Related papers: Scalable Parallel Factorizations of SDD Matrices a…

Sparse matrix-vector and matrix-matrix multiplication (SpMV and SpMM) are fundamental in both conventional (graph analytics, scientific computing) and emerging (sparse DNN, GNN) domains. Workload-balancing and parallel-reduction are…

Sampling is a critical operation in Graph Neural Network (GNN) training that helps reduce the cost. Previous literature has explored improving sampling algorithms via mathematical and statistical methods. However, there is a gap between…

Graph sparsification underlies a large number of algorithms, ranging from approximation algorithms for cut problems to solvers for linear systems in the graph Laplacian. In its strongest form, "spectral sparsification" reduces the number of…

The Massive Parallel Computation (MPC) model is a theoretical framework for popular parallel and distributed platforms such as MapReduce, Hadoop, or Spark. We consider the task of computing a large matching or small vertex cover in this…

We describe a computationally efficient, stochastic graph-regularization technique that can be utilized for the semi-supervised training of deep neural networks in a parallel or distributed setting. We utilize a technique, first described…

Distributed maximization of a submodular function in the MapReduce (MR) model has received much attention, culminating in two frameworks that allow a centralized algorithm to be run in the MR setting without loss of approximation, as long…

Uniform sampling of simple graphs having a given degree sequence is a known problem with exponential complexity in the square of the mean degree. For undirected graphs, randomised approximation algorithms have nonetheless been shown to…

We introduce a new scalable approximation for Gaussian processes with provable guarantees which hold simultaneously over its entire parameter space. Our approximation is obtained from an improved sample complexity analysis for sparse…

In this paper, we present a simple combinatorial algorithm that solves symmetric diagonally dominant (SDD) linear systems in nearly-linear time. It uses very little of the machinery that previously appeared to be necessary for a such an…

Dijkstra's algorithm for the Single-Source Shortest Path (SSSP) problem is notoriously hard to parallelize in $o(n)$ depth, $n$ being the number of vertices in the input graph, without increasing the required parallel work unreasonably.…

Symmetric submodular maximization is an important class of combinatorial optimization problems, including MAX-CUT on graphs and hyper-graphs. The state-of-the-art algorithm for the problem over general constraints has an approximation ratio…

Graphs arising in statistical problems, signal processing, large networks, combinatorial optimization, and data analysis are often dense, which causes both computational and storage bottlenecks. One way of \textit{sparsifying} a…

We describe a simple algorithm for spectral graph sparsification, based on iterative computations of weighted spanners and uniform sampling. Leveraging the algorithms of Baswana and Sen for computing spanners, we obtain the first…

Partitioning the vertices of a graph into two roughly equal parts while minimizing the number of edges crossing the cut is a fundamental problem (called Balanced Separator) that arises in many settings. For this problem, and variants such…

Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral…

Machine learning models, and deep neural networks in particular, are increasingly deployed in risk-sensitive domains such as healthcare, environmental forecasting, and finance, where reliable quantification of predictive uncertainty is…

Mathematical modelling, particularly through approaches such as structured sparse support vector machines (SS-SVM), plays a crucial role in processing data with complex feature structures, yet efficient algorithms for distributed…

We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…

In this paper we describe a parallel Gaussian elimination algorithm for matrices with entries in a finite field. Unlike previous approaches, our algorithm subdivides a very large input matrix into smaller submatrices by subdividing both…

Gaussian Mixture Models (GMMs) range among the most frequently used models in machine learning. However, training large, general GMMs becomes computationally prohibitive for datasets that have many data points $N$ of high-dimensionality…