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

Compressed sensing (sparse signal recovery) often encounters nonnegative data (e.g., images). Recently we developed the methodology of using (dense) Compressed Counting for recovering nonnegative K-sparse signals. In this paper, we adopt…

Given some binary matrix $M$, suppose we are presented with the collection of its rows and columns in independent arbitrary orderings. From this information, are we able to recover the unique original orderings and matrix? We present an…

Random matrices are widely used in sparse recovery problems, and the relevant properties of matrices with i.i.d. entries are well understood. The current paper discusses the recently introduced Restricted Eigenvalue (RE) condition, which is…

The most frequently used condition for sampling matrices employed in compressive sampling is the restricted isometry (RIP) property of the matrix when restricted to sparse signals. At the same time, imposing this condition makes it…

We give the distribution of $M_n$, the maximum of a sequence of $n$ observations from a moving average of order 1. Solutions are first given in terms of repeated integrals and then for the case where the underlying independent random…

Let $M$ 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 $\{0, 1\}^n$ containing exactly $d$ ones, with $d=pn$ for some fixed constant $p\in…

Consider an n-dimensional linear system where it is known that there are at most k<n non-zero components in the initial state. The observability problem, that is the recovery of the initial state, for such a system is considered. We obtain…

We consider the problem of recovering a low-multilinear-rank tensor from a small amount of linear measurements. We show that the Riemannian gradient algorithm initialized by one step of iterative hard thresholding can reconstruct an…

Random sampling in compressive sensing (CS) enables the compression of large amounts of input signals in an efficient manner, which is useful for many applications. CS reconstructs the compressed signals exactly with overwhelming…

This note presents a unified analysis of the recovery of simple objects from random linear measurements. When the linear functionals are Gaussian, we show that an s-sparse vector in R^n can be efficiently recovered from 2s log n…

We address the problem of variable selection in a high-dimensional but sparse mean model, under the additional constraint that only privatised data are available for inference. The original data are vectors with independent entries having a…

We consider the problem of recovering sparse vectors from underdetermined linear measurements via $\ell_p$-constrained basis pursuit. Previous analyses of this problem based on generalized restricted isometry properties have suggested that…

In this work, we consider the controllability of a discrete-time linear dynamical system with sparse control inputs. Sparsity constraints on the input arises naturally in networked systems, where activating each input variable adds to the…

In solving a system of $n$ linear equations in $d$ variables $Ax=b$, the condition number of the $n,d$ matrix $A$ measures how much errors in the data $b$ affect the solution $x$. Estimates of this type are important in many inverse…

Finding a suitable measurement matrix is an important topic in compressed sensing. Though the known random matrix, whose entries are drawn independently from a certain probability distribution, can be used as a measurement matrix and…

This paper studies the problem of differentially private empirical risk minimization (DP-ERM) for binary linear classification. We obtain an efficient $(\varepsilon,\delta)$-DP algorithm with an empirical zero-one risk bound of…

An oblivious subspace embedding (OSE), characterized by parameters $m,n,d,\epsilon,\delta$, is a random matrix $\Pi\in \mathbb{R}^{m\times n}$ such that for any $d$-dimensional subspace $T\subseteq \mathbb{R}^n$, $\Pr_\Pi[\forall x\in T,…

We extend the theory of matrix completion to the case where we make Poisson observations for a subset of entries of a low-rank matrix. We consider the (now) usual matrix recovery formulation through maximum likelihood with proper…

We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…

This paper studies controllability of a discrete-time linear dynamical system using nonnegative and sparse inputs. These constraints on the control input arise naturally in many real-life systems where the external influence on the system…