The inverse problem for neuronal networks is to infer its topology from analyzing its dynamics. Recently, transfer entropy[1], an information theoretical measure of directed interactions has become more popular for solving the inverse problem[2]. Due to its model-free nature, it can easily be applied to data in a variety of fields such as neuroscience, physiology, climate research and financial markets. However, transfer entropy, being interpreted as predictive information transfer does not distinguish among different types of interaction, such as positive and negative. By using transfer entropy to analyze the time series of extensive neuronal network simulations with excitatory and inhibitory synapses, not only are we able to reconstruct correctly the motif topologies from its neuronal dynamics, we are also able to classify the type of interaction by performing a principal component analysis on the individual terms of transfer entropy. 

[1] Schreiber, Thomas. “Measuring Information Transfer.” Physical Review Letters 85, no. 2 (2000): 461.
[2] Wibral, Michael, Raul Vicente, and Joseph T Lizier. “Directed Information Measures in Neuroscience”(2014)