Minimax entropy models for human whole-brain activity

In the human brain, cognitive functions like sensing, planning, and decision-making emerge from intricate networks of correlations between brain regions. Yet it remains unclear which correlations are most important for explaining the patterns of whole-brain activity measured in experiments. In general, the most important correlations, which provide the best description of the system, are the ones that produce the maximum entropy model with minimum entropy. Here we apply this "minimax entropy" principle to study whole-brain activity in humans, measured using functional magnetic resonance imaging (fMRI) during rest and several cognitive tasks. Given a set of covariances—which can be visualized as a network linking different brain regions—we construct maximum entropy models, which are equivalent to multi-variate Gaussians. We then develop an optimization algorithm for identifying the most important covariances—that is, the optimal whole-brain network. We compare the structure of these optimal networks to the underlying physical connectivity between brain regions. We also examine how the optimal networks vary across individuals and tasks. Generally, we discover that the vast majority of information in whole-brain activity—defined precisely using information theory—is explained by only a sparse network of the covariances between brain regions.