Related papers: Parallel QR Factorization of Block Low-Rank Matric…

Kernel matrices appear in machine learning and non-parametric statistics. Given $N$ points in $d$ dimensions and a kernel function that requires $\mathcal{O}(d)$ work to evaluate, we present an $\mathcal{O}(dN\log N)$-work algorithm for the…

The QR factorization and the SVD are two fundamental matrix decompositions with applications throughout scientific computing and data analysis. For matrices with many more rows than columns, so-called "tall-and-skinny matrices," there is a…

The QR Decomposition (QRD) of communication channel matrices is a fundamental prerequisite to several detection schemes in Multiple-Input Multiple-Output (MIMO) communication systems. Herein, the main feature of the QRD is to transform the…

This paper develops and analyzes a new algorithm for QR decomposition with column pivoting (QRCP) of rectangular matrices with many more rows than columns. The algorithm carefully combines methods from randomized numerical linear algebra to…

We provide a number of algorithmic results for the following family of problems: For a given binary m\times n matrix A and integer k, decide whether there is a "simple" binary matrix B which differs from A in at most k entries. For an…

Many applications in scientific computing and data science require the computation of a rank-revealing factorization of a large matrix. In many of these instances the classical algorithms for computing the singular value decomposition are…

Firms earning prediction plays a vital role in investment decisions, dividends expectation, and share price. It often involves multiple tensor-compatible datasets with non-linear multi-way relationships, spatiotemporal structures, and…

Identifying discrete patterns in binary data is an important dimensionality reduction tool in machine learning and data mining. In this paper, we consider the problem of low-rank binary matrix factorisation (BMF) under Boolean arithmetic.…

The Restricted Boltzmann Machine (RBM) is a stochastic neural network capable of solving a variety of difficult tasks such as NP-Hard combinatorial optimization problems and integer factorization. The RBM architecture is also very compact;…

Boolean matrix factorization (BMF) approximates a given binary input matrix as the product of two smaller binary factors. Unlike binary matrix factorization based on standard arithmetic, BMF employs the Boolean OR and AND operations for the…

We introduce a task-parallel algorithm for sparse incomplete Cholesky factorization that utilizes a 2D sparse partitioned-block layout of a matrix. Our factorization algorithm follows the idea of algorithms-by-blocks by using the block…

The pivoted QLP decomposition is computed through two consecutive pivoted QR decompositions, and provides an approximation to the singular value decomposition. This work is concerned with a partial QLP decomposition of low-rank matrices…

We present factorization and solution phases for a new linear complexity direct solver designed for concurrent batch operations on fine-grained parallel architectures, for matrices amenable to hierarchical representation. We focus on the…

Minimum Bayes Risk (MBR) decoding is a powerful decoding strategy widely used for text generation tasks, but its quadratic computational complexity limits its practical application. This paper presents a novel approach for approximating MBR…

Many tasks in data mining and related fields can be formalized as matching between objects in two heterogeneous domains, including collaborative filtering, link prediction, image tagging, and web search. Machine learning techniques,…

We propose a new algorithm called higher-order QR iteration (HOQRI) for computing low multilinear rank approximation (LMLRA), also known as the Tucker decomposition, of large and sparse tensors. Compared to the celebrated higher-order…

The Cholesky QR algorithm is an efficient communication-minimizing algorithm for computing the QR factorization of a tall-skinny matrix. Unfortunately it has the inherent numerical instability and breakdown when the matrix is…

Matrix Factorization (MF) on large scale matrices is computationally as well as memory intensive task. Alternative convergence techniques are needed when the size of the input matrix is higher than the available memory on a Central…

We are interested in parallelizing the Least Angle Regression (LARS) algorithm for fitting linear regression models to high-dimensional data. We consider two parallel and communication avoiding versions of the basic LARS algorithm. The two…

When faced with learning a set of inter-related tasks from a limited amount of usable data, learning each task independently may lead to poor generalization performance. Multi-Task Learning (MTL) exploits the latent relations between tasks…