  Gene regulatory networks play a crucial role in controlling an organism's
biological processes, which is why there is significant interest in developing
computational methods that are able to extract their structure from
high-throughput genetic data. A typical approach consists of a series of
conditional independence tests on the covariance structure meant to
progressively reduce the space of possible causal models. We propose a novel
efficient Bayesian method for discovering the local causal relationships among
triplets of (normally distributed) variables. In our approach, we score the
patterns in the covariance matrix in one go and we incorporate the available
background knowledge in the form of priors over causal structures. Our method
is flexible in the sense that it allows for different types of causal
structures and assumptions. We apply the approach to the task of inferring gene
regulatory networks by learning regulatory relationships between gene
expression levels. We show that our algorithm produces stable and conservative
posterior probability estimates over local causal structures that can be used
to derive an honest ranking of the most meaningful regulatory relationships. We
demonstrate the stability and efficacy of our method both on simulated data and
on real-world data from an experiment on yeast.
