Related papers: A covariate-dependent Cholesky decomposition for h…
Covariance estimation for high-dimensional datasets is a fundamental problem in modern day statistics with numerous applications. In these high dimensional datasets, the number of variables p is typically larger than the sample size n. A…
While covariance matrices have been widely studied in many scientific fields, relatively limited progress has been made on estimating conditional covariances that permits a large covariance matrix to vary with high-dimensional subject-level…
Fitting high-dimensional data involves a delicate tradeoff between faithful representation and the use of sparse models. Too often, sparsity assumptions on the fitted model are too restrictive to provide a faithful representation of the…
In this paper we propose a new regression interpretation of the Cholesky factor of the covariance matrix, as opposed to the well known regression interpretation of the Cholesky factor of the inverse covariance, which leads to a new class of…
The modified Cholesky decomposition is commonly used for precision matrix estimation given a specified order of random variables. However, the order of variables is often not available or cannot be pre-determined. In this work, we propose…
Finding an unconstrained and statistically interpretable reparameterization of a covariance matrix is still an open problem in statistics. Its solution is of central importance in covariance estimation, particularly in the recent…
Sparse covariance matrices play crucial roles by encoding the interdependencies between variables in numerous fields such as genetics and neuroscience. Despite substantial studies on sparse covariance matrices, existing methods face several…
Distributional regression is extended to Gaussian response vectors of dimension greater than two by parameterizing the covariance matrix $\Sigma$ of the response distribution using the entries of its Cholesky decomposition. The more common…
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…
We introduce a new sparse sliced inverse regression estimator called Cholesky matrix penalization and its adaptive version for achieving sparsity in estimating the dimensions of the central subspace. The new estimators use the Cholesky…
This paper studies the estimation of a large covariance matrix. We introduce a novel procedure called ChoSelect based on the Cholesky factor of the inverse covariance. This method uses a dimension reduction strategy by selecting the pattern…
Estimating covariance parameters for multivariate spatial Gaussian random fields is computationally challenging, as the number of parameters grows rapidly with the number of variables, and likelihood evaluation requires operations of order…
Identifying co-varying causal elements in very high dimensional feature space with internal structures, e.g., a space with as many as millions of linearly ordered features, as one typically encounters in problems such as whole genome…
In this paper, we present a novel framework incorporating a combination of sparse models in different domains. We posit the observed data as generated from a linear combination of a sparse Gaussian Markov model (with a sparse precision…
Estimating large covariance matrices has been a longstanding important problem in many applications and has attracted increased attention over several decades. This paper deals with two methods based on pre-existing works to impose sparsity…
Estimation of large sparse covariance matrices is of great importance for statistical analysis, especially in the high-dimensional settings. The traditional approach such as the sample covariance matrix performs poorly due to the high…
Multivariate regression model is a natural generalization of the classical univari- ate regression model for fitting multiple responses. In this paper, we propose a high- dimensional multivariate conditional regression model for…
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…
We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…
The paper proposes a new covariance estimator for large covariance matrices when the variables have a natural ordering. Using the Cholesky decomposition of the inverse, we impose a banded structure on the Cholesky factor, and select the…