Multivariate autoregressive model estimation for high-dimensional intracranial electrophysiological data

Abstract

Fundamental to elucidating the functional organization of the brain is the assessment of causal interactions between different brain regions. Multivariate autoregressive (MVAR) modeling techniques applied to multisite electrophysiological recordings are a promising avenue for identifying such causal links. They estimate the degree to which past activity in one or more brain regions is predictive of another region's present activity, while simultaneously accounting for the mediating effects of other regions. Including as many mediating variables as possible in the model has the benefit of drastically reducing the odds of detecting spurious causal connectivity. However, effective bounds on the number of MVAR model coefficients that can be estimated reliably from limited data make exploiting the potential of MVAR models challenging for even modest numbers of recording sites. Here, we utilize well-established dimensionality-reduction techniques to fit MVAR models to human intracranial data from ∼100 – 200 recording sites spanning dozens of anatomically and functionally distinct cortical regions. First, we show that high-dimensional MVAR models can be successfully estimated from long segments of data and yield plausible connectivity profiles. Next, we use these models to generate synthetic data with known ground-truth connectivity to explore the utility of applying principal component analysis and group least absolute shrinkage and selection operator (gLASSO) to reduce the number of parameters (connections) during model fitting to shorter data segments. We show that gLASSO is highly effective for recovering ground-truth connectivity in the limited data regime, capturing important features of connectivity for high-dimensional models with as little as 10 seconds of data. The methods presented here have broad applicability to the analysis of high-dimensional time series data in neuroscience, facilitating the elucidation of the neural basis of sensation, cognition, and arousal.