Full-stack inference of low-dimensional effective models

Key to understanding the dynamics of large neural populations is the use of low-dimensional models, which must attempt to capture a rich variety of observed behaviors while maintaining interpretability and analytical tractability. One approach is to keep a simple functional form, but adjust its parameters to capture the effect of neglected interactions. We are interested in finding good such effective parameters for population models of interacting neurons, which cannot feasibly be derived from a more detailed theory.

We have previously shown (René 2020) that dozens of effective parameters can be simultaneously inferred by maximizing their likelihood, assuming that inputs to the system can be accurately observed. This assumption however is far beyond the current capabilities of neuroscience experiments. In the present work, we recover both model parameters and input sequences from noisy observations of a Wilson-Cowan model driven by unobserved stochastic inputs. The model is placed near a bifurcation, reproducing conditions that were previously used to study the onset of epileptic seizures. In particular, we find that bifurcation analysis can be performed on either recovered or true parameters with similar results.