Related papers: Graphical Models and Exponential Families
Diffusion probabilistic models (DPMs), widely recognized for their potential to generate high-quality samples, tend to go unnoticed in representation learning. While recent progress has highlighted their potential for capturing visual…
Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…
We introduce a new family of network models, called hierarchical network models, that allow us to represent in an explicit manner the stochastic dependence among the dyads (random ties) of the network. In particular, each member of this…
In this paper we introduce a family of planar, modular and self-similar graphs which have small-world and scale-free properties. The main parameters of this family are comparable to those of networks associated to complex systems, and…
Markov networks and Bayesian networks are effective graphic representations of the dependencies embedded in probabilistic models. It is well known that independencies captured by Markov networks (called graph-isomorphs) have a finite…
Graphical models can represent a multivariate distribution in a convenient and accessible form as a graph. Causal models can be viewed as a special class of graphical models that not only represent the distribution of the observed system…
The growing availability of network data and of scientific interest in distributed systems has led to the rapid development of statistical models of network structure. Typically, however, these are models for the entire network, while the…
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 representation learning is a fundamental problem for modeling relational data and benefits a number of downstream applications. Traditional Bayesian-based graph models and recent deep learning based GNN either suffer from…
In this work, we consider an extension of graphical models to random graphs, trees, and other objects. To do this, many fundamental concepts for multivariate random variables (e.g., marginal variables, Gibbs distribution, Markov properties)…
We consider the problem of estimating the parameters in a pairwise graphical model in which the distribution of each node, conditioned on the others, may have a different parametric form. In particular, we assume that each node's…
Auto-encoders are perhaps the best-known non-probabilistic methods for representation learning. They are conceptually simple and easy to train. Recent theoretical work has shed light on their ability to capture manifold structure, and drawn…
We study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological…
Bayesian causal discovery offers the power to quantify epistemic uncertainties among a broad range of structurally diverse causal theories potentially explaining the data, represented in forms of directed acyclic graphs (DAGs). However,…
Strong external difference families (SEDFs) have applications to cryptography and are rich combinatorial structures in their own right; until now, all SEDFs have been in abelian groups. In this paper, we consider SEDFs in both abelian and…
Chain Event Graphs (CEGs) are a widely applicable class of probabilistic graphical model that can represent context-specific independence statements and asymmetric unfoldings of events in an easily interpretable way. Existing model…
Motivated by modern applications in which one constructs graphical models based on a very large number of features, this paper introduces a new class of cluster-based graphical models, in which variable clustering is applied as an initial…
Semi-implicit graph variational auto-encoder (SIG-VAE) is proposed to expand the flexibility of variational graph auto-encoders (VGAE) to model graph data. SIG-VAE employs a hierarchical variational framework to enable neighboring node…
We investigate a generic problem of learning pairwise exponential family graphical models with pairwise sufficient statistics defined by a global mapping function, e.g., Mercer kernels. This subclass of pairwise graphical models allow us to…
We consider core-periphery structured graphs, which are graphs with a group of densely and sparsely connected nodes, respectively, referred to as core and periphery nodes. The so-called core score of a node is related to the likelihood of…