  Studying neural connectivity is considered one of the most promising and
challenging areas of modern neuroscience. The underpinnings of cognition are
hidden in the way neurons interact with each other. However, our experimental
methods of studying real neural connections at a microscopic level are still
arduous and costly. An efficient alternative is to infer connectivity based on
the neuronal activations using computational methods. A reliable method for
network inference, would not only facilitate research of neural circuits
without the need of laborious experiments but also reveal insights on the
underlying mechanisms of the brain. In this work, we perform a review of
methods for neural circuit inference given the activation time series of the
neural population. Approaching it from machine learning perspective, we divide
the methodologies into unsupervised and supervised learning. The methods are
based on correlation metrics, probabilistic point processes, and neural
networks. Furthermore, we add a data mining methodology inspired by influence
estimation in social networks as a new supervised learning approach. For
comparison, we use the small version of the Chalearn Connectomics competition,
that is accompanied with ground truth connections between neurons. The
experiments indicate that unsupervised learning methods perform better,
however, supervised methods could surpass them given enough data and resources.
