Related papers: Sparse Nonparametric Graphical Models
A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…
In this contribution we deal with the problem of learning an undirected graph which encodes the conditional dependence relationship between variables of a complex system, given a set of observations of this system. This is a very central…
Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…
We discuss the Gaussian graphical model (GGM; an undirected network of partial correlation coefficients) and detail its utility as an exploratory data analysis tool. The GGM shows which variables predict one-another, allows for sparse…
This article introduces a novel nonparametric methodology for Generalized Linear Models which combines the strengths of the binary regression and latent variable formulations for categorical data, while overcoming their disadvantages.…
Identifying the Markov properties or conditional independencies of a collection of random variables is a fundamental task in statistics for modeling and inference. Existing approaches often learn the structure of a probabilistic graphical…
Recently there has been increased interest in fitting generative graph models to real-world networks. In particular, Bl\"asius et al. have proposed a framework for systematic evaluation of the expressivity of random graph models. We extend…
Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…
Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…
Nonparametric Bayesian models are used routinely as flexible and powerful models of complex data. Many times, a statistician may have additional informative beliefs about data distribution of interest, e.g., its mean or subset components,…
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…
We develop a framework for learning sparse nonparametric directed acyclic graphs (DAGs) from data. Our approach is based on a recent algebraic characterization of DAGs that led to a fully continuous program for score-based learning of DAG…
We propose a novel Bayesian nonparametric method to learn translation-invariant relationships on non-Euclidean domains. The resulting graph convolutional Gaussian processes can be applied to problems in machine learning for which the input…
We introduce a novel class of graphical models, termed profile graphical models, that represent, within a single graph, how an external factor influences the dependence structure of a multivariate set of variables. This class is quite…
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…
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…
Gaussian graphical models are used throughout the natural sciences, social sciences, and economics to model the statistical relationships between variables of interest in the form of a graph. We here provide a pedagogic introduction to…
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…
Graph convolutional neural networks (GCNN) have been successfully applied to many different graph based learning tasks including node and graph classification, matrix completion, and learning of node embeddings. Despite their impressive…
We design algorithms for fitting a high-dimensional statistical model to a large, sparse network without revealing sensitive information of individual members. Given a sparse input graph $G$, our algorithms output a…