Related papers: Analysis of randomized CholeskyQR for sparse matri…

We consider the problem of recovering an $n_1 \times n_2$ low-rank matrix with $k$-sparse singular vectors from a small number of linear measurements (sketch). We propose a sketching scheme and an algorithm that can recover the singular…

We present a set of methods to generate less complex error channels by quantum circuit parallelisation. The resulting errors are simplified as a consequence of their symmetrisation and randomisation. Initially, the case of a single error…

Pairwise Markov Random Fields (MRFs) or undirected graphical models are parsimonious representations of joint probability distributions. Variables correspond to nodes of a graph, with edges between nodes corresponding to conditional…

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…

The Kaczmarz algorithm is popular for iteratively solving an overdetermined system of linear equations. The traditional Kaczmarz algorithm can approximate the solution in few sweeps through the equations but a randomized version of the…

This paper describes a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as…

Estimation of large sparse covariance matrices is of great importance for statistical analysis, especially in the high-dimensional settings. The traditional approach such as the sample covariance matrix performs poorly due to the high…

There is a recent surge of interest in developing algorithms for finding sparse solutions of underdetermined systems of linear equations $y = \Phi x$. In many applications, extremely large problem sizes are envisioned, with at least tens of…

Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…

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…

In this work, we study a variant of nonnegative matrix factorization where we wish to find a symmetric factorization of a given input matrix into a sparse, Boolean matrix. Formally speaking, given $\mathbf{M}\in\mathbb{Z}^{m\times m}$, we…

Compressed sensing and its extensions have recently triggered interest in randomized signal acquisition. A key finding is that random measurements provide sparse signal reconstruction guarantees for efficient and stable algorithms with a…

This survey explores modern approaches for computing low-rank approximations of high-dimensional matrices by means of the randomized SVD, randomized subspace iteration, and randomized block Krylov iteration. The paper compares the…

Smoothness of the subdiagonals of the Cholesky factor of large covariance matrices is closely related to the degrees of nonstationarity of autoregressive models for time series and longitudinal data. Heuristically, one expects for a nearly…

Estimating covariance parameters for multivariate spatial Gaussian random fields is computationally challenging, as the number of parameters grows rapidly with the number of variables, and likelihood evaluation requires operations of order…

The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…

Randomized algorithms for low-rank approximation of quaternion matrices have gained increasing attention in recent years. However, existing methods overlook pass efficiency, the ability to limit the number of passes over the input…

Generalized matrix approximation plays a fundamental role in many machine learning problems, such as CUR decomposition, kernel approximation, and matrix low rank approximation. Especially with today's applications involved in larger and…

In tracking of time-varying low-rank models of time-varying matrices, we present a method robust to both uniformly-distributed measurement noise and arbitrarily-distributed ``sparse'' noise. In theory, we bound the tracking error. In…

We propose a new approach for metric learning by framing it as learning a sparse combination of locally discriminative metrics that are inexpensive to generate from the training data. This flexible framework allows us to naturally derive…