Related papers: A New Algorithm for Maximum Likelihood Estimation …
In graphical modelling, a bi-directed graph encodes marginal independences among random variables that are identified with the vertices of the graph. We show how to transform a bi-directed graph into a maximal ancestral graph that (i)…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
Analyzing multi-layered graphical models provides insight into understanding the conditional relationships among nodes within layers after adjusting for and quantifying the effects of nodes from other layers. We obtain the penalized maximum…
Graphical models describe associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models where the relationships are formalized by non-null entries of the…
In this work we present a rigorous application of the Expectation Maximization algorithm to determine the marginal distributions and the dependence structure in a Gaussian copula model with missing data. We further show how to circumvent a…
We study maximum likelihood estimation in Gaussian graphical models from a geometric point of view. An algebraic elimination criterion allows us to find exact lower bounds on the number of observations needed to ensure that the maximum…
Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of…
We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…
Probabilistic graphical models (PGMs) are powerful tools for representing statistical dependencies through graphs in high-dimensional systems. However, they are limited to pairwise interactions. In this work, we propose the simplicial…
In Gaussian graphical models, the likelihood equations must typically be solved iteratively. We investigate two algorithms: A version of iterative proportional scaling which avoids inversion of large matrices, and an algorithm based on…
Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the…
We provide a selected overview of methodology and theory for estimation and inference on the edge weights in high-dimensional directed and undirected Gaussian graphical models. For undirected graphical models, two main explicit…
The maximum likelihood threshold of a graph is the smallest number of data points that guarantees that maximum likelihood estimates exist almost surely in the Gaussian graphical model associated to the graph. We show that this graph…
Despite major methodological developments, Bayesian inference for Gaussian graphical models remains challenging in high dimension due to the tremendous size of the model space. This article proposes a method to infer the marginal and…
The graphical lasso is a widely used algorithm for fitting undirected Gaussian graphical models. However, for inference on functionals of edge values in the learned graph, standard tools lack formal statistical guarantees, such as control…
We introduce a general framework for undirected graphical models. It generalizes Gaussian graphical models to a wide range of continuous, discrete, and combinations of different types of data. The models in the framework, called exponential…
Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…
The maximum likelihood threshold (MLT) of a graph $G$ is the minimum number of samples to almost surely guarantee existence of the maximum likelihood estimate in the corresponding Gaussian graphical model. Recently a new characterization of…
We are interested in modeling networks in which the connectivity among the nodes and node attributes are random variables and interact with each other. We propose a probabilistic model that allows one to formulate jointly a probability…
Gaussian Graphical Models (GGM) are often used to describe the conditional correlations between the components of a random vector. In this article, we compare two families of GGM inference methods: nodewise edge selection and penalised…