometry. Langer's inequality gives a lower bound on the number of incidences between a point set and its spanned lines, and was…
We introduce novel convergence results for asynchronous iterations that appear in the analysis of parallel and distributed optimization algorithms. The results are simple to apply and give explicit estimates for how the degree of asynchrony…
In many learning tasks, certain requirements on the processing of individual data samples should arguably be formalized as strict constraints in the underlying optimization problem, rather than by means of arbitrary penalties. We show that,…
We investigate the asymptotic behavior of Halpern-type iterations applied to quasi-nonexpansive operators arising in best approximation problems over the intersection of finitely many closed convex sets in $\mathbb{R}^n$. Assuming a local…
We present a parallelized bijective graph matching algorithm that leverages seeds and is designed to match very large graphs. Our algorithm combines spectral graph embedding with existing state-of-the-art seeded graph matching procedures.…
An improved inference method for densely connected systems is presented. The approach is based on passing condensed messages between variables, representing macroscopic averages of microscopic messages. We extend previous work that showed…
Energy-based learning algorithms are alternatives to backpropagation and are well-suited to distributed implementations in analog electronic devices. However, a rigorous theory of convergence is lacking. We make a first step in this…
We study a version of the randomized Kaczmarz algorithm for solving systems of linear equations where the iterates are confined to the solution space of a selected subsystem. We show that the subspace constraint leads to an accelerated…
We find explicit formulas for the Hilbert series of residual intersections of a scheme in terms of the Hilbert series of its conormal modules. In a previous paper we proved that such formulas should exist. We give applications to the…
In a recent paper, a distributed algorithm was proposed for solving linear algebraic equations of the form $Ax = b$ assuming that the equation has at least one solution. The equation is presumed to be solved by $m$ agents assuming that each…
Modern supervised learning techniques, particularly those using deep nets, involve fitting high dimensional labelled data sets with functions containing very large numbers of parameters. Much of this work is empirical. Interesting phenomena…
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…
Consider a family of sets and a single set, called the query set. How can one quickly find a member of the family which has a maximal intersection with the query set? Time constraints on the query and on a possible preprocessing of the set…
In present work, we find a class of Lie algebras, which are defined from the symmetrizable generalized intersection matrices. However, such algebras are different from generalized intersection matrix algebras and intersection matrix…
We consider the popular and classical method of alternating projections for finding a point in the intersection of two closed sets. By situating the algorithm in a metric space, equipped only with well-behaved geodesics and angles (in the…
In the vicinity of a solution of a nonlinear programming problem at which both strict complementarity and linear independence of the active constraints may fail to hold, we describe a technique for distinguishing weakly active from strongly…
We present a class of linear programming approximations for constrained optimization problems. In the case of mixed-integer polynomial optimization problems, if the intersection graph of the constraints has bounded tree-width our…
We study the growth behaviour of rational linear recurrence sequences. We show that for low-order sequences, divergence is decidable in polynomial time. We also exhibit a polynomial-time algorithm which takes as input a divergent rational…
The relation between densities of cycles and the spectrum of a graphon, which implies that the spectra of convergent graphons converge, fundamentally relies on the self-adjointness of the linear operator associated with a graphon. In this…
Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…