  Neurons in cortical circuits exhibit coordinated spiking activity, and can
produce correlated synchronous spikes during behavior and cognition. We
recently developed a method for estimating the dynamics of correlated ensemble
activity by combining a model of simultaneous neuronal interactions (e.g., a
spin-glass model) with a state-space method (Shimazaki et al. 2012 PLoS Comput
Biol 8 e1002385). This method allows us to estimate stimulus-evoked dynamics of
neuronal interactions which is reproducible in repeated trials under identical
experimental conditions. However, the method may not be suitable for detecting
stimulus responses if the neuronal dynamics exhibits significant variability
across trials. In addition, the previous model does not include effects of past
spiking activity of the neurons on the current state of ensemble activity. In
this study, we develop a parametric method for simultaneously estimating the
stimulus and spike-history effects on the ensemble activity from single-trial
data even if the neurons exhibit dynamics that is largely unrelated to these
effects. For this goal, we model ensemble neuronal activity as a latent process
and include the stimulus and spike-history effects as exogenous inputs to the
latent process. We develop an expectation-maximization algorithm that
simultaneously achieves estimation of the latent process, stimulus responses,
and spike-history effects. The proposed method is useful to analyze an
interaction of internal cortical states and sensory evoked activity.
