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We will amalgamate the Rash model (for rectangular binary tables) and the newly introduced $\alpha$-$\beta$ models (for random undirected graphs) in the framework of a semiparametric probabilistic graph model. Our purpose is to give a…
The exponential family random graph modeling (ERGM) framework provides a flexible approach for the statistical analysis of networks. As ERGMs typically involve normalizing factors that are costly to compute, practical inference relies on a…
Tensor networks are a tool first employed in the context of many-body quantum physics that now have a wide range of uses across the computational sciences, from numerical methods to machine learning. Methods integrating tensor networks into…
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…
This paper describes an expectation propagation (EP) method for multi-class classification with Gaussian processes that scales well to very large datasets. In such a method the estimate of the log-marginal-likelihood involves a sum across…
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…
The exponential family of random graphs represents an important and challenging class of network models. Despite their flexibility, conventionally used exponential random graphs have one shortcoming. They cannot directly model weighted…
We consider probabilistic multinomial probit classification using Gaussian process (GP) priors. The challenges with the multiclass GP classification are the integration over the non-Gaussian posterior distribution, and the increase of the…
The paper demonstrates the use of LASSO-based estimation in network models. Taking the Exponential Random Graph Model (ERGM) as a flexible and widely used model for network data analysis, the paper focuses on the question of how to specify…
Until recently obtaining data on populations of networks was typically rare. However, with the advancement of automatic monitoring devices and the growing social and scientific interest in networks, such data has become more widely…
Bayesian inference of Gibbs random fields (GRFs) is often referred to as a doubly intractable problem, since the likelihood function is intractable. The exploration of the posterior distribution of such models is typically carried out with…
High-dimensional networks play a key role in understanding complex relationships. These relationships are often dynamic in nature and can change with multiple external factors (e.g., time and groups). Methods for estimating graphical models…
Machine learning provides algorithms that can learn from data and make inferences or predictions on data. Bayesian networks are a class of graphical models that allow to represent a collection of random variables and their condititional…
Gaussian graphical model is one of the powerful tools to analyze conditional independence between two variables for multivariate Gaussian-distributed observations. When the dimension of data is moderate or high, penalized likelihood methods…
Gaussian graphical models are useful tools for conditional independence structure inference of multivariate random variables. Unfortunately, Bayesian inference of latent graph structures is challenging due to exponential growth of…
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…
We consider the problem of estimating multiple related but distinct graphical models on the basis of a high-dimensional data set with observations that belong to distinct classes. A motivating example occurs in the analysis of gene…
Node features and structural information of a graph are both crucial for semi-supervised node classification problems. A variety of graph neural network (GNN) based approaches have been proposed to tackle these problems, which typically…
Knowledge graph reasoning, which aims at predicting the missing facts through reasoning with the observed facts, is critical to many applications. Such a problem has been widely explored by traditional logic rule-based approaches and recent…
We present a technique to characterize differentially expressed genes in terms of their position in a high-dimensional co-expression network. The set-up of Gaussian graphical models is used to construct representations of the co-expression…