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Sparse additive models are an attractive choice in circumstances calling for modelling flexibility in the face of high dimensionality. We study the signal detection problem and establish the minimax separation rate for the detection of a…
We study signals that are sparse in graph spectral domain and develop explicit algorithms to reconstruct the support set as well as partial components from samples on few vertices of the graph. The number of required samples is independent…
We propose a statistical model for graphs with a core-periphery structure. To do this we define a precise notion of what it means for a graph to have this structure, based on the sparsity properties of the subgraphs of core and periphery…
Spectral graph sparsification aims to find ultra-sparse subgraphs which can preserve spectral properties of original graphs. In this paper, a new spectral criticality metric based on trace reduction is first introduced for identifying…
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…
An analysis of the influence of missing samples in signals exhibiting sparsity in the Hermite transform domain is provided. Based on the statistical properties derived for the Hermite coefficients of randomly undersampled signal, the…
Recently, a new class of so-called \emph{hierarchical thresholding algorithms} was introduced to optimally exploit the sparsity structure in joint user activity and channel detection problems. In this paper, we take a closer look at the…
Advances of information-theoretic understanding of sparse sampling of continuous uncoded signals at sampling rates exceeding the Landau rate were reported in recent works. This work examines sparse sampling of coded signals at sub-Landau…
Higher criticism is a large-scale testing procedure that can attain the optimal detection boundary for sparse and faint signals. However, there has been a lack of knowledge in most existing works about its asymptotic distribution for more…
With the advancements in technology and monitoring tools, we often encounter multivariate graph signals, which can be seen as the realizations of multivariate graph processes, and revealing the relationship between their constituent…
One of the key challenges in sensor networks is the extraction of information by fusing data from a multitude of distinct, but possibly unreliable sensors. Recovering information from the maximum number of dependable sensors while…
The application of graph signal processing (GSP) on partially observed graph signals with missing nodes has gained attention recently. This is because processing data from large graphs are difficult, if not impossible due to the lack of…
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…
The problem of consistently estimating the sparsity pattern of a vector $\betastar \in \real^\mdim$ based on observations contaminated by noise arises in various contexts, including subset selection in regression, structure estimation in…
We are given a set of $n$ points that might be uniformly distributed in the unit square $[0,1]^2$. We wish to test whether the set, although mostly consisting of uniformly scattered points, also contains a small fraction of points sampled…
We consider the problem of detecting sparse heterogeneous mixtures in a two-sample setting from a nonparametric perspective, where the effect manifests itself as a positive shift. We suggest a two-sample higher criticism test, and show that…
In this paper, we analyze the information theoretic lower bound on the necessary number of samples needed for recovering a sparse signal under different compressed sensing settings. We focus on the weighted graph model, a model-based…
We introduce methods for discovering and applying sparse feature circuits. These are causally implicated subnetworks of human-interpretable features for explaining language model behaviors. Circuits identified in prior work consist of…
Deep learning models have been shown to be vulnerable to adversarial attacks. This perception led to analyzing deep learning models not only from the perspective of their performance measures but also their robustness to certain types of…
We consider the compressive sensing of a sparse or compressible signal ${\bf x} \in {\mathbb R}^M$. We explicitly construct a class of measurement matrices, referred to as the low density frames, and develop decoding algorithms that produce…