Related papers: Sparse Confidence Sets for Normal Mean Models

Balancing predictive power and interpretability has long been a challenging research area, particularly in powerful yet complex models like neural networks, where nonlinearity obstructs direct interpretation. This paper introduces a novel…

Constructing valid inferential methods for constrained parameters in normal and Poisson distributions represents two fundamental and important problems in applied statistics, for which there is currently no unified framework for statistical…

Statistical inference in high dimensional settings has recently attracted enormous attention within the literature. However, most published work focuses on the parametric linear regression problem. This paper considers an important…

We introduce a general framework that extends Bayesian inference by allowing the researcher to explicitly encode confidence in each source of uncertainty within the model. This mechanism provides a new handle for model design and…

Many popular methods for building confidence intervals on causal effects under high-dimensional confounding require strong "ultra-sparsity" assumptions that may be difficult to validate in practice. To alleviate this difficulty, we here…

We consider a general regression model, without a scale parameter. Our aim is to construct a confidence interval for a scalar parameter of interest $\theta$ that utilizes the uncertain prior information that a distinct scalar parameter…

Regularized kernel methods such as, e.g., support vector machines and least-squares support vector regression constitute an important class of standard learning algorithms in machine learning. Theoretical investigations concerning…

Generally, convolutional neural networks (CNNs) process data on a regular grid, e.g. data generated by ordinary cameras. Designing CNNs for sparse and irregularly spaced input data is still an open research problem with numerous…

We propose a general framework for nonasymptotic covariance matrix estimation making use of concentration inequality-based confidence sets. We specify this framework for the estimation of large sparse covariance matrices through…

We consider the model {eqnarray*}y=X\theta^*+\xi, Z=X+\Xi,{eqnarray*} where the random vector $y\in\mathbb{R}^n$ and the random $n\times p$ matrix $Z$ are observed, the $n\times p$ matrix $X$ is unknown, $\Xi$ is an $n\times p$ random noise…

Let A be an n by m matrix with m>n, and suppose that the underdetermined linear system As=x admits a sparse solution s0 for which ||s0||_0 < 1/2 spark(A). Such a sparse solution is unique due to a well-known uniqueness theorem. Suppose now…

To successfully work on variable selection, sparse model structure has become a basic assumption for all existing methods. However, this assumption is questionable as it is hard to hold in most of cases and none of existing methods may…

We propose methodology for estimation of sparse precision matrices and statistical inference for their low-dimensional parameters in a high-dimensional setting where the number of parameters $p$ can be much larger than the sample size. We…

Random feature methods have been successful in various machine learning tasks, are easy to compute, and come with theoretical accuracy bounds. They serve as an alternative approach to standard neural networks since they can represent…

Robust uncertainty quantification is increasingly important in modern data analysis and is often formalized under Huber's model, which allows an $\varepsilon$-fraction of arbitrary corruptions. In many experimental sciences, however, the…

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…

Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…

In typical high dimensional statistical inference problems, confidence intervals and hypothesis tests are performed for a low dimensional subset of model parameters under the assumption that the parameters of interest are unconstrained.…

Given a large number of covariates $Z$, we consider the estimation of a high-dimensional parameter $\theta$ in an individualized linear threshold $\theta^T Z$ for a continuous variable $X$, which minimizes the disagreement between…

Estimating linear, mean-square continuous functionals is a pivotal challenge in statistics. In high-dimensional contexts, this estimation is often performed under the assumption of exact model sparsity, meaning that only a small number of…