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We investigate the properties of sparse matrix ensembles with particular regard for the spectral ergodicity hypothesis, which claims the identity of ensemble and spectral averages of spectral correlators. An apparent violation of the…
We study the problem of community recovery from coarse measurements of a graph. In contrast to the problem of community recovery of a fully observed graph, one often encounters situations when measurements of a graph are made at…
We focus on a multidimensional field with uncorrelated spectrum, and study the quality of the reconstructed signal when the field samples are irregularly spaced and affected by independent and identically distributed noise. More…
We consider the problem of community detection from the joint observation of a high-dimensional covariate matrix and $L$ sparse networks, all encoding noisy, partial information about the latent community labels of $n$ subjects. In the…
The stochastic block model is a canonical model of communities in random graphs. It was introduced in the social sciences and statistics as a model of communities, and in theoretical computer science as an average case model for graph…
We obtain a perfect sampling characterization of weak ergodicity for backward products of finite stochastic matrices, and equivalently, simultaneous tail triviality of the corresponding nonhomogeneous Markov chains. Applying these ideas to…
In many applications, the observations can be represented as a signal defined over the vertices of a graph. The analysis of such signals requires the extension of standard signal processing tools. In this work, first, we provide a class of…
The detection of weak and rare effects in large amounts of data arises in a number of modern data analysis problems. Known results show that in this situation the potential of statistical inference is severely limited by the large-scale…
In this paper a new method of detection of homogeneous zones and singularity parts of a 1D signal is proposed. The entropy function is used to transform signal in piecewise linear one. The multiple regression permits to detect lines and…
Objective: To characterize the irregularity of the spectrum of a signal, spectral entropy is a widely adopted measure. However, such a metric is invariant under any permutation of the estimations of the powers of individual frequency…
This paper presents a performance analysis framework for linear detection in fast-fading channels with possibly correlated channel and noise. The framework is both accurate and adaptable, making it well-suited for analyzing a wide range of…
The information-theoretic limits of community detection have been studied extensively for network models with high levels of symmetry or homogeneity. The contribution of this paper is to study a broader class of network models that allow…
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…
This paper presents a regularized regression model with a two-level structural sparsity penalty applied to locate individual atoms in a noisy scanning transmission electron microscopy image (STEM). In crystals, the locations of atoms is…
Recovering an unknown but structured signal from its measurements is a challenging problem with significant applications in fields such as imaging restoration, wireless communications, and signal processing. In this paper, we consider the…
This paper is motivated by the reconstruction problem on the sparse stochastic block model. Mossel, et. al. proved that a reconstruction algorithm that recovers an optimal fraction of the communities in the symmetric, 2-community case. The…
Financial stock return correlations have been analyzed through the lens of random matrix theory to differentiate the underlying signal from spurious correlations. The continuous spectrum of the eigenvalue distribution derived from the stock…
Understanding the dynamics of feature learning in neural networks (NNs) remains a significant challenge. The work of (Mousavi-Hosseini et al., 2023) analyzes a multiple index teacher-student setting and shows that a two-layer student…
This paper investigates the problem of signal estimation from undersampled noisy sub-Gaussian measurements under the assumption of a cosparse model. Based on generalized notions of sparsity, we derive novel recovery guarantees for the…
This paper considers the problem of recovering a group sparse signal matrix $\mathbf{Y} = [\mathbf{y}_1, \cdots, \mathbf{y}_L]$ from sparsely corrupted measurements $\mathbf{M} = [\mathbf{A}_{(1)}\mathbf{y}_{1}, \cdots,…