Related papers: Sparse Recovery over Graph Incidence Matrices

Most constraint-based causal learning algorithms provably return the correct causal graph under certain correctness conditions, such as faithfulness. By representing any constraint-based causal learning algorithm using the notion of a…

Auto-Encoders are unsupervised models that aim to learn patterns from observed data by minimizing a reconstruction cost. The useful representations learned are often found to be sparse and distributed. On the other hand, compressed sensing…

Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a…

Sparse graph recovery methods work well where the data follows their assumptions but often they are not designed for doing downstream probabilistic queries. This limits their adoption to only identifying connections among the input…

This paper considers the problem of interpolating signals defined on graphs. A major presumption considered by many previous approaches to this problem has been lowpass/ band-limitedness of the underlying graph signal. However, inspired by…

We discuss a general notion of "sparsity structure" and associated recoveries of a sparse signal from its linear image of reduced dimension possibly corrupted with noise. Our approach allows for unified treatment of (a) the "usual sparsity"…

In this paper, we propose a novel sparse recovery method based on the generalized error function. The penalty function introduced involves both the shape and the scale parameters, making it very flexible. The theoretical analysis results in…

We study the stable recovery of complex $k$-sparse signals from as few phaseless measurements as possible. The main result is to show that one can employ $\ell_1$ minimization to stably recover complex $k$-sparse signals from $m\geq O(k\log…

Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to…

In the synthesis model signals are represented as a sparse combinations of atoms from a dictionary. Dictionary learning describes the acquisition process of the underlying dictionary for a given set of training samples. While ideally this…

In many data acquisition systems it is common to observe signals whose amplitudes have been clipped. We present two new algorithms for recovering a clipped signal by leveraging the model assumption that the underlying signal is sparse in…

Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…

Dictionary learning, the problem of recovering a sparsely used matrix $\mathbf{D} \in \mathbb{R}^{M \times K}$ and $N$ $s$-sparse vectors $\mathbf{x}_i \in \mathbb{R}^{K}$ from samples of the form $\mathbf{y}_i = \mathbf{D}\mathbf{x}_i$, is…

Suppose we wish to recover an n-dimensional real-valued vector x_0 (e.g. a digital signal or image) from incomplete and contaminated observations y = A x_0 + e; A is a n by m matrix with far fewer rows than columns (n << m) and e is an…

Stochastic optimization algorithms update models with cheap per-iteration costs sequentially, which makes them amenable for large-scale data analysis. Such algorithms have been widely studied for structured sparse models where the sparsity…

We show that the problem of recovering the topology and admittance of an electrical network from power and voltage data at all vertices is often ill-posed, and sometimes it even has multiple solutions. We reformulate the problem to seek for…

In compressive sensing, sparse signals are recovered from underdetermined noisy linear observations. One of the interesting problems which attracted a lot of attention in recent times is the support recovery or sparsity pattern recovery…

We are motivated by problems that arise in a number of applications such as Online Marketing and explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…

This paper presents an algorithm tailored for the efficient recovery of sparse probability measures incorporating $\ell_0$-sparse regularization within the probability simplex constraint. Employing the Bregman proximal gradient method, our…

We study signals that are sparse in graph spectral domain and develop explicit algorithms to reconstruct the support set as well as partial components from samples on few vertices of the graph. The number of required samples is independent…