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

In this thesis we study adaptive nonparametric regression with noise misspecification and the complexity of approximation of random fields in dependence of the dimension. First, we consider the problem of pointwise estimation in…

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…

The multi-scale factor models are particularly appealing for analyzing matrix- or tensor-valued data, due to their adaptiveness to local geometry and intuitive interpretation. However, the reliance on the binary tree for recursive…

We propose Bayesian methods for Gaussian graphical models that lead to sparse and adaptively shrunk estimators of the precision (inverse covariance) matrix. Our methods are based on lasso-type regularization priors leading to parsimonious…

Large-scale precision matrix estimation is of fundamental importance yet challenging in many contemporary applications for recovering Gaussian graphical models. In this paper, we suggest a new approach of innovated scalable efficient…

The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different…

In this paper, we propose two new algorithms for maximum-likelihood estimation (MLE) of high dimensional sparse covariance matrices. Unlike most of the state of-the-art methods, which either use regularization techniques or penalize the…

Gaussian process (GP) regression is a flexible, nonparametric approach to regression that naturally quantifies uncertainty. In many applications, the number of responses and covariates are both large, and a goal is to select covariates that…

This paper is concerned with the selection of fixed effects along with the estimation of fixed effects, random effects and variance components in the linear mixed-effects model. We introduce a selection procedure based on an adaptive ridge…

We propose a new sparse regression method called the component lasso, based on a simple idea. The method uses the connected-components structure of the sample covariance matrix to split the problem into smaller ones. It then solves the…

We consider the solution of large linear systems of equations that arise when two-dimensional singularly perturbed reaction-diffusion equations are discretized. Standard methods for these problems, such as central finite differences, lead…

We consider a high-dimensional regression model with a possible change-point due to a covariate threshold and develop the Lasso estimator of regression coefficients as well as the threshold parameter. Our Lasso estimator not only selects…

Among all the deterministic CholeskyQR-type algorithms, Shifted CholeskyQR3 is specifically designed to address the QR factorization of ill-conditioned matrices. This algorithm introduces a shift parameter $s$ to prevent failure during the…

In this paper, we propose and analyse a family of generalised stochastic composite mirror descent algorithms. With adaptive step sizes, the proposed algorithms converge without requiring prior knowledge of the problem. Combined with an…

The factor modeling for high-dimensional time series is powerful in discovering latent common components for dimension reduction and information extraction. Most available estimation methods can be divided into two categories: the…

In this paper, we investigate diagonal estimation for large or implicit matrices, aiming to develop a novel and efficient stochastic algorithm that incorporates adaptive parameter selection. We explore the influence of different eigenvalue…

Estimation of the precision matrix (or inverse covariance matrix) is of great importance in statistical data analysis and machine learning. However, as the number of parameters scales quadratically with the dimension $p$, computation…

The covariance matrix plays a fundamental role in many modern exploratory and inferential statistical procedures, including dimensionality reduction, hypothesis testing, and regression. In low-dimensional regimes, where the number of…

The recent literature on first order methods for smooth optimization shows that significant improvements on the practical convergence behaviour can be achieved with variable stepsize and scaling for the gradient, making this class of…

High dimensional covariance estimation and graphical models is a contemporary topic in statistics and machine learning having widespread applications. An important line of research in this regard is to shrink the extreme spectrum of the…