Michigan State University - Research Groups

Simultaneously observed V1 cortical neurons often exhibit time-varying correlated firing activity in response to sensory stimuli. This correlation may be reminiscent of network state transitions that characterize the dynamics of the stimulus. Pairwise maximum entropy models were suggested to fit instantaneous network states (spatial correlation) in small populations (Schneidman et al. 2006), but did not account for the temporal correlations that likely represent the effect of spiking history on network state transition. To account for temporal correlations, hidden Markov models of deterministic patterns have been suggested as a framework to estimate these transitions (Escola et al. 2011), but did not include a stochastic element that enables adequate prediction of possible new patterns. To account for both temporal and spatial correlations with a stochastic element, a maximum entropy first-order Markov model has been suggested to fit to in vivo data collected in the cat parietal cortex in different sleep states(Marre et al. 2009).

Here we introduce a maximum entropy graphical model that accounts for correlations over longer temporal intervals among V1 neurons recorded in vivo. The proposed model not only includes instantaneous and transitional coupling terms among neuronal elements, but also exploits some additional terms to learn the non-uniform distribution that explain the characteristics of network state transitions. This model provides a better fit to the data and converges much more rapidly compared to the model proposed by Marre et al. despite the larger number of parameters. We evaluated the performance of the proposed graphical model in predicting the network states of V1 cortical neurons in response to drifting grating stimuli, in which a population of 21 neurons were simultaneously recorded. We evaluated the predictive power of this model by computing the Kullback-Leibler (KL) divergence between the estimated and true distributions of patterns and compared it to that of the pairwise maximum entropy model, as well as an independent model. We demonstrate that our model reduces the KL divergence by 20 percent compared to the previous models.