Related papers: On the Existence of the MLE for a Directed Random …
The p_1 model is a directed random graph model used to describe dyadic interactions in a social network in terms of effects due to differential attraction (popularity) and expansiveness, as well as an additional effect due to reciprocation.…
Social networks and other large sparse data sets pose significant challenges for statistical inference, as many standard statistical methods for testing model fit are not applicable in such settings. Algebraic statistics offers a…
Networks are often characterized by node heterogeneity for which nodes exhibit different degrees of interaction and link homophily for which nodes sharing common features tend to associate with each other. In this paper, we propose a new…
Maximum likelihood estimation (MLE) is a fundamental problem in statistics. Characteristics of the MLE problem for discrete algebraic statistical models are reflected in the geometry of the $\textit{likelihood correspondence}$, a variety…
We study conditional independence relationships for random networks and their interplay with exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their…
We define Gaussian graphical models on directed acyclic graphs with coloured vertices and edges, calling them RDAG (restricted directed acyclic graph) models. If two vertices or edges have the same colour, their parameters in the model must…
In the process of building (structural learning) a probabilistic graphical model from a set of observed data, the directional, cyclic dependencies between the random variables of the model are often found. Existing graphical models such as…
Data in the form of graphs, or networks, arise naturally in a number of contexts; examples include social networks and biological networks. We are often faced with the availability of multiple graphs on a single set of nodes. In this…
Ron et al (1998) introduced a rich family of models for discrete longitudinal data, called acyclic probabilistic finite automata. These may be described as context-specific graphical models, since they are represented as directed…
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…
A model for network panel data is discussed, based on the assumption that the observed data are discrete observations of a continuous-time Markov process on the space of all directed graphs on a given node set, in which changes in tie…
Biological networks are one of the most studied object in computational biology. Several methods have been developed for studying qualitative properties of biological networks. Last decade had seen the improvement of molecular techniques…
Directed acyclic graph (DAG) models, also called Bayesian networks, impose conditional independence constraints on a multivariate probability distribution, and are widely used in probabilistic reasoning, machine learning and causal…
We investigate probabilistic graphical models that allow for both cycles and latent variables. For this we introduce directed graphs with hyperedges (HEDGes), generalizing and combining both marginalized directed acyclic graphs (mDAGs) that…
Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet, and the network of followers on Twitter among many others. The challenge, however, is to create a network model that…
Designing reliable networks consists in finding topological structures, which are able to successfully carry out desired processes and operations. When this set of activities performed within a network are unknown and the only available…
We study random graph models for directed acyclic graphs, an important class of networks that includes citation networks, food webs, and feed-forward neural networks among others. We propose two specific models, roughly analogous to the…
While relations among individuals make an important part of data with scientific and business interests, existing statistical modeling of relational data has mainly been focusing on dyadic relations, i.e., those between two individuals.…
We develop a maximum-likelihood based method for regression in a setting where the dependent variable is a random graph and covariates are available on a graph-level. The model generalizes the well-known $\beta$-model for random graphs by…
Reciprocity--the tendency of individuals to form mutual ties--is a fundamental structural feature of many directed networks. Despite its ubiquity, reciprocity remains insufficiently integrated into statistical network models, particularly…