  We propose a data-driven approach to represent neuronal network dynamics as a
Probabilistic Graphical Model (PGM). Our approach learns the PGM structure by
employing dimension reduction to network response dynamics evoked by stimuli
applied to each neuron separately. The outcome model captures how stimuli
propagate through the network and thus represents functional dependencies
between neurons, i.e., functional connectome. The benefit of using a PGM as the
functional connectome is that posterior inference can be done efficiently and
circumvent the complexities in direct inference of response pathways in dynamic
neuronal networks. In particular, posterior inference reveals the relations
between known stimuli and downstream neurons or allows to query which stimuli
are associated with downstream neurons. For validation and as an example for
our approach we apply our methodology to a model of Caenorhabiditis elegans
nervous system which structure and dynamics are well-studied. From its
dynamical model we collect time series of the network response and use singular
value decomposition to obtain a low-dimensional projection of the time series
data. We then extract dominant patterns in each data matrix to get pairwise
dependency information and create a graphical model for the full somatic
nervous system. The PGM enables us to obtain and verify underlying neuronal
pathways dominant for known behavioral scenarios and to detect possible
pathways for novel scenarios.
