相关论文: On Statistical Inference with High Dimensional Spa…

Statistical inference for tensors has emerged as a critical challenge in analyzing high-dimensional data in modern data science. This paper introduces a unified framework for inferring general and low-Tucker-rank linear functionals of…

We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…

We develop theoretical results that establish a connection across various regression methods such as the non-negative least squares, bounded variable least squares, simplex constrained least squares, and lasso. In particular, we show in…

Graphical models have become a very popular tool for representing dependencies within a large set of variables and are key for representing causal structures. We provide results for uniform inference on high-dimensional graphical models…

We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors where the vector of coefficients can vary from sparse to dense. In this setting, we propose a combination of probabilistic…

It is well-known that the statistical performance of Lasso can suffer significantly when the covariates of interest have strong correlations. In particular, the prediction error of Lasso becomes much worse than computationally inefficient…

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…

We consider a novel Bayesian approach to estimation, uncertainty quantification, and variable selection for a high-dimensional linear regression model under sparsity. The number of predictors can be nearly exponentially large relative to…

Motivated by differential co-expression analysis in genomics, we consider in this paper estimation and testing of high-dimensional differential correlation matrices. An adaptive thresholding procedure is introduced and theoretical…

Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low…

For data segmentation in high-dimensional linear regression settings, the regression parameters are often assumed to be sparse segment-wise, which enables many existing methods to estimate the parameters locally via $\ell_1$-regularised…

We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…

High-dimensional inference methods often rely on coefficient sparsity, an assumption that can be restrictive when signals are dense but individually weak. In such settings, valid inference may still be possible if the covariates exhibit…

We present a method for estimating sparse high-dimensional inverse covariance and partial correlation matrices, which exploits the connection between the inverse covariance matrix and linear regression. The method is a two-stage estimation…

The linear regression model is widely used in empirical work in Economics, Statistics, and many other disciplines. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We…

We study the high-dimensional inference of a rank-one signal corrupted by sparse noise. The noise is modelled as the adjacency matrix of a weighted undirected graph with finite average connectivity in the large size limit. Using the replica…

Sparse canonical correlation analysis (CCA) is a useful statistical tool to detect latent information with sparse structures. However, sparse CCA works only for two datasets, i.e., there are only two views or two distinct objects. To…

The focus of this paper is to extend Fisher's linear discriminant analysis (LDA) to both densely re-corded functional data and sparsely observed longitudinal data for general $c$-category classification problems. We propose an efficient…

In high-dimensions, many variable selection methods, such as the lasso, are often limited by excessive variability and rank deficiency of the sample covariance matrix. Covariance sparsity is a natural phenomenon in high-dimensional…

Repeated measurements are common in many fields, where random variables are observed repeatedly across different subjects. Such data have an underlying hierarchical structure, and it is of interest to learn covariance/correlation at…