Related papers: Computational and statistical lower bounds for low…
In this paper, we study a spiked Wigner problem with an inhomogeneous noise profile. Our aim in this problem is to recover the signal passed through an inhomogeneous low-rank matrix channel. While the information-theoretic performances are…
Structural matrix-variate observations routinely arise in diverse fields such as multi-layer network analysis and brain image clustering. While data of this type have been extensively investigated with fruitful outcomes being delivered, the…
We study low-rank matrix estimation for a generic inhomogeneous output channel through which the matrix is observed. This generalizes the commonly considered spiked matrix model with homogeneous noise to include for instance the dense…
We study here the so-called spiked Wigner and Wishart models, where one observes a low-rank matrix perturbed by some Gaussian noise. These models encompass many classical statistical tasks such as sparse PCA, submatrix localization,…
Spectral methods are widely used to estimate eigenvectors of a low-rank signal matrix subject to noise. These methods use the leading eigenspace of an observed matrix to estimate this low-rank signal. Typically, the entrywise estimation…
We study the statistical decision process of detecting the signal from a `signal+noise' type matrix model with an additive Wigner noise. We propose a hypothesis test based on the linear spectral statistics of the data matrix, which does not…
Spectral estimators are fundamental in lowrank matrix models and arise throughout machine learning and statistics, with applications including network analysis, matrix completion and PCA. These estimators aim to recover the leading…
We consider the weak detection problem in a rank-one spiked Wigner data matrix where the signal-to-noise ratio is small so that reliable detection is impossible. We propose a hypothesis test on the presence of the signal by utilizing the…
We propose a unified framework for estimating low-rank matrices through nonconvex optimization based on gradient descent algorithm. Our framework is quite general and can be applied to both noisy and noiseless observations. In the general…
The prototypical high-dimensional statistics problem entails finding a structured signal in noise. Many of these problems exhibit an intriguing phenomenon: the amount of data needed by all known computationally efficient algorithms far…
This paper presents a graph signal processing algorithm to uncover the intrinsic low-rank components and the underlying graph of a high-dimensional, graph-smooth and grossly-corrupted dataset. In our problem formulation, we assume that the…
We study the problem of estimating a rank one signal matrix from an observed matrix generated by corrupting the signal with additive rotationally invariant noise. We develop a new class of approximate message-passing algorithms for this…
We consider a group synchronization problem with multiple frequencies which involves observing pairwise relative measurements of group elements on multiple frequency channels, corrupted by Gaussian noise. We study the computational phase…
One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…
Low-rank pseudoinverses are widely used to approximate matrix inverses in scalable machine learning, optimization, and scientific computing. However, real-world matrices are often observed with noise, arising from sampling, sketching, and…
This paper proposes novel spectrum sensing algorithms for cognitive radio networks. By assuming known transmitter pulse shaping filter, synchronous and asynchronous receiver scenarios have been considered. For each of these scenarios, the…
The interplay between computational efficiency and statistical accuracy in high-dimensional inference has drawn increasing attention in the literature. In this paper, we study computational and statistical boundaries for submatrix…
We consider a prototypical problem of Bayesian inference for a structured spiked model: a low-rank signal is corrupted by additive noise. While both information-theoretic and algorithmic limits are well understood when the noise is a…
Estimating the clutter-plus-noise covariance matrix in high-dimensional STAP is challenging in the presence of Internal Clutter Motion (ICM) and a high noise floor. The problem becomes more difficult in low-sample regimes, where the Sample…
Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…