  The models in statistical physics such as an Ising model offer a convenient
way to characterize stationary activity of neural populations. Such stationary
activity of neurons may be expected for recordings from in vitro slices or
anesthetized animals. However, modeling activity of cortical circuitries of
awake animals has been more challenging because both spike-rates and
interactions can change according to sensory stimulation, behavior, or an
internal state of the brain. Previous approaches modeling the dynamics of
neural interactions suffer from computational cost; therefore, its application
was limited to only a dozen neurons. Here by introducing multiple analytic
approximation methods to a state-space model of neural population activity, we
make it possible to estimate dynamic pairwise interactions of up to 60 neurons.
More specifically, we applied the pseudolikelihood approximation to the
state-space model, and combined it with the Bethe or TAP mean-field
approximation to make the sequential Bayesian estimation of the model
parameters possible. The large-scale analysis allows us to investigate dynamics
of macroscopic properties of neural circuitries underlying stimulus processing
and behavior. We show that the model accurately estimates dynamics of network
properties such as sparseness, entropy, and heat capacity by simulated data,
and demonstrate utilities of these measures by analyzing activity of monkey V4
neurons as well as a simulated balanced network of spiking neurons.
