Inferring Causation from Correlation in Sparse Networks

We discuss the applicability of a recently proposed method to reconstruct cerebral network structure (Pernice and Rotter, 2013) on the data supplied in the Neural Connectomics Challenge. This method is based on a model of linear dynamics which provides a relation between activity covariances and the underlying network. Even for very limited sampling resolution, an estimate of the directed connections can be obtained under the assumption of sparse connectivity, if indirect connections contribute significantly to the covariance matrix. Surprisingly, and possibly due to the low importance of indirect connections in the provided data, the sparsest estimator resulted in only limited performance. Our best estimation relies on the inverse covariance matrix which has been adapted based on insights gained from the model.