Method for analyzing spike patterns with Markov transition matrices and Kullback-Leibler divergence

We test this method on both simulated data and experimental data from primary visual cortex of cats, publicly available through CRCNS [1–3]. Interspike intervals are simulated based on exponential and gamma distributions fit to the corresponding experimental ISI distributions. Artificial data is also constructed by randomly reshuffling the temporal order of the experimental ISI sequences. Figure 1 shows a comparison between the experimental and simulated data for a typical neuron in the study. After comparison, we find that the Kullback-Leibler divergence for the experimental data is significantly greater than it is for the simulated data, but only for the bins at the extreme ends of the distribution. For spike time transitions after both the smallest and longest 10% of ISIs in the experimental data, the Kullback-Leibler divergence for these quantile groups is in many cases almost double the Kullback-Leibler divergence of the simulated data, and it can be more than an order of magnitude higher in some rarer cases. However, for transitions in the middle range, the Kullback-Leibler divergence is on average less than for the distribution tails, and the values for the experimental and numerical data are more similar.