相关论文: Sparse recovery properties of discrete random matr…

Let $\log^{2+\varepsilon} n \le d \le n/2$ for some fixed $\varepsilon \in (0,1)$, and let $M_n$ be an $n\times n$ random matrix with entries in ${0,1}$, where each row is independently and uniformly sampled from the set of all vectors in…

A matrix is given in ``shredded'' form if we are presented with the multiset of rows and the multiset of columns, but not told which row is which or which column is which. The matrix is reconstructible if it is uniquely determined by this…

This paper investigates total variation minimization in one spatial dimension for the recovery of gradient-sparse signals from undersampled Gaussian measurements. Recently established bounds for the required sampling rate state that uniform…

We have developed an approximate signal recovery algorithm with low computational cost for compressed sensing on the basis of randomly constructed sparse measurement matrices. The law of large numbers and the central limit theorem suggest…

Previous studies yielded discouraging results for item-level locally differentially private linear regression with $s^*$-sparsity assumption, where the minimax rate for $nm$ samples is $\mathcal{O}(s^{*}d / nm\varepsilon^2)$. This can be…

Let $\mathbf{A}$ be an $n\times n$-matrix over $\mathbb{F}_2$ whose every entry equals $1$ with probability $d/n$ independently for a fixed $d>0$. Draw a vector $\mathbf{y}$ randomly from the column space of $\mathbf{A}$. It is a simple…

Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…

We revisit the asymptotic analysis of probabilistic construction of adjacency matrices of expander graphs proposed in [4]. With better bounds we derived a new reduced sample complexity for the number of nonzeros per column of these…

It is well known that the performance of sparse vector recovery algorithms from compressive measurements can depend on the distribution underlying the non-zero elements of a sparse vector. However, the extent of these effects has yet to be…

Spectral properties of random matrices play an important role in statistics, machine learning, communications, and many other areas. Engaging results regarding the convergence of the empirical spectral distribution (ESD) and the…

We give a new deterministic construction of integer sensing matrices that can be used for the recovery of integer-valued signals in compressed sensing. This is a family of $n \times d$ integer matrices, $d \geq n$, with bounded sup-norm and…

We consider the problem of learning a graph modeling the statistical relations of the $d$ variables from a dataset with $n$ samples $X \in \mathbb{R}^{n \times d}$. Standard approaches amount to searching for a precision matrix $\Theta$…

Let $Q_{n,d}$ denote the random combinatorial matrix whose rows are independent of one another and such that each row is sampled uniformly at random from the subset of vectors in $\{0,1\}^n$ having precisely $d$ entries equal to $1$. We…

Let $T$ be an $n\times n$ random matrix, such that each diagonal entry $T_{i,i}$ is a continuous random variable, independent from all the other entries of $T$. Then for every $n\times n$ matrix $A$ and every $t\ge0$ $$…

We study block-diagonal random matrices with i.i.d. subexponential entries and show that, despite their highly structured form, they already guarantee exact sparse recovery from a nearly optimal number of measurements. When the matrix…

This article provides a new toolbox to derive sparse recovery guarantees from small deviations on extreme singular values or extreme eigenvalues obtained in Random Matrix Theory. This work is based on Restricted Isometry Constants (RICs)…

We discuss the universality of the L1 recovery threshold in compressed sensing. Previous studies in the fields of statistical mechanics and random matrix integration have shown that L1 recovery under a random matrix with orthogonal symmetry…

The paper considers the problem of identifying the sparse different components between two high dimensional means of column-wise dependent random vectors. We show that the dependence can be utilized to lower the identification boundary for…

We revisit the probabilistic construction of sparse random matrices where each column has a fixed number of nonzeros whose row indices are drawn uniformly at random. These matrices have a one-to-one correspondence with the adjacency…

Random contractions (sub-unitary random matrices) appear naturally when considering quantized chaotic maps within a general theory of open linear stationary systems with discrete time. We analyze statistical properties of complex…