Related papers: Low rank and sparse dynamical maps and repeated en…

In this paper, we focus on developing randomized algorithms for the computation of low multilinear rank approximations of tensors based on the random projection and the singular value decomposition. Following the theory of the singular…

We study matrix multiplication in the low-bandwidth model: There are $n$ computers, and we need to compute the product of two $n \times n$ matrices. Initially computer $i$ knows row $i$ of each input matrix. In one communication round each…

Motivated by a problem in computational complexity, we consider the behavior of rank functions for tensors and polynomial maps under random coordinate restrictions. We show that, for a broad class of rank functions called natural rank…

This paper presents a tensor-recovery method to solve probabilistic power flow problems. Our approach generates a high-dimensional and sparse generalized polynomial-chaos expansion that provides useful statistical information. The result…

We study the problem of reconstructing an unknown matrix M of rank r and dimension d using O(rd poly log d) Pauli measurements. This has applications in quantum state tomography, and is a non-commutative analogue of a well-known problem in…

Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors…

The Rank Minimization Problem asks to find a matrix of lowest rank inside a linear variety of the space of n x n matrices. The Low Rank Matrix Completion problem asks to complete a partially filled matrix such that the resulting matrix has…

Many data-analysis problems involve large dense matrices that describe the covariance of stationary noise processes; the computational cost of inverting these matrices, or equivalently of solving linear systems that contain them, is often a…

Parsimony, including sparsity and low rank, has been shown to successfully model data in numerous machine learning and signal processing tasks. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an…

We develop fast and memory efficient numerical methods for learning functions of many variables that admit sparse representations in terms of general bounded orthonormal tensor product bases. Such functions appear in many applications…

We propose a new method for computing the $\varphi$-functions of large sparse matrices with low rank or fast decaying singular values. The key is to reduce the computation of $\varphi_{\ell}$-functions of a large matrix to…

This note shows that the matrix forms of several one-parameter distribution families satisfy a hierarchical low-rank structure. Such families of distributions include binomial, Poisson, and $\chi^2$ distributions. The proof is based on a…

This paper focuses studies the following low rank + sparse (LR+S) column-wise compressive sensing problem. We aim to recover an $n \times q$ matrix, $\X^* =[ \x_1^*, \x_2^*, \cdots , \x_q^*]$ from $m$ independent linear projections of each…

Sparse tensor computing is a core computational part of numerous applications in areas such as data science, graph processing, and scientific computing. Sparse tensors offer the potential of skipping unnecessary computations caused by zero…

Let $\mathbf{a} = (a_{i})_{i \geq 1}$ be a sequence in a field $\mathbb{F}$, and $f \colon \mathbb{F} \times \mathbb{F} \to \mathbb{F}$ be a function such that $f(a_{i},a_{i}) \neq 0$ for all $i \geq 1$. For any tournament $T$ over $[n]$,…

The paper introduces the butterfly factorization as a data-sparse approximation for the matrices that satisfy a complementary low-rank property. The factorization can be constructed efficiently if either fast algorithms for applying the…

The topic of recovery of a structured model given a small number of linear observations has been well-studied in recent years. Examples include recovering sparse or group-sparse vectors, low-rank matrices, and the sum of sparse and low-rank…

There are many classes of mathematical problems which give rise to matrices, where a large number of the elements are zero. In this case it makes sense to have a special matrix type to handle this class of problems where only the non-zero…

In this paper, we develop a nonconvex approach to the problem of low-rank and sparse matrix decomposition. In our nonconvex method, we replace the rank function and the $l_{0}$-norm of a given matrix with a non-convex fraction function on…

We multiply two $n \times n$ matrices $S,T$ over semirings in the Congested Clique model, where $n$ fully connected nodes communicate synchronously using $O(\log n)$-bit messages, within $O(nz(S)^{1/3} nz(T)^{1/3}/n + 1)$ rounds of…