  Large interacting systems in biology often exhibit emergent dynamics, such as
coexistence of multiple time scales, manifested by fat tails in the
distribution of waiting times. While existing tools in statistical inference,
such as maximum entropy models, reproduce the empirical steady state
distributions, it remains challenging to learn dynamical models. We present a
novel inference method, called generalized Glauber dynamics. Constructed
through a non-Markovian fluctuation dissipation theorem, generalized Glauber
dynamics tunes the dynamics of an interacting system, while keeping the steady
state distribution fixed. We motivate the need for the method on real data from
Eco-HAB, an automated habitat for testing behavior in groups of mice under
semi-naturalistic conditions, and present it on simple Ising spin systems. We
show its applicability for experimental data, by inferring dynamical models of
social interactions in a group of mice that reproduce both its collective
behavior and the long tails observed in individual dynamics.
