Related papers: Sharp Variable Selection of a Sparse Submatrix in …
We consider the densest submatrix problem, which seeks the submatrix of fixed size of a given binary matrix that contains the most nonzero entries. This problem is a natural generalization of fundamental problems in combinatorial…
We consider the following detection problem: given a realization of a symmetric matrix ${\mathbf{X}}$ of dimension $n$, distinguish between the hypothesis that all upper triangular variables are i.i.d. Gaussians variables with mean 0 and…
We consider an $n\times n$ matrix of independent real Gaussian random variables and determine the asymptotic distribution of the smallest gaps between complex eigenvalues.
An increasing number of applications is concerned with recovering a sparse matrix from noisy observations. In this paper, we consider the setting where each row of the unknown matrix is sparse. We establish minimax optimal rates of…
Let $M$ be a random $m \times n$ matrix with binary entries and i.i.d. rows. The weight (i.e., number of ones) of a row has a specified probability distribution, with the row chosen uniformly at random given its weight. Let $N(n,m)$ denote…
Consider the Gaussian vector model with mean value {\theta}. We study the twin problems of estimating the number |{\theta}|_0 of non-zero components of {\theta} and testing whether |{\theta}|_0 is smaller than some value. For testing, we…
The model interpretation is essential in many application scenarios and to build a classification model with a ease of model interpretation may provide useful information for further studies and improvement. It is common to encounter with a…
We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance…
We develop novel empirical Bernstein inequalities for the variance of bounded random variables. Our inequalities hold under constant conditional variance and mean, without further assumptions like independence or identical distribution of…
We study $\textit{sparse singular value certificates}$ for random rectangular matrices. If $M$ is an $n \times d$ matrix with independent Gaussian entries, we give a new family of polynomial-time algorithms which can certify upper bounds on…
We prove nonasymptotic matrix concentration inequalities for the spectral norm of (sub)gaussian random matrices with centered independent entries that capture fluctuations at the Tracy-Widom scale. This considerably improves previous bounds…
We consider the regression model with observation error in the design: y=X\theta* + e, Z=X+N. Here the random vector y in R^n and the random n*p matrix Z are observed, the n*p matrix X is unknown, N is an n*p random noise matrix, e in R^n…
Gaussian graphical models are used for determining conditional relationships between variables. This is accomplished by identifying off-diagonal elements in the inverse-covariance matrix that are non-zero. When the ratio of variables (p) to…
Although the standard formulations of prediction problems involve fully-observed and noiseless data drawn in an i.i.d. manner, many applications involve noisy and/or missing data, possibly involving dependence, as well. We study these…
The most frequently used condition for sampling matrices employed in compressive sampling is the restricted isometry (RIP) property of the matrix when restricted to sparse signals. At the same time, imposing this condition makes it…
Forward regression is a statistical model selection and estimation procedure which inductively selects covariates that add predictive power into a working statistical regression model. Once a model is selected, unknown regression parameters…
In this paper we study sharp thresholds for detecting sparse signals in $\beta$-models for potentially sparse random graphs. The results demonstrate interesting interplay between graph sparsity, signal sparsity, and signal strength. In…
We show that when a high-dimensional data matrix is the sum of a low-rank matrix and a random error matrix with independent entries, the low-rank component can be consistently estimated by solving a convex minimization problem. We develop a…
Graphical modeling explores dependences among a collection of variables by inferring a graph that encodes pairwise conditional independences. For jointly Gaussian variables, this translates into detecting the support of the precision…
Many computer vision and medical imaging problems are faced with learning from large-scale datasets, with millions of observations and features. In this paper we propose a novel efficient learning scheme that tightens a sparsity constraint…