Causal inference in biomolecular pathways using a Bayesian network approach and an Implicit method.

We introduce here the concept of Implicit networks which provide, like Bayesian networks, a graphical modelling framework that encodes the joint probability distribution for a set of random variables within a directed acyclic graph. We show that Implicit networks, when used in conjunction with appropriate statistical techniques, are very attractive for their ability to understand and analyze biological data. Particularly, we consider here the use of Implicit networks for causal inference in biomolecular pathways. In such pathways, an Implicit network encodes dependencies among variables (proteins, genes), can be trained to learn causal relationships (regulation, interaction) between them and then used to predict the biological response given the status of some key proteins or genes in the network. We show that Implicit networks offer efficient methodologies for learning from observations without prior knowledge and thus provide a good alternative to classical inference in Bayesian networks when priors are missing. We illustrate our approach by an application to simulated data for a simplified signal transduction pathway of the epidermal growth factor receptor (EGFR) protein.