Related papers: Adapting to Unknown Sparsity by controlling the Fa…
Multiple testing adjustments, such as the Benjamini and Hochberg (1995) step-up procedure for controlling the false discovery rate (FDR), are typically applied to families of tests that control significance level in the classical sense: for…
Multiple comparison procedures that control a family-wise error rate or false discovery rate provide an achieved error rate as the adjusted p-value for each hypothesis tested. However, since such p-values are not probabilities that the null…
This paper investigates asymptotic minimaxity properties of Bayesian multiple testing rules in the sparse Gaussian sequence model using a broad class of global-local scale mixtures of normals as priors for the means. Minimaxity is studied…
Sparse recovery is among the most well-studied problems in learning theory and high-dimensional statistics. In this work, we investigate the statistical and computational landscapes of sparse recovery with $\ell_\infty$ error guarantees.…
In networked control systems, communication resource constraints often necessitate the use of \emph{sparse} control input vectors. A prototypical problem is how to ensure controllability of a linear dynamical system when only a limited…
Recent advances in noiseless non-adaptive group testing have led to a precise asymptotic characterization of the number of tests required for high-probability recovery in the sublinear regime $k = n^{\theta}$ (with $\theta \in (0,1)$), with…
We address the issue of estimating the regression vector $\beta$ in the generic $s$-sparse linear model $y = X\beta+z$, with $\beta\in\R^{p}$, $y\in\R^{n}$, $z\sim\mathcal N(0,\sg^2 I)$ and $p> n$ when the variance $\sg^{2}$ is unknown. We…
We address the problem of recovering a sparse $n$-vector within a given subspace. This problem is a subtask of some approaches to dictionary learning and sparse principal component analysis. Hence, if we can prove scaling laws for recovery…
Various regularized linear discriminant analysis (LDA) methods have been proposed to address the problems of the classic methods in high-dimensional settings. Asymptotic optimality has been established for some of these methods in high…
The goal of Sparse Convex Optimization is to optimize a convex function $f$ under a sparsity constraint $s\leq s^*\gamma$, where $s^*$ is the target number of non-zero entries in a feasible solution (sparsity) and $\gamma\geq 1$ is an…
We observe an unknown regression function of $d$ variables $f(\boldsymbol{t})$, $\boldsymbol{t} \in[0,1]^d$, in the Gaussian white noise model of intensity $\varepsilon>0$. We assume that the function $f$ is regular and that it is a sum of…
In sparse recovery, the unique sparsest solution to an under-determined system of linear equations is of main interest. This scheme is commonly proposed to be applied to signal acquisition. In most cases, the signals are not sparse…
There are a number of ways to test for the absence/presence of a spatial signal in a completely observed fine-resolution image. One of these is a powerful nonparametric procedure called Enhanced False Discovery Rate (EFDR). A drawback of…
Much effort has been done to control the "false discovery rate" (FDR) when $m$ hypotheses are tested simultaneously. The FDR is the expectation of the "false discovery proportion" $\text{FDP}=V/R$ given by the ratio of the number of false…
Controlling false discovery rate (FDR) while leveraging the side information of multiple hypothesis testing is an emerging research topic in modern data science. Existing methods rely on the test-level covariates while ignoring possible…
We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…
Thanks to its fine balance between model flexibility and interpretability, the nonparametric additive model has been widely used, and variable selection for this type of model has been frequently studied. However, none of the existing…
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…
We consider the problem of estimating a deterministic sparse vector x from underdetermined measurements Ax+w, where w represents white Gaussian noise and A is a given deterministic dictionary. We analyze the performance of three sparse…
The effective utilization of structural information in data while ensuring statistical validity poses a significant challenge in false discovery rate (FDR) analyses. Conformal inference provides rigorous theory for grounding complex machine…