  In this paper, we conduct theoretical analyses on inferring the structure of
gene regulatory networks. Depending on the experimental method and data type,
the inference problem is classified into 20 different scenarios. For each
scenario, we discuss the problem that with enough data, under what assumptions,
what can be inferred about the structure. For scenarios that have been covered
in the literature, we provide a brief review. For scenarios that have not been
covered in literature, if the structure can be inferred, we propose new
mathematical inference methods and evaluate them on simulated data. Otherwise,
we prove that the structure cannot be inferred.
