  We consider the problem of joint modelling of metabolic signals and gene
expression in systems biology applications. We propose an approach based on
input-output factorial hidden Markov models and propose a structured
variational inference approach to infer the structure and states of the model.
We start from the classical free form structured variational mean field
approach and use a expectation propagation to approximate the expectations
needed in the variational loop. We show that this corresponds to a factored
expectation constrained approximate inference. We validate our model through
extensive simulations and demonstrate its applicability on a real world
bacterial data set.
