Related papers: Probability distributions with summary graph struc…

Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact…

We consider data structures for graphs where we maintain a subset of the nodes called sites, and allow proximity queries, such as asking for the closest site to a query node, and update operations that enable or disable nodes as sites. We…

In real world domains, most graphs naturally exhibit a hierarchical structure. However, data-driven graph generation is yet to effectively capture such structures. To address this, we propose a novel approach that recursively generates…

We study combinatorial structures arising from finite-time transition probabilities of the Totally Asymmetric Simple Exclusion Process with open boundary conditions. While much of the existing combinatorial theory regarding the TASEP…

Graphical network inference is used in many fields such as genomics or ecology to infer the conditional independence structure between variables, from measurements of gene expression or species abundances for instance. In many practical…

Sampling algorithms, hypergraph degree sequences, and polytopes play a crucial role in statistical analysis of network data. This article offers a brief overview of open problems in this area of discrete mathematics from the point of view…

A variety of statistical graphical models have been defined to represent the conditional independences underlying a random vector of interest. Similarly, many different graphs embedding various types of preferential independences, as for…

Any network studied in the literature is inevitably just a sampled representative of its real-world analogue. Additionally, network sampling is lately often applied to large networks to allow for their faster and more efficient analysis.…

In a random graph, counts for the number of vertices with given degrees will typically be dependent. We show via a multivariate normal and a Poisson process approximation that, for graphs which have independent edges, with a possibly…

Confining an answer to the question whether and how the coherent operation of network elements is determined by the the network structure is the topic of our work. We map the structure of signal flow in directed networks by analysing the…

The local Markov condition for a DAG to be an independence map of a probability distribution is well known. For DAGs with latent variables, represented as bi-directed edges in the graph, the local Markov property may invoke exponential…

Separation systems are posets with additional structure that form an abstract setting in which tangle-like clusters in graphs, matroids and other combinatorial structures can be expressed and studied. This paper offers some basic theory…

In recent years, there have been intense research efforts to develop efficient methods for probabilistic inference in probabilistic influence diagrams or belief networks. Many people have concluded that the best methods are those based on…

We construct and analyze a random graph model for discrete choice with social interaction and several groups of equal size. We concentrate on the case of two groups of equal sizes and we allow the interaction strength within a group to…

Suppose we are given the conditional probability of one variable given some other variables.Normally the full joint distribution over the conditioning variablesis required to determine the probability of the conditioned variable.Under what…

There are hierarchical characteristics in the network and how to effectively reveal the hierarchical characteristics in the network is a problem in the research of network structure. If a node is assigned to the community to which it…

Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of…

Graph transformations definable in logic can be described using the notion of transductions. By understanding transductions as a basic embedding mechanism, which captures the possibility of encoding one graph in another graph by means of…

Statisticians and quantitative neuroscientists have actively promoted the use of independence relationships for investigating brain networks, genomic networks, and other measurement technologies. Estimation of these graphs depends on two…

Probabilistic graphical models provide a powerful tool to describe complex statistical structure, with many real-world applications in science and engineering from controlling robotic arms to understanding neuronal computations. A major…