Related papers: Asymptotic minimaxity of False Discovery Rate thre…
We propose a sparse deep ReLU network (SDRN) estimator of the regression function obtained from regularized empirical risk minimization with a Lipschitz loss function. Our framework can be applied to a variety of regression and…
$\ell_1$ minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity (the size of the support set), under which with high probability a sparse signal…
Simultaneously performing variable selection and inference in high-dimensional regression models is an open challenge in statistics and machine learning. The increasing availability of vast amounts of variables requires the adoption of…
Multiple hypothesis testing is a central topic in statistics, but despite abundant work on the false discovery rate (FDR) and the corresponding Type-II error concept known as the false non-discovery rate (FNR), a fine-grained understanding…
This paper proposes novel inferential procedures for discovering the network Granger causality in high-dimensional vector autoregressive models. In particular, we mainly offer two multiple testing procedures designed to control the false…
We construct minimax optimal non-asymptotic confidence sets for low rank matrix recovery algorithms such as the Matrix Lasso or Dantzig selector. These are employed to devise adaptive sequential sampling procedures that guarantee recovery…
In massive data analysis, training and testing data often come from very different sources, and their probability distributions are not necessarily identical. A feature example is nonparametric classification in posterior drift model where…
Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…
Protection against disclosure is a legal and ethical obligation for agencies releasing microdata files for public use. Consider a microdata sample of size $n$ from a finite population of size $\bar{n}=n+\lambda n$, with $\lambda>0$, such…
This paper studies the semi-supervised novelty detection problem where a set of "typical" measurements is available to the researcher. Motivated by recent advances in multiple testing and conformal inference, we propose AdaDetect, a…
The support recovery problem consists of determining a sparse subset of variables that is relevant in generating a set of observations. In this paper, we study the support recovery problem in the phase retrieval model consisting of noisy…
Considering the case where the response variable is a categorical variable and the predictor is a random function, two novel functional sufficient dimensional reduction (FSDR) methods are proposed based on mutual information and square loss…
We calculate analytically the fluctuation-dissipation ratio (FDR) for Ising ferromagnets quenched to criticality, both for the long-range model and its short-range analogue in the limit of large dimension. Our exact solution shows that, for…
In this paper, we study the sparse nonnegative tensor factorization and completion problem from partial and noisy observations for third-order tensors. Because of sparsity and nonnegativity, the underlying tensor is decomposed into the…
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…
Multisine excitations are widely used for identifying multi-input multi-output systems due to their periodicity, data compression properties, and control over the input spectrum. Despite their popularity, the finite sample statistical…
False discovery rate (FDR) control methods are essential for voxel-wise multiple testing in neuroimaging data analysis, where hundreds of thousands or even millions of tests are conducted to detect brain regions associated with…
In many applications in compressed sensing, the measurement matrix is a Fourier matrix, i.e., it measures the Fourier transform of the underlying signal at some specified `base' frequencies $\{u_i\}_{i=1}^M$, where $M$ is the number of…
In multiple hypothesis testing, it is well known that adaptive procedures can enhance power via incorporating information about the number of true nulls present. Under independence, we establish that two adaptive false discovery rate (FDR)…
We study nonparametric density estimation in non-stationary drift settings. Given a sequence of independent samples taken from a distribution that gradually changes in time, the goal is to compute the best estimate for the current…