arXiv research

Unified approach for robust low rank matrix estimation with adversaries.

Weight normalization speeds up matrix sensing problems.

Paper improves compressed sensing with prior probability information.

New method proves asymptotic normality for matrix sensing problems.

New method tackles over-parameterized matrix sensing with FGD, improving statistical and computational complexity.

This letter proposes a dictionary learning algorithm for blind one bit compressed sensing. In the blind one bit compressed sensing framework, the original signal to be reconstructed from one bit linear random measurements is sparse in an unknown domain. In this context, the multiplication of measurement matrix $\Ab$ an…

We improve existing results in the field of compressed sensing and matrix completion when sampled data may be grossly corrupted. We introduce three new theorems. 1) In compressed sensing, we show that if the m \times n sensing matrix has independent Gaussian entries, then one can recover a sparse signal x exactly by tr…

Paper develops a decoder for sparse codes without encoder matrix, achieving optimal recovery.

Paper shows robustness of gradient descent in matrix sensing despite perturbations.

Gradient descent solves asymmetric low-rank matrix sensing without balancing.

Paper offers robust recovery for 1-bit sensing with partial Gaussian circulant matrices.

Mirror descent algorithm recovers low-rank matrices in matrix sensing.

Paper studies asymmetric matrix sensing, proving gradient descent converges to low-rank solutions.

We characterize the performance of sequential information guided sensing, Info-Greedy Sensing, when there is a mismatch between the true signal model and the assumed model, which may be a sample estimate. In particular, we consider a setup where the signal is low-rank Gaussian and the measurements are taken in the dire…

SNN architecture shows gradient descent converges to regularized solution in matrix sensing problems.

This letter proposes a low-computational Bayesian algorithm for noisy sparse recovery in the context of one bit compressed sensing with sensing matrix perturbation. The proposed algorithm which is called BHT-MLE comprises a sparse support detector and an amplitude estimator. The support detector utilizes Bayesian hypot…

Study exact limits of matrix reconstruction from noisy projections.

APGD algorithm efficiently recovers over-parameterized matrices from noisy measurements.

Optimizing the acquisition matrix is useful for compressed sensing of signals that are sparse in overcomplete dictionaries, because the acquisition matrix can be adapted to the particular correlations of the dictionary atoms. In this paper a novel formulation of the optimization problem is proposed, in the form of a ra…

We consider the non-square matrix sensing problem, under restricted isometry property (RIP) assumptions. We focus on the non-convex formulation, where any rank-$r$ matrix $X \in \mathbb{R}^{m \times n}$ is represented as $UV^\top$, where $U \in \mathbb{R}^{m \times r}$ and $V \in \mathbb{R}^{n \times r}$. In this paper…

In this paper we develop a new framework that captures the common landscape underlying the common non-convex low-rank matrix problems including matrix sensing, matrix completion and robust PCA. In particular, we show for all above problems (including asymmetric cases): 1) all local minima are also globally optimal; 2) …

Unified approach for learning quantum operations from measurements.

Spectral clustering is one of the most widely used techniques for extracting the underlying global structure of a data set. Compressed sensing and matrix completion have emerged as prevailing methods for efficiently recovering sparse and partially observed signals respectively. We combine the distance preserving measur…

GD learns matrix solutions incrementally, revealing insights into generalization.

We give a new, very general, formulation of the compressed sensing problem in terms of coordinate projections of an analytic variety, and derive sufficient sampling rates for signal reconstruction. Our bounds are linear in the coherence of the signal space, a geometric parameter independent of the specific signal and m…

New coherence parameter for GNNs with Fourier measurements improves signal recovery.

Consider a movie recommendation system where apart from the ratings information, side information such as user's age or movie's genre is also available. Unlike standard matrix completion, in this setting one should be able to predict inductively on new users/movies. In this paper, we study the problem of inductive matr…

Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be known exactly in advance. However, uncertainties exist due to sampling distortion, …

Sharp asymptotics reveal how network width controls learnability in quadratic neural networks.

Paper quantizes heavy-tailed data for near optimal estimation rates.

Study compares LRMC algorithms under dependent sampling in various applications.

Improved convergence for overparameterized low-rank matrix sensing.

Paper proposes a 1-bit quantization scheme for high-dimensional statistical estimation.

UPCA solves data matrix completion with permuted columns.

Compressed sensing (CS) is a sampling theory that allows reconstruction of sparse (or compressible) signals from an incomplete number of measurements, using of a sensing mechanism implemented by an appropriate projection matrix. The CS theory is based on random Gaussian projection matrices, which satisfy recovery guara…

We develop an efficient alternating framework for learning a generalized version of Factorization Machine (gFM) on steaming data with provable guarantees. When the instances are sampled from $d$ dimensional random Gaussian vectors and the target second order coefficient matrix in gFM is of rank $k$, our algorithm conve…

We discuss the question of how to pick a matrix uniformly (in an appropriate sense) at random from groups big and small. We give algorithms in some cases, and indicate interesting problems in others.

Paper recovers multi-subspace matrices from permuted data.

Optimized sampling scheme for compressed sensing combining randomness and determinism.

We consider whether algorithmic choices in over-parameterized linear matrix factorization introduce implicit regularization. We focus on noiseless matrix sensing over rank-$r$ positive semi-definite (PSD) matrices in $\mathbb{R}^{n \times n}$, with a sensing mechanism that satisfies restricted isometry properties (RIP)…

Study robust recovery of low-rank matrices from corrupted measurements without rank prior.

We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex optimization problem of matrix sensing. Our algorithm is applicable to both noisy and…

The paper analyzes how over-parameterization affects GD convergence in matrix sensing problems.

Networked sensing, where the goal is to perform complex inference using a large number of inexpensive and decentralized sensors, has become an increasingly attractive research topic due to its applications in wireless sensor networks and internet-of-things. To reduce the communication, sensing and storage complexity, t…

New guarantees for recovering matrices as low-rank plus sparse from fewer measurements.

This paper considers \emph{volume minimization} (VolMin)-based structured matrix factorization (SMF). VolMin is a factorization criterion that decomposes a given data matrix into a basis matrix times a structured coefficient matrix via finding the minimum-volume simplex that encloses all the columns of the data matrix.…

Paper proposes robust compressed sensing using generative models.

Framework for joint inference of network topology and interaction types in heterogeneous systems.