Study of brain connectivity is important for characterizing the brain, its working and its various diseases. In general, brain connectivity analysis can be of three types: structural, functional and effective. Structural connectivity involves the study of anatomical links between brain regions while functional and effective connectivity analyses involve the study of statistical dependencies and causal influences respectively, arising due to the neural activity in these regions. While structural connectivity has been studied from the very beginning of neuroscience, recently functional and effective connectivity have become important with the realization that information processing and information flow between brain regions may play an important role in the functioning of the brain. Since neuronal signals are complex and corrupted with multiple artefacts and interferences, robust methods for connectivity inference need to be developed and appropriately applied to signals originating at different scales. I will discuss some novel methods that we have formulated to ensure robust and model-free estimation of functional and effective connectivities in different scenarios. Compression-complexity causality, a causal discovery method developed by us, has been shown to perform well for short-term stationary signals, as well as signals suffering from low temporal resolution and filtering artefacts. We apply this method to infer causal interactions between brain regions of macaques in awake and anaesthesia states using electrocorticography recordings. The aim of this study was to quantify changes in causal connectivity occurring as a result of changes in the degree of consciousness associated with different brain states. Another technique based on Granger Causality was designed in order to study interactions between neuronal spike trains and applied to recordings from the prefrontal cortex of rats. This novel technique was required as sparsity of neuronal spike trains limits the applicability of usual methods of causal discovery. Finally, I will describe a method called Weighted Imaginary Coherence that helps to eliminate spurious connectivity often observed due to conductivity effects that are common in electroencephalography recordings. We employ this method to infer changes in connectivity of depression patients undergoing antidepressant treatment with an aim to predict their response to the treatment at an early stage.
Biomedical (in particular, neural) signal processing and data analysis require resilient and rigorous tools for diagnostic and therapeutic purposes. I will discuss my future research plans of bringing in ideas from nonlinear dynamics, information theory, time-series analysis and machine learning to develop such tools