Inferring minimax entropy models from neural responses to natural movies

Novel experimental techniques allow us to simultaneously record the response of hundreds of neurons to visual stimuli over timescales as long as days. Maximum entropy models provide a promising means of quantifying these responses over time by finding a parametrized maximum entropy distribution that reproduces a set of desired observables; however, as neuronal population size increases, we lack an adequate number of samples to dependably infer all parameters of these models. If we limit our search to maximum entropy models with at most K constraints, the “minimax entropy” principle dictates that we should choose the one with the lowest possible entropy. Thus, to remedy the issue of under-sampling, we consider a subset of minimax entropy models that are analytically tractable and constrain only a tree-like network of maximally informative pairwise correlations between neurons. Here, we employ this method to analyze recordings from large populations of neurons in the retina and visual cortex of vertebrates presented with natural movies over several sessions, and find that the model reliably captures many features of collective firing behavior that were not fed in as explicit constraints on the model. We show that within both the retina and other areas of the visual cortex, the maximally informative tree is composed primarily of strong, positive interactions. We compare these tree-like networks of interactions across scenes and observe conserved network structure across many repeats of time-varying naturalistic stimuli despite large changes in stimulus-dependent activity in individual cells. In addition, we discuss tractable analytical corrections to the tree-like model to account for weak and negative background pairwise interactions which do not appear in the original tree of maximally informative correlations.