Related papers: Energy Landscape for large average submatrix detec…

This paper investigates the fundamental limits for detecting a high-dimensional sparse matrix contaminated by white Gaussian noise from both the statistical and computational perspectives. We consider $p\times p$ matrices whose rows and…

Consider a $N\times n$ matrix $\Sigma_n=\frac{1}{\sqrt{n}}R_n^{1/2}X_n$, where $R_n$ is a nonnegative definite Hermitian matrix and $X_n$ is a random matrix with i.i.d. real or complex standardized entries. The fluctuations of the linear…

Subspace learning and matrix factorization problems have great many applications in science and engineering, and efficient algorithms are critical as dataset sizes continue to grow. Many relevant problem formulations are non-convex, and in…

In the past 20 years, the study of real eigenvalues of non-symmetric real random matrices has seen important progress. Notwithstanding, central questions still remain open, such as the characterization of their asymptotic statistics and the…

We consider the problem of estimating a large rank-one tensor ${\boldsymbol u}^{\otimes k}\in({\mathbb R}^{n})^{\otimes k}$, $k\ge 3$ in Gaussian noise. Earlier work characterized a critical signal-to-noise ratio $\lambda_{Bayes}= O(1)$…

Motivated by problems in controlled experiments, we study the discrepancy of random matrices with continuous entries where the number of columns $n$ is much larger than the number of rows $m$. Our first result shows that if $\omega(1) = m =…

It is well known that Gaussian symplectic ensemble (GSE) is defined on the space of $n\times n$ quaternion self-dual Hermitian matrices with Gaussian random elements. There is a huge body of literature regarding this kind of matrices. As a…

We continue the study of the Hermitian random matrix ensemble with external source $\frac{1}{Z_n} e^{-n \Tr({1/2}M^2 -AM)} dM$ where $A$ has two distinct eigenvalues $\pm a$ of equal multiplicity. This model exhibits a phase transition for…

We analyze eigenvalues fluctuations of the Laplacian of various networks under the random matrix theory framework. Analyses of random networks, scale-free networks and small-world networks show that nearest neighbor spacing distribution of…

We study the universality of spectral statistics of large random matrices. We consider $N\times N$ symmetric, hermitian or quaternion self-dual random matrices with independent, identically distributed entries (Wigner matrices) where the…

We study largest singular values of large random matrices, each with mean of a fixed rank $K$. Our main result is a limit theorem as the number of rows and columns approach infinity, while their ratio approaches a positive constant. It…

We study the problem of detecting a change in the mean of one-dimensional Gaussian process data. This problem is investigated in the setting of increasing domain (customarily employed in time series analysis) and in the setting of fixed…

In the Densest k-Subgraph problem, given a graph G and a parameter k, one needs to find a subgraph of G induced on k vertices that contains the largest number of edges. There is a significant gap between the best known upper and lower…

We study the two inference problems of detecting and recovering an isolated community of \emph{general} structure planted in a random graph. The detection problem is formalized as a hypothesis testing problem, where under the null…

We observe a $N\times M$ matrix $Y_{ij}=s_{ij}+\xi_{ij}$ with $\xi_{ij}\sim {\mathcal {N}}(0,1)$ i.i.d. in $i,j$, and $s_{ij}\in \mathbb {R}$. We test the null hypothesis $s_{ij}=0$ for all $i,j$ against the alternative that there exists…

We compute exact asymptotic of the statistical density of random matrices belonging to the Generalized Gaussian orthogonal, unitary and symplectic ensembles such that there no eigenvalues in the interval $[\sigma, +\infty[$. In particular,…

We describe a general technique that yields the first {\em Statistical Query lower bounds} for a range of fundamental high-dimensional learning problems involving Gaussian distributions. Our main results are for the problems of (1) learning…

We consider the problem of localizing a submatrix with larger-than-usual entry values inside a data matrix, without the prior knowledge of the submatrix size. We establish an optimization framework based on a multiscale scan statistic, and…

In the past we have considered Gaussian random matrix ensembles in the presence of an external matrix source. The reason was that it allowed, through an appropriate tuning of the eigenvalues of the source, to obtain results on non-trivial…

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…