Abstract
To resolve the issue of the exponentially increasing computational complexity of the expectation-maximization process as the emission space of a system operating according to the mechanics of a Hidden Markov Model (HMM) expands, a specialized HMM algorithm recontextualizing the possible inputs thereof as a Poisson process was developed and used by Gat et al., among others (1997). However, little work has been done to test how the ground truth parameters of the observation sequences used to train both the standard and Poisson HMMs can influence model predictions. To that end, a series of s simulations was conducted to compare the performances of the standard and Poisson HMMs with respect to the time step sizes of dummy datasets consisting of neuronal spike trains, firing rates of the constituent cells, and the total number of emission units or spiking neurons within the ground truth data. It was found that for spike trains with durations of 2 seconds, the standard HMM was unable to compensate for higher time bin sizes as the firing rates of the constituent neurons are increased, while at the same time, the Poisson HMM was able to effectively extract state transitions even for the highest time step sizes. Moreover, spike trains with multiple neurons firing at highly distinct rates in each firing state have been observed to give rise to more accurate predictions of state probabilities.