Related papers: Accurate and Scalable Matrix Mechanisms via Divide…

While MCMC methods have become a main work-horse for Bayesian inference, scaling them to large distributed datasets is still a challenge. Embarrassingly parallel MCMC strategies take a divide-and-conquer stance to achieve this by writing…

Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decimation' scheme that maps it to neural network models of…

We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…

Scientific Machine Learning (SciML) faces unique challenges for extreme-resolution data, with mitigations that often fail to scale or degrade the accuracy of trained models. While some specialized methods have achieved remarkable results in…

A parallel algorithm has perfect strong scaling if its running time on P processors is linear in 1/P, including all communication costs. Distributed-memory parallel algorithms for matrix multiplication with perfect strong scaling have only…

Divide-and-conquer Bayesian methods consist of three steps: dividing the data into smaller computationally manageable subsets, running a sampling algorithm in parallel on all the subsets, and combining parameter draws from all the subsets.…

Efficient task scheduling is paramount in parallel programming on multi-core architectures, where tasks are fundamental computational units. QR factorization is a critical sub-routine in Sequential Least Squares Quadratic Programming…

Zoned neutral atom architectures are emerging as a promising platform for large-scale quantum computing. Their growing scale, however, creates a critical need for efficient and automated compilation solutions. Yet, existing methods fail to…

Performing low-rank matrix completion with sensitive user data calls for privacy-preserving approaches. In this work, we propose a novel noise addition mechanism for preserving differential privacy where the noise distribution is inspired…

Matrix rank minimization (RM) problems recently gained extensive attention due to numerous applications in machine learning, system identification and graphical models. In RM problem, one aims to find the matrix with the lowest rank that…

Due to the ubiquity of spatial data applications and the large amounts of spatial data that these applications generate and process, there is a pressing need for scalable spatial query processing. In this paper, we present new techniques…

A Random SubMatrix method (RSM) is proposed to calculate the low-rank decomposition of large-scale matrices with known entry percentage \rho. RSM is very fast as the floating-point operations (flops) required are compared favorably with the…

Despite the prominence of neural network approaches in the field of recommender systems, simple methods such as matrix factorization with quadratic loss are still used in industry for several reasons. These models can be trained with…

Hierarchical matrices can be used to construct efficient preconditioners for partial differential and integral equations by taking advantage of low-rank structures in triangular factorizations and inverses of the corresponding stiffness…

In computer science, divide and conquer (D&C) is an algorithm design paradigm based on multi-branched recursion. A D&C algorithm works by recursively and monotonically breaking down a problem into sub problems of the same (or a related)…

Overparameterized models have proven to be powerful tools for solving various machine learning tasks. However, overparameterization often leads to a substantial increase in computational and memory costs, which in turn requires extensive…

As the structural databases continue to expand, efficient methods are required to search similar structures of the query structure from the database. There are many previous works about comparing protein 3D structures and scanning the…

Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix…

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…

The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the algorithms iteratively compute a basis matrix, in one of the…