Combining neural computation and genetic programming for observational causality detection and causal modelling

A methodology, to determine the causal relations between time series and to derive the set of equations describing the interacting systems, has been developed. The techniques proposed are completely data driven and they are based on ensembles of Time Delay Neural Networks (TDNNs) and Symbolic Regression (SR) via Genetic Programming (GP). With regard to the detection of the causal influences and the identification of graphical causal networks, the developed tools have better performances than those reported in the literature. For example, the TDNN ensembles can cope with evolving systems, non-Markovianity, feedback loops and multicausality. In its turn, on the basis of the information derived from the TDNN ensembles, SR via GP permits to identify the set of equations, i.e. the detailed model of the interacting systems. Numerical tests and real life examples from various disciplines prove the power and versatility of the developed tools, capable of handling tens of time series and even images. The excellent results obtained emphasize the importance of recording the time evolution of signals, which would allow a much better understanding of many issues, ranging from the physical to the social and medical sciences.