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The objective of this paper is to study the characteristics (geometric and otherwise) of very large attribute based undirected networks. Real-world networks are often very large and fast evolving. Their analysis and understanding present a…
Link prediction is a key problem for network-structured data, attracting considerable research efforts owing to its diverse applications. The current link prediction methods focus on general networks and are overly dependent on either the…
Record is used to reduce the time and cost of running experiments (Doostparast and Balakrishnan, 2010). It is important to check the adequacy of models upon which inferences or actions are based (Lawless, 2003, Chapter 10, p. 465). In the…
The problem of graphical model selection is to correctly estimate the graph structure of a Markov random field given samples from the underlying distribution. We analyze the information-theoretic limitations of the problem of graph…
We consider two division models for structured cell populations, where cells can grow, age and divide. These models have been introduced in the literature under the denomination of `mitosis' and `adder' models. In the recent years, there…
Effective information analysis generally boils down to properly identifying the structure or geometry of the data, which is often represented by a graph. In some applications, this structure may be partly determined by design constraints or…
Log-linear models are a family of probability distributions which capture relationships between variables. They have been proven useful in a wide variety of fields such as epidemiology, economics and sociology. The interest in using these…
Directed acyclic graphs (DAGs) are commonly used to represent causal relationships among random variables in graphical models. Applications of these models arise in the study of physical, as well as biological systems, where directed edges…
What kind of macroscopic structural and dynamical patterns can we observe in real-world hypergraphs? What can be underlying local dynamics on individuals, which ultimately lead to the observed patterns, beyond apparently random evolution?…
Social media platforms generate vast, complex graph-structured data, facilitating diverse tasks such as rumor detection, bot identification, and influence modeling. Real-world applications like public opinion monitoring and stock trading --…
Graph Neural Networks (GNNs) have excelled in predicting graph properties in various applications ranging from identifying trends in social networks to drug discovery and malware detection. With the abundance of new architectures and…
We consider the goodness of fit testing problem for linear stochastic differential equation (Ornstein-Uhlenbeck process). The basic hypothesis is supposed to be composite with two-dimensional unknown parameter. We study two goodness of fit…
Undirected probabilistic graphical models represent the conditional dependencies, or Markov properties, of a collection of random variables. Knowing the sparsity of such a graphical model is valuable for modeling multivariate distributions…
Latent position models are widely used for the analysis of networks in a variety of research fields. In fact, these models possess a number of desirable theoretical properties, and are particularly easy to interpret. However, statistical…
We propose an empirical likelihood test that is able to test the goodness of fit of a class of parametric and semi-parametric multiresponse regression models. The class includes as special cases fully parametric models; semi-parametric…
Being cognizant of the abundance of multi-body interactions in various complex systems, here we investigate a possible way to incorporate multi-body interactions in dynamical networks. Adopting hypergraph as the underlying architecture aids…
Recently, there has been a growing interest in the problem of learning rich implicit models - those from which we can sample, but can not evaluate their density. These models apply some parametric function, such as a deep network, to a base…
Understanding the data-generating process is essential for building machine learning models that generalise well while ensuring robustness and interpretability. This paper addresses the fundamental challenge of modelling the data generation…
We propose and study a general method for construction of consistent statistical tests on the basis of possibly indirect, corrupted, or partially available observations. The class of tests devised in the paper contains Neyman's smooth…
We propose an extension of the Contextual Graph Markov Model, a deep and probabilistic machine learning model for graphs, to model the distribution of edge features. Our approach is architectural, as we introduce an additional Bayesian…