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Volume 2017, Article ID 4518429, 13 pages
Research Article

Sparse Causality Network Retrieval from Short Time Series

Tomaso Aste1,2,3 and T. Di Matteo1,2,3,4

1Department of Computer Science, UCL, London, UK
2UCL Centre for Blockchain Technologies, UCL, London, UK
3Systemic Risk Centre, London School of Economics and Political Sciences, London, UK
4Department of Mathematics, King’s College London, London, UK

Correspondence should be addressed to Tomaso Aste;

Received 25 May 2017; Accepted 6 September 2017; Published 6 November 2017

Academic Editor: Diego Garlaschelli

Copyright © 2017 Tomaso Aste and T. Di Matteo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.