Related papers: Randomized Projection Methods for Linear Systems w…
This paper addresses the problem of estimating the positions of points from distance measurements corrupted by sparse outliers. Specifically, we consider a setting with two types of nodes: anchor nodes, for which exact distances to each…
This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse…
The Kaczmarz method is an iterative algorithm for solving systems of linear equations Ax=b. Theoretical convergence rates for this algorithm were largely unknown until recently when work was done on a randomized version of the algorithm. It…
Real data are rarely pure. Hence the past half-century has seen great interest in robust estimation algorithms that perform well even when part of the data is corrupt. However, their vast majority approach optimal accuracy only when given a…
Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…
A host of problems involve the recovery of structured signals from a dimensionality reduced representation such as a random projection; examples include sparse signals (compressive sensing) and low-rank matrices (matrix completion). Given…
We consider the problem of robust matrix completion, which aims to recover a low rank matrix $L_*$ and a sparse matrix $S_*$ from incomplete observations of their sum $M=L_*+S_*\in\mathbb{R}^{m\times n}$. Algorithmically, the robust matrix…
We propose a novel iterative algorithm for solving a large sparse linear system. The method is based on the EM algorithm. If the system has a unique solution, the algorithm guarantees convergence with a geometric rate. Otherwise,…
We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…
The randomized sparse Kaczmarz method, designed for seeking the sparse solutions of the linear systems $Ax=b$, selects the $i$-th projection hyperplane with likelihood proportional to $\|a_{i}\|_2^2$, where $a_{i}^T$ is $i$-th row of $A$.…
In the paper we consider the linear underdetermined system of a special type. Systems of this type appear in non-homogeneous network flow programming problems in the form of systems of constraints and can be characterized as systems with a…
System modeling is a classical approach to ensure their reliability since it is suitable both for a formal verification and for software testing techniques. In the context of model-based testing an approach combining random testing and…
In this paper we revisit random linear under-determined systems with sparse solutions. We consider $\ell_1$ optimization heuristic known to work very well when used to solve these systems. A collection of fundamental results that relate to…
Understanding the dynamics of complex systems is a central task in many different areas ranging from biology via epidemics to economics and engineering. Unexpected behaviour of dynamic systems or even system failure is sometimes difficult…
Gaussian graphical models are widely used to represent correlations among entities but remain vulnerable to data corruption. In this work, we introduce a modified trimmed-inner-product algorithm to robustly estimate the covariance in an…
The iterations of many sparse estimation algorithms are comprised of a fixed linear filter cascaded with a thresholding nonlinearity, which collectively resemble a typical neural network layer. Consequently, a lengthy sequence of algorithm…
Finding sparse solutions of underdetermined systems of linear equations is a fundamental problem in signal processing and statistics which has become a subject of interest in recent years. In general, these systems have infinitely many…
In this paper, the concept of matrix splitting is introduced to solve a large sparse ill-posed linear system via Tikhonov's regularization. In the regularization process, we convert the ill-posed system to a well-posed system. The…
We investigate entanglement detection when the local measurements only nearly correspond to those intended. This corresponds to a scenario in which measurement devices are not perfectly controlled, but nevertheless operate with bounded…
Recovery from linear measurements under sparse adversarial corruption is typically formulated as an exact-recovery problem: one seeks structural conditions on $A$ (e.g., the restricted isometry property) that guarantee unique recovery of…