Estimating nonstationary inputs from a single spike train based on a neuron model with adaptation.

Because every spike of a neuron is determined by input signals, a train of spikes may contain information about the dynamics of unobserved neurons. A state-space method based on the leaky integrate-and-fire model, describing neuronal transformation from input signals to a spike train has been proposed for tracking input parameters represented by their mean and fluctuation [11]. In the present paper, we propose to make the estimation more realistic by adopting an LIF model augmented with an adaptive moving threshold. Moreover, because the direct state-space method is computationally infeasible for a data set comprising thousands of spikes, we further develop a practical method for transforming instantaneous firing characteristics back to input parameters. The instantaneous firing characteristics, represented by the firing rate and non-Poisson irregularity, can be estimated using a computationally feasible algorithm. We applied our proposed methods to synthetic data to clarify that they perform well.