This paper proposes a framework which unifies graphical model theory and formal language theory through automata theory. Specifically, we propose Bayesian Network Automata (BNAs) as a formal framework for specifying graphical models of arbitrarily large structures, or equivalently, specifying probabilistic grammars in terms of graphical models. BNAs use a formal automaton to specify how to cons...

Two Bayesian-network structures are said to be equivalent if the set of distributions that can be represented with one of those structures is identical to the set of distributions that can be represented with the other. Many scoring criteria that are used to learn Bayesiannetwork structures from data are score equivalent; that is, these criteria do not distinguish among networks that are equiva...

We propose a measure for assessing the degree of influence of a set of edges of a Bayesian network on the overall fitness of the network, starting with probability distributions extracted from a data set. Standard fitness measures such as the Cooper-Herskowitz score or the score based on the minimum description length are computationally expensive and do not focus on local modifications of netw...

We describe, axiomatize, and implement, a new method for identifying community structures (groups of structurally equivalent nodes) from network data. The method is based on maximum likelihood estimation, a standard statistical tool. μ Copiμc and Jackson are at the Division of the Humanities and Social Sciences, California Institute of Technology, Pasadena, California 91125, USA, emails: jackso...

We present a new method for articulating scale-dependent topological descriptions of the network structure inherent in many complex systems. The technique is based on “Partition Decoupled Null Models,” a new class of null models that incorporate the interaction of clustered partitions into a random model and generalize the Gaussian ensemble. As an application we analyze a correlation matrix der...

Modern-day computers are characterized by a striking contrast between the processing power of the CPU and the latency of main memory accesses. If the data processed is both large compared to processor caches and sparse or high-dimensional in nature, as is commonly the case in complex network research, the main memory latency can become a performace bottleneck. In this Article, we present a cach...

Bayesian networks (BN) are a family of probabilistic graphical models representing a joint distribution for a set of random variables. Conditional dependencies between these variables are symbolized by a Directed Acyclic Graph (DAG). Two classical approaches are often encountered when automaticaly determining an appropriate graphical structure from a database of cases,. The first one consists i...

Traditionally, protein structures have been analysed by the secondary structure architecture and fold arrangement. An alternative approach that has shown promise is modelling proteins as a network of non-covalent interactions between amino acid residues. The network representation of proteins provide a systems approach to topological analysis of complex three-dimensional structures irrespective...

We propose a method for uncovering the structure of the adopters' network underlying the diffusion process, based on penetration data alone. By uncovering the traces that this network leaves on the dissemination process, the degree distribution of the network can be estimated. We show that the network's degree distribution has a significant effect on the contagion properties. Ignoring the netwo...