相关论文: RCHOL: Randomized Cholesky Factorization for Solvi…

Sparse, irregular graphs show up in various applications like linear algebra, machine learning, engineering simulations, robotic control, etc. These graphs have a high degree of parallelism, but their execution on parallel threads of modern…

Large graphs commonly appear in social networks, knowledge graphs, recommender systems, life sciences, and decision making problems. Summarizing large graphs by their high level properties is helpful in solving problems in these settings.…

Determining the degree of inherent parallelism in classical sequential algorithms and leveraging it for fast parallel execution is a key topic in parallel computing, and detailed analyses are known for a wide range of classical algorithms.…

Prior to computing the Cholesky factorization of a sparse, symmetric positive definite matrix, a reordering of the rows and columns is computed so as to reduce both the number of fill elements in Cholesky factor and the number of arithmetic…

We study the design of local algorithms for massive graphs. A local algorithm is one that finds a solution containing or near a given vertex without looking at the whole graph. We present a local clustering algorithm. Our algorithm finds a…

Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…

Distributed computing excels at processing large scale data, but the communication cost for synchronizing the shared parameters may slow down the overall performance. Fortunately, the interactions between parameter and data in many problems…

Recent years are characterized by an unprecedented quantity of available network data which are produced at an astonishing rate by an heterogeneous variety of interconnected sensors and devices. This high-throughput generation calls for the…

Clustering the nodes of a graph is a cornerstone of graph analysis and has been extensively studied. However, some popular methods are not suitable for very large graphs: e.g., spectral clustering requires the computation of the spectral…

This paper introduces a randomized Householder QR factorization (RHQR). This factorization can be used to obtain a well conditioned basis of a vector space and thus can be employed in a variety of applications. The RHQR factorization of the…

For a given nonnegative matrix $A=(A_{ij})$, the matrix scaling problem asks whether $A$ can be scaled to a doubly stochastic matrix $D_1AD_2$ for some positive diagonal matrices $D_1,D_2$.The Sinkhorn algorithm is a simple iterative…

This paper considers a high-dimensional linear regression problem where there are complex correlation structures among predictors. We propose a graph-constrained regularization procedure, named Sparse Laplacian Shrinkage with the Graphical…

Correlation clustering is a central topic in unsupervised learning, with many applications in ML and data mining. In correlation clustering, one receives as input a signed graph and the goal is to partition it to minimize the number of…

We consider the sparse inverse covariance regularization problem or graphical lasso with regularization parameter $\rho$. Suppose the co- variance graph formed by thresholding the entries of the sample covariance matrix at $\rho$ is…

We study recovering a 1D order from a noisy, locally sampled pairwise comparison matrix under a tight query budget. We recast the task as reconstructing a sparse, noisy line graph and present, to our knowledge, the first method that…

We introduce a new notion of graph sparsificaiton based on spectral similarity of graph Laplacians: spectral sparsification requires that the Laplacian quadratic form of the sparsifier approximate that of the original. This is equivalent to…

Embarrassingly (communication-free) parallel Markov chain Monte Carlo (MCMC) methods are commonly used in learning graphical models. However, MCMC cannot be directly applied in learning topic models because of the quasi-ergodicity problem…

We present an asymptotically faster algorithm for solving linear systems in well-structured 3-dimensional truss stiffness matrices. These linear systems arise from linear elasticity problems, and can be viewed as extensions of graph…

Mosaic Flow is a novel domain decomposition method designed to scale physics-informed neural PDE solvers to large domains. Its unique approach leverages pre-trained networks on small domains to solve partial differential equations on large…

Graph-based techniques and spectral graph theory have enriched the field of machine learning with a variety of critical advances. A central object in the analysis is the graph Laplacian L, which encodes the structure of the graph. We…