Spontaneous activity emerging from an inferred network model captures complex spatio-temporal dynamics of spike data

The combination of new recording techniques in neuroscience and powerful inference methods recently held the promise to recover useful effective models, at the single neuron or network level, directly from observed data. The value of a model of course should critically depend on its ability to reproduce the dynamical behavior of the modeled system; however, few attempts have been made to inquire into the dynamics of inferred models in neuroscience, and none, to our knowledge, at the network level. Here we introduce a principled modification of a widely used generalized linear model (GLM), and learn its structural and dynamic parameters from ex-vivo spiking data. We show that the new model is able to capture the most prominent features of the highly non-stationary and non-linear dynamics displayed by the biological network, where the reference GLM largely fails. Two ingredients turn out to be key for success. The first one is a bounded transfer function that makes the single neuron able to respond to its input in a saturating fashion; beyond its biological plausibility such property, by limiting the capacity of the neuron to transfer information, makes the coding more robust in the face of the highly variable network activity, and noise. The second ingredient is a super-Poisson spikes generative probabilistic mechanism; this feature, that accounts for the fact that observations largely undersample the network, allows the model neuron to more flexibly incorporate the observed activity fluctuations. Taken together, the two ingredients, without increasing complexity, allow the model to capture the key dynamic elements. When left free to generate its spontaneous activity, the inferred model proved able to reproduce not only the non-stationary population dynamics of the network, but also part of the fine-grained structure of the dynamics at the single neuron level.