Related papers: Accurate and Scalable Matrix Mechanisms via Divide…

In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing…

Real-world vision based applications require fine-grained classification for various area of interest like e-commerce, mobile applications, warehouse management, etc. where reducing the severity of mistakes and improving the classification…

Resource Description Framework (RDF) has been widely used to represent information on the web, while SPARQL is a standard query language to manipulate RDF data. Given a SPARQL query, there often exist many joins which are the bottlenecks of…

Noisy linear problems have been studied in various science and engineering disciplines. A class of "hard" noisy linear problems can be formulated as follows: Given a matrix $\hat{A}$ and a vector $\mathbf{b}$ constructed using a finite set…

The residual stream acts as a memory bus where transformer layers both store and access features (Elhage et al., 2021). We consider changing the mechanism for retrieving and storing information in the residual stream, and replace the…

We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning,…

Matrix factorization is a common machine learning technique for recommender systems. Despite its high prediction accuracy, the Bayesian Probabilistic Matrix Factorization algorithm (BPMF) has not been widely used on large scale data because…

A scalable algorithm for solving compact banded linear systems on distributed memory architectures is presented. The proposed method factorizes the original system into two levels of memory hierarchies, and solves it using parallel cyclic…

Matrix factorization is a very common machine learning technique in recommender systems. Bayesian Matrix Factorization (BMF) algorithms would be attractive because of their ability to quantify uncertainty in their predictions and avoid…

As the volume of the RDF data becomes increasingly large, it is essential for us to design a distributed database system to manage it. For distributed RDF data design, it is quite common to partition the RDF data into some parts, called…

The use of large-scale machine learning methods is becoming ubiquitous in many applications ranging from business intelligence to self-driving cars. These methods require a complex computation pipeline consisting of various types of…

Multiresolution Matrix Factorization (MMF) was recently introduced as an alternative to the dominant low-rank paradigm in order to capture structure in matrices at multiple different scales. Using ideas from multiresolution analysis (MRA),…

Query re-optimization is an adaptive query processing technique that re-invokes the optimizer at certain points in query execution. The goal is to dynamically correct the cardinality estimation errors using the statistics collected at…

Multiresolution Matrix Factorization (MMF) was recently introduced as a method for finding multiscale structure and defining wavelets on graphs/matrices. In this paper we derive pMMF, a parallel algorithm for computing the MMF…

Treemaps have been widely applied to the visualization of hierarchical data. A treemap takes a weighted tree and visualizes its leaves in a nested planar geometric shape, with sub-regions partitioned such that each sub-region has an area…

Reasoning tasks are crucial in many domains, especially in science and engineering. Although large language models (LLMs) have made progress in reasoning tasks using techniques such as chain-of-thought and least-to-most prompting, these…

This paper introduces RankMap, a platform-aware end-to-end framework for efficient execution of a broad class of iterative learning algorithms for massive and dense datasets. Our framework exploits data structure to factorize it into an…

Master Data Management (MDM) ensures data integrity, consistency, and reliability across an organization's systems. I introduce a novel complex match and merge algorithm optimized for real-time MDM solutions. The proposed method accurately…

We develop a message-passing algorithm for noisy matrix completion problems based on matrix factorization. The algorithm is derived by approximating message distributions of belief propagation with Gaussian distributions that share the same…

Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to…