Related papers: Conjugate gradient methods for high-dimensional GL…

Finite Gaussian mixture models provide a powerful and widely employed probabilistic approach for clustering multivariate continuous data. However, the practical usefulness of these models is jeopardized in high-dimensional spaces, where…

Modern biomedical datasets are increasingly high dimensional and exhibit complex correlation structures. Generalized Linear Mixed Models (GLMMs) have long been employed to account for such dependencies. However, proper specification of the…

Graphical models are ubiquitous tools to describe the interdependence between variables measured simultaneously such as large-scale gene or protein expression data. Gaussian graphical models (GGMs) are well-established tools for…

Graphical models serve as effective tools for visualizing conditional dependencies between variables. However, as the number of variables grows, interpretation becomes increasingly difficult, and estimation uncertainty increases due to 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…

Methods for inference and simulation of linearly constrained Gaussian Markov Random Fields (GMRF) are computationally prohibitive when the number of constraints is large. In some cases, such as for intrinsic GMRFs, they may even be…

We develop a framework to study posterior contraction rates in sparse high dimensional generalized linear models (GLM). We introduce a new family of GLMs, denoted by clipped GLM, which subsumes many standard GLMs and makes minor…

Generalized linear models (GLMs) -- such as logistic regression, Poisson regression, and robust regression -- provide interpretable models for diverse data types. Probabilistic approaches, particularly Bayesian ones, allow coherent…

The residual cutting (RC) method has been proposed for efficiently solving linear equations obtained from elliptic partial differential equations. Based on the RC, we have introduced the generalized residual cutting (GRC) method, which can…

Matrix computations, especially iterative PDE solving (and the sparse matrix vector multiplication subproblem within) using conjugate gradient algorithm, and LU/Cholesky decomposition for solving system of linear equations, form the kernel…

Gradient Descent (GD) and Conjugate Gradient (CG) methods are among the most effective iterative algorithms for solving unconstrained optimization problems, particularly in machine learning and statistical modeling, where they are employed…

The use of the Preconditioned Conjugate Gradient (PCG) method for computing the Generalized Least Squares (GLS) estimator of the General Linear Model (GLM) is considered. The GLS estimator is expressed in terms of the solution of an…

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…

We present a graph-based technique for estimating sparse covariance matrices and their inverses from high-dimensional data. The method is based on learning a directed acyclic graph (DAG) and estimating parameters of a multivariate Gaussian…

Gaussian Graphical Models (GGMs) are popular tools for studying network structures. However, many modern applications such as gene network discovery and social interactions analysis often involve high-dimensional noisy data with outliers or…

Estimation in generalized linear models (GLM) is complicated by the presence of constraints. One can handle constraints by maximizing a penalized log-likelihood. Penalties such as the lasso are effective in high dimensions, but often lead…

This paper introduces a method for studying the correlation structure of a range of responses modelled by a multivariate generalised linear mixed model (MGLMM). The methodology requires the existence of clusters of observations and that…

The Gaussian graphical model (GGM) incorporates an undirected graph to represent the conditional dependence between variables, with the precision matrix encoding partial correlation between pair of variables given the others. To achieve…

We present an approach for continual learning (CL) that is based on fully probabilistic (or generative) models of machine learning. In contrast to, e.g., GANs that are "generative" in the sense that they can generate samples, fully…

Gaussian Graphical Models (GGMs) are widely used in high-dimensional data analysis to synthesize the interaction between variables. In many applications, such as genomics or image analysis, graphical models rely on sparsity and clustering…