Related papers: Recovery Reductions, Conjectures, and Barriers
We study stochastic optimization from a joint continuous-discrete point of view. Starting from a second-order stochastic differential equation interpreted as a noisy accelerated gradient flow, we discretize the dynamics by a fully implicit…
Recent work in the matrix completion literature has shown that prior knowledge of a matrix's row and column spaces can be successfully incorporated into reconstruction programs to substantially benefit matrix recovery. This paper proposes a…
This paper focuses on recovering an underlying matrix from its noisy partial entries, a problem commonly known as matrix completion. We delve into the investigation of a non-convex regularization, referred to as transformed $L_1$ (TL1),…
We study lower bounds on adaptive sensing algorithms for recovering low rank matrices using linear measurements. Given an $n \times n$ matrix $A$, a general linear measurement $S(A)$, for an $n \times n$ matrix $S$, is just the inner…
An approximate sparse recovery system in $\ell_1$ norm consists of parameters $k$, $\epsilon$, $N$, an $m$-by-$N$ measurement $\Phi$, and a recovery algorithm, $\mathcal{R}$. Given a vector, $\mathbf{x}$, the system approximates $x$ by…
We consider the nonconvex regularized method for low-rank matrix recovery. Under the assumption on the singular values of the parameter matrix, we provide the recovery bound for any stationary point of the nonconvex method by virtue of…
Rational approximation schemes for reconstructing periodic signals from samples with poorly separated spectral content are described. These methods are automatic and adaptive, requiring no tuning or manual parameter selection. Collectively,…
Learning non-linear systems from noisy, limited, and/or dependent data is an important task across various scientific fields including statistics, engineering, computer science, mathematics, and many more. In general, this learning task is…
In this work, we study the robust phase retrieval problem where the task is to recover an unknown signal $\theta^* \in \mathbb{R}^d$ in the presence of potentially arbitrarily corrupted magnitude-only linear measurements. We propose an…
We study a class of real robust phase retrieval problems under a Gaussian assumption on the coding matrix when the received signal is sparsely corrupted by noise. The goal is to establish conditions on the sparsity under which the input…
We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…
Random and structured noise both affect seismic data, hiding the reflections of interest (primaries) that carry meaningful geophysical interpretation. When the structured noise is composed of multiple reflections, its adaptive cancellation…
We study the recovery of one-dimensional semipermeable barriers for a stochastic process in a planar domain. The considered process acts like Brownian motion when away from the barriers and is reflected upon contact until a sufficient but…
Sparse regression models are increasingly prevalent due to their ease of interpretability and superior out-of-sample performance. However, the exact model of sparse regression with an $\ell_0$ constraint restricting the support of the…
We study the problem of estimating a low-rank positive semidefinite (PSD) matrix from a set of rank-one measurements using sensing vectors composed of i.i.d. standard Gaussian entries, which are possibly corrupted by arbitrary outliers.…
We present new policy mirror descent (PMD) methods for solving reinforcement learning (RL) problems with either strongly convex or general convex regularizers. By exploring the structural properties of these overall highly nonconvex…
We propose a new probabilistic method for unsupervised recovery of corrupted data. Given a large ensemble of degraded samples, our method recovers accurate posteriors of clean values, allowing the exploration of the manifold of possible…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…
We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP)…
This paper studies the problem of deterministic rank-one matrix completion. It is known that the simplest semidefinite programming relaxation, involving minimization of the nuclear norm, does not in general return the solution for this…