Related papers: Generalization Bounds for Inductive Matrix Complet…
We study the subgradient method for factorized robust signal recovery problems, including robust PCA, robust phase retrieval, and robust matrix sensing. The resulting objectives are nonsmooth and nonconvex, and can have unbounded sublevel…
A novel matrix approximation problem is considered herein: observations based on a few fully sampled columns and quasi-polynomial structural side information are exploited. The framework is motivated by quantum chemistry problems wherein…
We revisit the inductive matrix completion problem that aims to recover a rank-$r$ matrix with ambient dimension $d$ given $n$ features as the side prior information. The goal is to make use of the known $n$ features to reduce sample and…
This paper studies the classification of high-dimensional Gaussian signals from low-dimensional noisy, linear measurements. In particular, it provides upper bounds (sufficient conditions) on the number of measurements required to drive the…
In some significant applications such as data forecasting, the locations of missing entries cannot obey any non-degenerate distributions, questioning the validity of the prevalent assumption that the missing data is randomly chosen…
We analyze a class of estimators based on convex relaxation for solving high-dimensional matrix decomposition problems. The observations are noisy realizations of a linear transformation $\mathfrak{X}$ of the sum of an approximately) low…
Blind inverse problems arise in many experimental settings where both the signal of interest and the forward operator are (partially) unknown. In this context, methods developed for the non-blind case cannot be adapted in a straightforward…
Numerous empirical evidences have corroborated the importance of noise in nonconvex optimization problems. The theory behind such empirical observations, however, is still largely unknown. This paper studies this fundamental problem through…
We consider the problem of sparse signal recovery from noisy measurements. Many of frequently used recovery methods rely on some sort of tuning depending on either noise or signal parameters. If no estimates for either of them are…
In this paper, we develop a relative error bound for nuclear norm regularized matrix completion, with the focus on the completion of full-rank matrices. Under the assumption that the top eigenspaces of the target matrix are incoherent, we…
We consider the problem of recovering a real-valued $n$-dimensional signal from $m$ phaseless, linear measurements and analyze the amplitude-based non-smooth least squares objective. We establish local convergence of subgradient descent…
In this paper, we leverage an information-theoretic upper bound on the maximum admissible level of noise (MALN) in convex Lipschitz-continuous zeroth-order optimisation to establish corresponding upper bounds for classes of strongly convex…
We study the asymmetric matrix factorization problem under a natural nonconvex formulation with arbitrary overparametrization. The model-free setting is considered, with minimal assumption on the rank or singular values of the observed…
We examine the relationship between the mutual information between the output model and the empirical sample and the generalization of the algorithm in the context of stochastic convex optimization. Despite increasing interest in…
The classical phase retrieval problem arises in contexts ranging from speech recognition to x-ray crystallography and quantum state tomography. The generalization to matrix frames is natural in the sense that it corresponds to quantum…
Generalization bounds which assess the difference between the true risk and the empirical risk, have been studied extensively. However, to obtain bounds, current techniques use strict assumptions such as a uniformly bounded or a Lipschitz…
The matrix completion problem aims to reconstruct a low-rank matrix based on a revealed set of possibly noisy entries. Prior works consider completing the entire matrix with generalization error guarantees. However, the completion accuracy…
This paper examines the asymptotic convergence properties of Lipschitz interpolation methods within the context of bounded stochastic noise. In the first part of the paper, we establish probabilistic consistency guarantees of the classical…
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 study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…