Related papers: Sparse Signal Detection in Heteroscedastic Gaussia…
We are motivated by problems that arise in a number of applications such as Online Marketing and Explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…
The problem of detecting a wide-sense stationary Gaussian signal process embedded in white Gaussian noise, where the power spectral density of the signal process exhibits uncertainty, is investigated. The performance of minimax robust…
We study predictive density estimation under Kullback-Leibler loss in $\ell_0$-sparse Gaussian sequence models. We propose proper Bayes predictive density estimates and establish asymptotic minimaxity in sparse models. A surprise is the…
We study nonasymptotic minimax estimation of the linear functional $L(\theta)=\eta^\top \theta$ for a high-dimensional $s$-sparse mean vector with an arbitrary loading vector $\eta$. For symmetric noise with exponentially decaying tails, we…
We study the rate of decay of the probability of error for distinguishing between a sparse signal with noise, modeled as a sparse mixture, from pure noise. This problem has many applications in signal processing, evolutionary biology,…
We consider exact asymptotics of the minimax risk for global testing against sparse alternatives in the context of high dimensional linear regression. Our results characterize the leading order behavior of this minimax risk in several…
In the pivotal variable selection problem, we derive the exact non-asymptotic minimax selector over the class of all $s$-sparse vectors, which is also the Bayes selector with respect to the uniform prior. While this optimal selector is, in…
Robust statistical inference often faces a severe computational-statistical gap when dealing with complex parameter spaces. We investigate minimax signal detection in the Gaussian sequence model under strong $\epsilon$-contamination, where…
In the first part of the series papers, we set out to answer the following question: given specific restrictions on a set of samplers, what kind of signal can be uniquely represented by the corresponding samples attained, as the foundation…
Inspired by graph-based methodologies, we introduce a novel graph-spanning algorithm designed to identify changes in both offline and online data across low to high dimensions. This versatile approach is applicable to Euclidean and…
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 consider the problem of high-dimensional Gaussian graphical model selection. We identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is based on thresholding of empirical conditional…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
Towards understanding the fundamental limits of estimation from data of varied quality, we study the problem of estimating a mean parameter from heteroskedastic Gaussian observations where the variances are unknown and may vary arbitrarily…
In this paper, we investigate the theoretical guarantees of penalized $\lun$ minimization (also called Basis Pursuit Denoising or Lasso) in terms of sparsity pattern recovery (support and sign consistency) from noisy measurements with…
We propose a two-step procedure to detect cointegration in high-dimensional settings, focusing on sparse relationships. First, we use the adaptive LASSO to identify the small subset of integrated covariates driving the equilibrium…
We develop new efficient online algorithms for detecting transient sparse signals in TEM video sequences, by adopting the recently developed framework for sequential detection jointly with online convex optimization [1]. We cast the problem…
Statistical dependence between hypotheses poses a significant challenge to the stability of large scale multiple hypotheses testing. Ignoring it often results in an unacceptably large spread in the false positive proportion even though the…
This paper addresses the problem of sparse phase retrieval, a fundamental inverse problem in applied mathematics, physics, and engineering, where a signal need to be reconstructed using only the magnitude of its transformation while phase…
Since its development, the minimax framework has been one of the corner stones of theoretical statistics, and has contributed to the popularity of many well-known estimators, such as the regularized M-estimators for high-dimensional…