Related papers: Minimax rates for sparse signal detection under co…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…
Compressed sensing is a new scheme which shows the ability to recover sparse signal from fewer measurements, using $l_1$ minimization. Recently, Chartrand and Staneva shown in \cite{CS1} that the $l_p$ minimization with $0<p<1$ recovers…
The problem of quickest detection of a change in the distribution of a $n\times p$ random matrix based on a sequence of observations having a single unknown change point is considered. The forms of the pre- and post-change distributions of…
Donoho and Kipnis (2022) showed that the the higher criticism (HC) test statistic has a non-Gaussian phase transition but remarked that it is probably not optimal, in the detection of sparse differences between two large frequency tables…
The inverse covariance matrix provides considerable insight for understanding statistical models in the multivariate setting. In particular, when the distribution over variables is assumed to be multivariate normal, the sparsity pattern in…
We investigate minimax testing for detecting local signals or linear combinations of such signals when only indirect data is available. Naturally, in the presence of noise, signals that are too small cannot be reliably detected. In a…
The large scale behavior of systems having a large number of interacting degrees of freedom is suitably described using renormalization group, from non-Gaussian distributions. Renormalization group techniques used in physics are then…
This paper studies the problem of robust signal detection in Gaussian noise under quadratically convex orthosymmetric (QCO) constraints. We consider a minimax testing framework where the signal belongs to a QCO set and is separated from…
We observe $n$ independent $p-$dimensional Gaussian vectors with missing coordinates, that is each value (which is assumed standardized) is observed with probability $a>0$. We investigate the problem of minimax nonparametric testing that…
We study sparse principal components analysis in the high-dimensional setting, where $p$ (the number of variables) can be much larger than $n$ (the number of observations). We prove optimal, non-asymptotic lower and upper bounds on the…
A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical…
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…
Phase modulation is a commonly used modulation mode in digital communication, which usually brings phase sparsity to digital signals. It is naturally to connect the sparsity with the newly emerged theory of compressed sensing (CS), which…
We study the problem of detection of a p-dimensional sparse vector of parameters in the linear regression model with Gaussian noise. We establish the detection boundary, i.e., the necessary and sufficient conditions for the possibility of…
Compressive sensing predicts that sufficiently sparse vectors can be recovered from highly incomplete information. Efficient recovery methods such as $\ell_1$-minimization find the sparsest solution to certain systems of equations. Random…
We study the problem of detecting a structured, low-rank signal matrix corrupted with additive Gaussian noise. This includes clustering in a Gaussian mixture model, sparse PCA, and submatrix localization. Each of these problems is…
Detection of correlation in a pair of random graphs is a fundamental statistical and computational problem that has been extensively studied in recent years. In this work, we consider a pair of correlated (sparse) stochastic block models…
Cross-correlation is a popular signal processing technique used in numerous location tracking systems for obtaining reliable range information. However, its efficient design and practical implementation has not yet been achieved on mote…
This paper studies the problem of clustering in the two-component Gaussian mixture model where the centers are separated by $2\Delta$ for some $\Delta>0$. We characterize the exact phase transition threshold, given by $$ \bar{\Delta}_n^{2}…
We establish a sprinkled decoupling inequality for increasing events of Gaussian vectors with an error that depends only on the maximum pairwise correlation. As an application we prove the non-triviality of the percolation phase transition…