  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.
