Analysis of causal interactions among neural signals using Genetic Programming

Human brain is a complex system which involves generation and processing of various signals that govern emotional and physical functions of the body. These signals can be recorded using techniques such as electroencephalogram (EEG) and functional magnetic resonance imaging   (fMRI) and converted to time series data. Synchronization and correlation methods are generally used to analyze and interpret these signals and obtain the underlying connectivity network however; such connections lack directions. In order to investigate the direction of interrelations, rigorous research efforts in neuroinformatics have identified application of phenomenon of causality for analyzing the neural signals. The central idea for applying causality between two signals is to improve chances of predicting a particular signal by incorporating the information obtained from the processing of the preceding signals. Methodologies such as auto-regressive modeling and Granger causality (GC) have shown promising results in determining the causal interactions in EEG and fMRI data sets.

The knowledge obtained, in form of multivariate auto-regressive (MAR) models can help in inferring the interactions among the various neural signals processed within the human brain. We propose a genetic programming based methodology which can be applied to detect the causal interactions among various dynamic neural signals. Our proposed genetic programming based causality detection (GPCD) methodology blends the evolutionary computation based procedures with the parameter estimation methods to develop a final MAR model of the system. We have tested the proposed methodology on various simulated and experimental data sets. These data sets have been obtained by either simulating the causality based models available in literature or have been kindly provided by the authors of available publications on request. A comparison of the results obtained so far has indicated that the GPCD methodology outperforms the GC findings, mainly in terms of detecting non-linear interactions. Further, GP is promising for it is able to capture the causal interactions that are otherwise overlooked using GC. Moreover, even though GP may also exhibit some latent and false causal interactions like any other method, the frequency of such predictions made using GP is lesser as compared to that with GC.

Keywords: Genetic programming, Granger causality, Multivariate autoregressive models, Causality, neuroinformatics.