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The fields of compressed sensing (CS) and matrix completion have shown that high-dimensional signals with sparse or low-rank structure can be effectively projected into a low-dimensional space (for efficient acquisition or processing) when…
We study the theoretical properties of the fused lasso procedure originally proposed by \cite{tibshirani2005sparsity} in the context of a linear regression model in which the regression coefficient are totally ordered and assumed to be…
We consider inference in regression discontinuity designs when the running variable only takes a moderate number of distinct values. In particular, we study the common practice of using confidence intervals (CIs) based on standard errors…
Choice models, which capture popular preferences over objects of interest, play a key role in making decisions whose eventual outcome is impacted by human choice behavior. In most scenarios, the choice model, which can effectively be viewed…
Over the past years, there are increasing interests in recovering the signals from undersampling data where such signals are sparse under some orthogonal dictionary or tight framework, which is referred to be sparse synthetic model. More…
The problem of constructing confidence sets in the high-dimensional linear model with $n$ response variables and $p$ parameters, possibly $p\ge n$, is considered. Full honest adaptive inference is possible if the rate of sparse estimation…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…
The performance of Orthogonal Matching Pursuit (OMP) for variable selection is analyzed for random designs. When contrasted with the deterministic case, since the performance is here measured after averaging over the distribution of the…
The bound that arises out of sparse recovery analysis in compressed sensing involves input signal sparsity and some property of the sensing matrix. An effort has therefore been made in the literature to optimize sensing matrices for optimal…
Dantzig selector (DS) and LASSO problems have attracted plenty of attention in statistical learning, sparse data recovery and mathematical optimization. In this paper, we provide a theoretical analysis of the sparse recovery stability of…
In this paper, {the goal is to design deterministic sampling patterns on the sphere and the rotation group} and, thereby, construct sensing matrices for sparse recovery of band-limited functions. It is first shown that random sensing…
The restricted isometry property (RIP) has become well-known in the compressed sensing community. Recently, a weaken version of RIP was proposed for exact sparse recovery under weak moment assumptions. In this note, we prove that the weaken…
In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate…
In the context of compressed sensing (CS), both Subspace Pursuit (SP) and Compressive Sampling Matching Pursuit (CoSaMP) are very important iterative greedy recovery algorithms which could reduce the recovery complexity greatly comparing…
We study sparse recovery with structured random measurement matrices having independent, identically distributed, and uniformly bounded rows and with a nontrivial covariance structure. This class of matrices arises from random sampling of…
Penalized regression models are popularly used in high-dimensional data analysis to conduct variable selection and model fitting simultaneously. Whereas success has been widely reported in literature, their performances largely depend on…
Random matrices are widely used in sparse recovery problems, and the relevant properties of matrices with i.i.d. entries are well understood. The current paper discusses the recently introduced Restricted Eigenvalue (RE) condition, which is…
Although a majority of the theoretical literature in high-dimensional statistics has focused on settings which involve fully-observed data, settings with missing values and corruptions are common in practice. We consider the problems of…
The LASSO estimator is an $\ell_1$-norm penalized least-squares estimator, which was introduced for variable selection in the linear model. When the design matrix satisfies, e.g. the Restricted Isometry Property, or has a small coherence…
The purpose of this note is to establish a new generalized Dictionary-Restricted Isometry Property (D-RIP) sparsity bound constant for compressed sensing. For fulfilling D-RIP, the constant $\delta_k$ is used in the definition: $(1…