相关论文: Adaptive estimation of covariance matrices via Cho…

Given $n$ i.i.d. observations of a random vector $(X,Z)$, where $X$ is a high-dimensional vector and $Z$ is a low-dimensional index variable, we study the problem of estimating the conditional inverse covariance matrix $\Omega(z) =…

Assuming a banded structure is one of the common practice in the estimation of high-dimensional precision matrix. In this case, estimating the bandwidth of the precision matrix is a crucial initial step for subsequent analysis. Although…

The purpose of this article is to provide an adaptive estimator of the baseline function in the Cox model with high-dimensional covariates. We consider a two-step procedure : first, we estimate the regression parameter of the Cox model via…

Performing Bayesian inference on large spatio-temporal models requires extracting inverse elements of large sparse precision matrices for marginal variances, as well as estimating model hyperparameters. Although direct matrix factorizations…

We present an algorithm where only the Cholesky basis is determined in the decomposition procedure. This allows for improved screening and a partitioned matrix decomposition scheme, both of which significantly reduce memory usage and…

This paper introduces a subspace method for the estimation of an array covariance matrix. It is shown that when the received signals are uncorrelated, the true array covariance matrices lie in a specific subspace whose dimension is…

Maximizing the likelihood has been widely used for estimating the unknown covariance parameters of spatial Gaussian processes. However, evaluating and optimizing the likelihood function can be computationally intractable, particularly for…

In addition to recent developments in computing speed and memory, methodological advances have contributed to significant gains in the performance of stochastic simulation. In this paper, we focus on variance reduction for matrix…

We propose a method for estimating a covariance matrix that can be represented as a sum of a low-rank matrix and a diagonal matrix. The proposed method compresses high-dimensional data, computes the sample covariance in the compressed…

The present paper concerns large covariance matrix estimation via composite minimization under the assumption of low rank plus sparse structure. In this approach, the low rank plus sparse decomposition of the covariance matrix is recovered…

This paper studies simultaneous feature selection and extraction in supervised and unsupervised learning. We propose and investigate selective reduced rank regression for constructing optimal explanatory factors from a parsimonious subset…

The problem of decomposing a given covariance matrix as the sum of a positive semi-definite matrix of given rank and a positive semi-definite diagonal matrix, is considered. We present a projection-type algorithm to address this problem.…

Given a sample covariance matrix, we solve a maximum likelihood problem penalized by the number of nonzero coefficients in the inverse covariance matrix. Our objective is to find a sparse representation of the sample data and to highlight…

To achieve scalable and accurate inference for latent Gaussian processes, we propose a variational approximation based on a family of Gaussian distributions whose covariance matrices have sparse inverse Cholesky (SIC) factors. We combine…

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…

This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…

We introduce an estimation method of covariance matrices in a high-dimensional setting, i.e., when the dimension of the matrix, , is larger than the sample size . Specifically, we propose an orthogonally equivariant estimator. The…

We propose a novel algorithm for efficiently computing a sparse directed adjacency matrix from a group of time series following a causal graph process. Our solution is scalable for both dense and sparse graphs and automatically selects the…

Many popular statistical models, such as factor and random effects models, give arise a certain type of covariance structures that is a summation of low rank and sparse matrices. This paper introduces a penalized approximation framework to…

Undirected graphs are often used to describe high dimensional distributions. Under sparsity conditions, the graph can be estimated using $\ell_1$-penalization methods. We propose and study the following method. We combine a multiple…