  The inference of causal relationships using observational data from partially
observed multivariate systems with hidden variables is a fundamental question
in many scientific domains. Methods extracting causal information from
conditional independencies between variables of a system are common tools for
this purpose, but are limited in the lack of independencies. To surmount this
limitation, we capitalize on the fact that the laws governing the generative
mechanisms of a system often result in substructures embodied in the generative
functional equation of a variable, which act as sufficient statistics for the
influence that other variables have on it. These functional sufficient
statistics constitute intermediate hidden variables providing new conditional
independencies to be tested. We propose to use the Information Bottleneck
method, a technique commonly applied for dimensionality reduction, to find
underlying sufficient sets of statistics. Using these statistics we formulate
new additional rules of causal orientation that provide causal information not
obtainable from standard structure learning algorithms, which exploit only
conditional independencies between observable variables. We validate the use of
sufficient statistics for structure learning both with simulated systems built
to contain specific sufficient statistics and with benchmark data from
regulatory rules previously and independently proposed to model biological
signal transduction networks.
