Related papers: Nonasymptotic Guarantees for Spiked Matrix Recover…

Single-Index Models are high-dimensional regression problems with planted structure, whereby labels depend on an unknown one-dimensional projection of the input via a generic, non-linear, and potentially non-deterministic transformation. As…

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…

The traditional approach of hand-crafting priors (such as sparsity) for solving inverse problems is slowly being replaced by the use of richer learned priors (such as those modeled by deep generative networks). In this work, we study the…

We study the robust one-bit compressed sensing problem whose goal is to design an algorithm that faithfully recovers any sparse target vector $\theta_0\in\mathbb{R}^d$ \textit{uniformly} via $m$ quantized noisy measurements. Specifically,…

We study the graph matching problem in the presence of vertex feature information using shallow graph neural networks. Specifically, given two graphs that are independent perturbations of a single random geometric graph with sparse binary…

Common problem in signal processing is reconstruction of the missing signal samples. Missing samples can occur by intentionally omitting signal coefficients to reduce memory requirements, or to speed up the transmission process. Also, noisy…

For the problem of reconstructing a low-rank matrix from a few linear measurements, two classes of algorithms have been widely studied in the literature: convex approaches based on nuclear norm minimization, and non-convex approaches that…

Adaptive learning is necessary for non-stationary environments where the learning machine needs to forget past data distribution. Efficient algorithms require a compact model update to not grow in computational burden with the incoming data…

The non-negative solution to an underdetermined linear system can be uniquely recovered sometimes, even without imposing any additional sparsity constraints. In this paper, we derive conditions under which a unique non-negative solution for…

Consider the $n$-dimensional vector $y=X\be+\e$, where $\be \in \R^p$ has only $k$ nonzero entries and $\e \in \R^n$ is a Gaussian noise. This can be viewed as a linear system with sparsity constraints, corrupted by noise. We find a…

We consider the matrix completion problem of recovering a structured low rank matrix with partially observed entries with mixed data types. Vast majority of the solutions have proposed computationally feasible estimators with strong…

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…

In this paper, we consider the matrix recovery from rank-one projection measurements proposed in [Cai and Zhang, Ann. Statist., 43(2015), 102-138], via nonconvex minimization. We establish a sufficient identifiability condition, which can…

We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural…

In this paper the problem of restoration of non-negative sparse signals is addressed in the Bayesian framework. We introduce a new probabilistic hierarchical prior, based on the Generalized Hyperbolic (GH) distribution, which explicitly…

This paper addresses the classical problem of one-bit compressed sensing using a deep learning-based reconstruction algorithm that leverages a trained generative model to enhance the signal reconstruction performance. The generator, a…

We investigate non-negative least squares (NNLS) for the recovery of sparse non-negative vectors from noisy linear and biased measurements. We build upon recent results from [1] showing that for matrices whose row-span intersects the…

Recently, greedy algorithm has received much attention as a cost-effective means to reconstruct the sparse signals from compressed measurements. Much of previous work has focused on the investigation of a single candidate to identify the…

In this paper, we study the problem of recovering a low-rank matrix (the principal components) from a high-dimensional data matrix despite both small entry-wise noise and gross sparse errors. Recently, it has been shown that a convex…

The problem of low rank matrix completion is considered in this paper. To exploit the underlying low-rank structure of the data matrix, we propose a hierarchical Gaussian prior model, where columns of the low-rank matrix are assumed to…