Related papers: Weighted dependency graphs
Directed acyclic graphs provide a fundamental tool for representing directed dependence structures in multivariate network data, and are widely used to model financial and economic networks. However, accurate and interpretable estimation…
We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables. These constructions will generalize, strengthen and unify previous notions of…
Global variational approximation methods in graphical models allow efficient approximate inference of complex posterior distributions by using a simpler model. The choice of the approximating model determines a tradeoff between the…
In this paper, we hope to bring closer graph theory and consensus algorithms. Firstly, we give a brief introduction to graph theory by listing a concise definition. Then we analyze and visualize some commonly used graphs. Secondly, we…
A crucial assumption in most statistical learning theory is that samples are independently and identically distributed (i.i.d.). However, for many real applications, the i.i.d. assumption does not hold. We consider learning problems in…
An $n$-vertex graph $G$ of edge density $p$ is considered to be quasirandom if it shares several important properties with the random graph $G(n,p)$. A well-known theorem of Chung, Graham and Wilson states that many such `typical'…
We introduce a directed, weighted random graph model, where the edge-weights are independent and beta-distributed with parameters depending on their endpoints. We will show that the row- and column-sums of the transformed edge-weight matrix…
Dependency networks (Heckerman et al., 2000) are potential probabilistic graphical models for systems comprising a large number of variables. Like Bayesian networks, the structure of a dependency network is represented by a directed graph,…
The assumption that data samples are independent and identically distributed (iid) is standard in many areas of statistics and machine learning. Nevertheless, in some settings, such as social networks, infectious disease modeling, and…
Real-world complex systems are often modelled by sets of equations with endogenous and exogenous variables. What can we say about the causal and probabilistic aspects of variables that appear in these equations without explicitly solving…
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…
An important problem in network analysis is predicting a node attribute using both network covariates, such as graph embedding coordinates or local subgraph counts, and conventional node covariates, such as demographic characteristics.…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
The purpose of this article is to present a general method to find limiting laws for some renormalized statistics on random permutations. The model considered here is Ewens sampling model, which generalizes uniform random permutations. We…
We develop further the graph limit theory for dense weighted graph sequences. In particular, we consider probability graphons, which have recently appeared in graph limit theory as continuum representations of weighted graphs, and we…
This paper revisits the classical concept of network modularity and its spectral relaxations used throughout graph data analysis. We formulate and study several modularity statistic variants for which we establish asymptotic distributional…
We consider situations where data have been collected such that the sampling depends on the outcome of interest and possibly further covariates, as for instance in case-control studies. Graphical models represent assumptions about the…
Gaussian graphical models represent the backbone of the statistical toolbox for analyzing continuous multivariate systems. However, due to the intrinsic properties of the multivariate normal distribution, use of this model family may hide…
Assessing the statistical significance of network patterns is crucial for understanding whether such patterns indicate the presence of interesting network phenomena, or whether they simply result from less interesting processes, such as…
Random intersection graphs have received much attention recently and been used in a wide range of applications ranging from key predistribution in wireless sensor networks to modeling social networks. For these graphs, each node is equipped…