Related papers: Randomized low-rank approximations beyond Gaussian…
Estimation of the covariance matrix has attracted a lot of attention of the statistical research community over the years, partially due to important applications such as Principal Component Analysis. However, frequently used empirical…
Let A be an n*n random matrix with mean zero and independent inhomogeneous non-constant subgaussian entries. We get that for any k<c\sqrt{n}, the probability of the matrix has a lower rank than n-k that is sub-exponential. Furthermore, we…
This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…
The problem of low rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to…
Motivated by the popularity of stochastic rounding in the context of machine learning and the training of large-scale deep neural network models, we consider stochastic nearness rounding of real matrices $\mathbf{A}$ with many more rows…
Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…
Random matrices tend to be well conditioned, and we employ this well known property to advance matrix computations. We prove that our algorithms employing Gaussian random matrices are efficient, but in our tests the algorithms have…
Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the…
We consider $\ell_1$-Rank-$r$ Approximation over GF(2), where for a binary $m\times n$ matrix ${\bf A}$ and a positive integer $r$, one seeks a binary matrix ${\bf B}$ of rank at most $r$, minimizing the column-sum norm $||{\bf A} -{\bf…
We develop and analyze stochastic inexact Gauss-Newton methods for nonlinear least-squares problems and for nonlinear systems ofequations. Random models are formed using suitable sampling strategies for the matrices involved in the…
Low-rank tensor approximations have shown great potential for uncertainty quantification in high dimensions, for example, to build surrogate models that can be used to speed up large-scale inference problems (Eigel et al., Inverse Problems…
Recently, randomized algorithms for low-rank approximation of quaternion matrices have received increasing attention. However, for large-scale problems, existing quaternion orthonormalizations are inefficient, leading to slow rangefinders.…
This paper presents new results allowing an unknown non-Gaussian positive matrix-valued random field to be identified through a stochastic elliptic boundary value problem, solving a statistical inverse problem. A new general class of…
Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…
In the Bayesian approach to inverse problems, data are often informative, relative to the prior, only on a low-dimensional subspace of the parameter space. Significant computational savings can be achieved by using this subspace to…
Nowadays, low-rank approximations of matrices are an important component of many methods in science and engineering. Traditionally, low-rank approximations are considered in unitary invariant norms, however, recently element-wise…
Low rank approximation is an important tool used in many applications of signal processing and machine learning. Recently, randomized sketching algorithms were proposed to effectively construct low rank approximations and obtain approximate…
In recent years, several algorithms, which approximate matrix decomposition, have been developed. These algorithms are based on metric conservation features for linear spaces of random projection types. We show that an i.i.d sub-Gaussian…
In the fields of control theory and machine learning, the dynamic low-rank approximation for large-scale matrices has received substantial attention. Considering large-scale semilinear stiff matrix differential equations, we propose…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…