Factored expectation propagation for input-output FHMM models in systems biology

The advent of high throughput technologies in biology has opened novel opportunities to investigate biological processes from a comprehensive point of view. At the same time, the noisy and high dimensional nature of these data sets gives rise to formidable statistical challenges, and has led to systems biology becoming a fertile area for machine learning applications, as well as a motivation for novel modelling methodologies. In this paper, we are interested in jointly modelling mRNA measurements (transcrip-tomics) together with metabolite measurements in order to provide a platform for understanding the chemical regulation of gene expression. From the statistical perspective, this is naturally addressed using a latent variables framework: mRNA transcription is known to be controlled by the activation state of a class of proteins, transcription factors (TFs), which mediate metabolic signals through fast conformational changes (Alon, 2006). However, due to their fast dynamic and often low concentrations, TFs are particularly difficult to assay experimentally, leading to the need for statistical inference methodologies (Asif & Sanguinetti, 2011; Shi et al., 2008). Here, we adopt a model of transcriptional regulation which is based on a binary representation of transcription factor states, a Factorial Hidden Markov Model (FHMM).