Causality Networks

While correlation measures are used to discern statistical relationships between observed variables in almost all branches of data-driven scientific inquiry, what we are really interested in is the existence of causal dependence. Designing an efficient causality test, that may be carried out in the absence of restrictive pre-suppositions on the underlying dynamical structure of the data at hand, is non-trivial. Nevertheless, ability to computationally infer statistical prima facie evidence of causal dependence may yield a far more discriminative tool for data analysis compared to the calculation of simple correlations. In the present work, we present a new non-parametric test of Granger causality for quantized or symbolic data streams generated by ergodic stationary sources. In contrast to state-of-art binary tests, our approach makes precise and computes the degree of causal dependence between data streams, without making any restrictive assumptions, linearity or otherwise. Additionally, without any a priori imposition of specific dynamical structure, we infer explicit generative models of causal cross-dependence, which may be then used for prediction. These explicit models are represented as generalized probabilistic automata, referred to crossed automata, and are shown to be sufficient to capture a fairly general class of causal dependence. The proposed algorithms are computationally efficient in the PAC sense; $i.e.$, we find good models of cross-dependence with high probability, with polynomial run-times and sample complexities. The theoretical results are applied to weekly search-frequency data from Google Trends API for a chosen set of socially "charged" keywords. The causality network inferred from this dataset reveals, quite expectedly, the causal importance of certain keywords. It is also illustrated that correlation analysis fails to gather such insight.