Minimax entropy: The statistical physics of optimal models

When constructing models of the world, one would like to uncover a small set of features that explain a wide range of behaviors. The maximum entropy principle provides the unique mapping from features to behaviors, yet it does not tell us which features to include in a model. Here we show that, counterintuitively, the optimal features are the ones that produce the maximum entropy model with minimum entropy. The resulting “minimax entropy” principle provides a link from statistical physics to optimal descriptions of complex systems. We apply this principle to understand the emergence of collective neural activity across scales, from networks of neurons to whole-brain activity in humans.