Sparse causality network retrieval from short time series

We investigate how efficiently a known underlying sparse causality structure of a simulated multivariate linear process can be retrieved from the analysis of time series of short lengths. Causality is quantified from conditional transfer entropy and the network is constructed by retaining only the statistically validated contributions. We compare results from three methodologies: two commonly used regularization methods, Glasso and ridge, and a newly introduced technique, LoGo, based on the combination of information filtering network and graphical modelling. For these three methodologies we explore the regions of time series lengths and model-parameters where a significant fraction of true causality links is retrieved. We conclude that when time series are short, with their lengths shorter than the number of variables, sparse models are better suited to uncover true causality links with LoGo retrieving the true causality network more accurately than Glasso and ridge.