相关论文: Sparse Hanson-Wright Inequality for a Bilinear For…

A nonparametric Bayes approach is proposed for the problem of estimating a sparse sequence based on Gaussian random variables. We adopt the popular two-group prior with one component being a point mass at zero, and the other component being…

This work addresses the problem of high-dimensional classification by exploring the generalized Bayesian logistic regression method under a sparsity-inducing prior distribution. The method involves utilizing a fractional power of the…

The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a…

In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…

In recent years, a considerable amount of work has been devoted to generalizing linear discriminant analysis to overcome its incompetence for high-dimensional classification (Witten & Tibshirani 2011, Cai & Liu 2011, Mai et al. 2012, Fan et…

We discuss Bayesian inference for a known-mean Gaussian model with a compound symmetric variance-covariance matrix. Since the space of such matrices is a linear subspace of that of positive definite matrices, we utilize the methods of…

Approximations to Gaussian processes based on inducing variables, combined with variational inference techniques, enable state-of-the-art sparse approaches to infer GPs at scale through mini batch-based learning. In this work, we address…

Ising models describe the joint probability distribution of a vector of binary feature variables. Typically, not all the variables interact with each other and one is interested in learning the presumably sparse network structure of the…

We introduce a Bernstein-type inequality which serves to uniformly control quadratic forms of gaussian variables. The latter can for example be used to derive sharp model selection criteria for linear estimation in linear regression and…

Bayesian approach to inverse problems is studied in the case where the forward map is a linear hypoelliptic pseudodifferential operator and measurement error is additive white Gaussian noise. The measurement model for an unknown Gaussian…

In this paper we consider the uniformity testing problem for high-dimensional discrete distributions (multinomials) under sparse alternatives. More precisely, we derive sharp detection thresholds for testing, based on $n$ samples, whether a…

We consider drawing statistical inferences based on data subject to non-Gaussian measurement error. Unlike most existing methods developed under the assumption of Gaussian measurement error, the proposed strategy exploits hypercomplex…

Inference and prediction under the sparsity assumption have been a hot research topic in recent years. However, in practice, the sparsity assumption is difficult to test, and more importantly can usually be violated. In this paper, to study…

We tackle estimating sparse coefficients in a linear regression when the covariates are sampled from an $L$-subexponential random vector. This vector belongs to a class of distributions that exhibit heavier tails than Gaussian random…

Consider the Gaussian vector model with mean value {\theta}. We study the twin problems of estimating the number |{\theta}|_0 of non-zero components of {\theta} and testing whether |{\theta}|_0 is smaller than some value. For testing, we…

We consider testing the equality of two high-dimensional covariance matrices by carrying out a multi-level thresholding procedure, which is designed to detect sparse and faint differences between the covariances. A novel U-statistic…

Sparse linear inverse problems appear in a variety of settings, but often the noise contaminating observations cannot accurately be described as bounded by or arising from a Gaussian distribution. Poisson observations in particular are a…

Donoho and Kipnis (2022) showed that the the higher criticism (HC) test statistic has a non-Gaussian phase transition but remarked that it is probably not optimal, in the detection of sparse differences between two large frequency tables…

We use the very recent approach developed by Lacey in [23] and extended by Bernicot-Frey-Petermichl in [3], in order to control Bochner-Riesz operators by a sparse bilinear form. In this way, new quantitative weighted estimates, as well as…

We prove concentration inequalities for functions of independent random variables {under} sub-gaussian and sub-exponential conditions. The utility of the inequalities is demonstrated by an extension of the now classical method of Rademacher…