Kyoungjae Lee

In this paper we study the high-dimensional sparse directed acyclic graph (DAG) models under the empirical sparse Cholesky prior. Among our results, strong model selection consistency or graph selection consistency is obtained under more general conditions than those in the existing literature. Compared to Cao, Khare and Ghosh [Ann. Statist. (2019) 47 319–348], the required conditions are weakened in terms of the dimensionality, sparsity and lower bound of the nonzero elements in the Cholesky fa

We consider Bayesian logistic regression models with group-structured covariates. In high-dimensional settings, it is often assumed that only a small portion of groups are significant, and thus, consistent group selection is of significant importance. While consistent frequentist group selection methods have been proposed, theoretical properties of Bayesian group selection methods for logistic regression models have not been investigated yet. In this paper, we consider a hierarchical group spike

We introduce the $k$-banded Cholesky prior for estimating a high-dimensional bandable precision matrix via the modified Cholesky decomposition. The bandable assumption is imposed on the Cholesky factor of the decomposition. We obtained the P-loss convergence rate under the spectral norm and the matrix $\ell_{\infty}$ norm and the minimax lower bounds. Since the P-loss convergence rate (Lee and Lee (2017)) is stronger than the posterior convergence rate, the rates obtained are also posterior conv

Parkinson’s disease is a progressive, chronic, and neurodegenerative disorder that is primarily diagnosed by clinical examinations and magnetic resonance imaging (MRI). In this paper, we propose a Bayesian model to predict Parkinson’s disease employing a functional MRI (fMRI) based radiomics approach. We consider a spike and slab prior for variable selection in high-dimensional logistic regression models, and present an approximate Gibbs sampler by replacing a logistic distribution with a t-dist

In this paper, we consider high-dimensional Gaussian graphical models where the true underlying graph is decomposable. A hierarchical G-Wishart prior is proposed to conduct a Bayesian inference for the precision matrix and its graph structure. Although the posterior asymptotics using the G-Wishart prior has received increasing attention in recent years, most of the results assume moderate high-dimensional settings, where the number of variables p is smaller than the sample size n. However, this

High-dimensional variable selection is an important research topic in modern statistics. While methods using nonlocal priors have been thoroughly studied for variable selection in linear regression, the crucial high-dimensional model selection properties for nonlocal priors in generalized linear models have not been investigated. In this paper, we consider a hierarchical generalized linear regression model with the product moment nonlocal prior over coefficients and examine its properties. Under

Statistical inference for sparse covariance matrices is crucial to reveal dependence structure of large multivariate data sets, but lacks scalable and theoretically supported Bayesian methods. In this paper, we propose beta-mixture shrinkage prior, computationally more efficient than the spike and slab prior, for sparse covariance matrices and establish its minimax optimality in high-dimensional settings. The proposed prior consists of beta-mixture shrinkage and gamma priors for off-diagonal and

In this work, we propose a scalable Bayesian procedure for learning the local dependence structure in a high-dimensional model where the variables possess a natural ordering. The ordering of variables can be indexed by time, the vicinities of spatial locations, and so on, with the natural assumption that variables far apart tend to have weak correlations. Applications of such models abound in a variety of fields such as finance, genome associations analysis and spatial modeling. We adopt a flexi

Covariance is of universal prevalence across various disciplines within statistics. We provide a rich collection of geometric and inferential tools for convenient analysis of covariance structures, topics including distance measures, mean covariance estimator, covariance hypothesis test for one-sample and two-sample cases, and covariance estimation. For an introduction to covariance in multivariate statistical analysis, see Schervish (1987) &lt;<a href="https://doi.org/10.1214%2Fss%2F1177013111"

Assuming a banded structure is one of the common practice in the estimation of high-dimensional precision matrices. In this case, estimating the bandwidth of the precision matrix is a crucial initial step for subsequent analysis. Although there exist some consistent frequentist tests for the bandwidth parameter, bandwidth selection consistency for precision matrices has not been established in a Bayesian framework. In this paper, we propose a prior distribution tailored to the bandwidth estimati

In this paper, we propose a scalable Bayesian method for sparse covariance matrix estimation by incorporating a continuous shrinkage prior with a screening procedure. In the first step of the procedure, the off-diagonal elements with small correlations are screened based on their sample correlations. In the second step, the posterior of the covariance with the screened elements fixed at 0 is computed with the beta-mixture prior. The screened elements of the covariance significantly increase the

In this paper, we study the high-dimensional sparse directed acyclic graph (DAG) models under the empirical sparse Cholesky prior. Among our results, strong model selection consistency or graph selection consistency is obtained under more general conditions than those in the existing literature. Compared to Cao, Khare and Ghosh (2017), the required conditions are weakened in terms of the dimensionality, sparsity and lower bound of the nonzero elements in the Cholesky factor. Furthermore, our res