Asymptotic Information-Theoretic Detection of Dynamical Organization in Complex Systems.

The identification of emergent structures in complex dynamical systems is a formidable challenge. We propose a computationally efficient methodology to address such a challenge, based on modeling the state of the system as a set of random variables. Specifically, we present a sieving algorithm to navigate the huge space of all subsets of variables and compare them in terms of a simple index that can be computed without resorting to simulations. We obtain such a simple index by studying the asymptotic distribution of an information-theoretic measure of coordination among variables, when there is no coordination at all, which allows us to fairly compare subsets of variables having different cardinalities. We show that increasing the number of observations allows the identification of larger and larger subsets. As an example of relevant application, we make use of a paradigmatic case regarding the identification of groups in autocatalytic sets of reactions, a chemical situation related to the origin of life problem.

Bayesian learning of multiple directed networks from observational data.

Graphical modeling represents an established methodology for identifying complex dependencies in biological networks, as exemplified in the study of co-expression, gene regulatory, and protein interaction networks. The available observations often exhibit an intrinsic heterogeneity, which impacts on the network structure through the modification of specific pathways for distinct groups, such as disease subtypes. We propose to infer the resulting multiple graphs jointly in order to benefit from potential similarities across groups; on the other hand our modeling framework is able to accommodate group idiosyncrasies. We consider directed acyclic graphs (DAGs) as network structures, and develop a Bayesian method for structural learning of multiple DAGs. We explicitly account for Markov equivalence of DAGs, and propose a suitable prior on the collection of graph spaces that induces selective borrowing strength across groups. The resulting inference allows in particular to compute the posterior probability of edge inclusion, a useful summary for representing flow directions within the network. Finally, we detail a simulation study addressing the comparative performance of our method, and present an analysis of two protein networks together with a substantive interpretation of our findings.

Objective Bayesian search of Gaussian directed acyclic graphical models for ordered variables with non-local priors.

Directed acyclic graphical (DAG) models are increasingly employed in the study of physical and biological systems to model direct influences between variables. Identifying the graph from data is a challenging endeavor, which can be more reasonably tackled if the variables are assumed to satisfy a given ordering; in this case we simply have to estimate the presence or absence of each potential edge. Working under this assumption, we propose an objective Bayesian method for searching the space of Gaussian DAG models, which provides a rich output from minimal input. We base our analysis on non-local parameter priors, which are especially suited for learning sparse graphs, because they allow a faster learning rate, relative to ordinary local parameter priors, when the true unknown sampling distribution belongs to a simple model. We implement an efficient stochastic search algorithm, which deals effectively with data sets having sample size smaller than the number of variables, and apply our method to a variety of simulated and real data sets. Our approach compares favorably, in terms of the ROC curve for edge hit rate versus false alarm rate, to current state-of-the-art frequentist methods relying on the assumption of ordered variables; under this assumption it exhibits a competitive advantage over the PC-algorithm, which can be considered as a frequentist benchmark for unordered variables. Importantly, we find that our method is still at an advantage for learning the skeleton of the DAG, when the ordering of the variables is only moderately mis-specified. Prospectively, our method could be coupled with a strategy to learn the order of the variables, thus dropping the known ordering assumption.