  Tuning curves characterizing the response selectivities of biological neurons
often exhibit large degrees of irregularity and diversity across neurons.
Theoretical network models that feature heterogeneous cell populations or
random connectivity also give rise to diverse tuning curves. However, a general
framework for fitting such models to experimentally measured tuning curves is
lacking. We address this problem by proposing to view mechanistic network
models as generative models whose parameters can be optimized to fit the
distribution of experimentally measured tuning curves. A major obstacle for
fitting such models is that their likelihood function is not explicitly
available or is highly intractable to compute. Recent advances in machine
learning provide ways for fitting generative models without the need to
evaluate the likelihood and its gradient. Generative Adversarial Networks (GAN)
provide one such framework which has been successful in traditional machine
learning tasks. We apply this approach in two separate experiments, showing how
GANs can be used to fit commonly used mechanistic models in theoretical
neuroscience to datasets of measured tuning curves. This fitting procedure
avoids the computationally expensive step of inferring latent variables, e.g.
the biophysical parameters of individual cells or the particular realization of
the full synaptic connectivity matrix, and directly learns model parameters
which characterize the statistics of connectivity or of single-cell properties.
Another strength of this approach is that it fits the entire, joint
distribution of experimental tuning curves, instead of matching a few summary
statistics picked a priori by the user. More generally, this framework opens
the door to fitting theoretically motivated dynamical network models directly
to simultaneously or non-simultaneously recorded neural responses.
