Construction of point process adaptive filter algorithms for neural systems using sequential Monte Carlo methods

The stochastic state point process filter (SSPPF) and steepest descent point process filter (SDPPF) are adaptive filter algorithms for state estimation from point process observations that have been used to track neural receptive field plasticity and to decode the representations of biological signals in ensemble neural spiking activity. The SSPPF and SDPPF are constructed using, respectively, Gaussian and steepest descent approximations to the standard Bayes and Chapman-Kolmogorov (BCK) system of filter equations. To extend these approaches for constructing point process adaptive filters, we develop sequential Monte Carlo (SMC) approximations to the BCK equations in which the SSPPF and SDPPF serve as the proposal densities. We term the two new SMC point process filters SMC-PPFs and SMC-PPFD, respectively. We illustrate the new filter algorithms by decoding the wind stimulus magnitude from simulated neural spiking activity in the cricket cereal system. The SMC-PPFS and SMC-PPFD provide more accurate state estimates at low number of particles than a conventional bootstrap SMC filter algorithm in which the state transition probability density is the proposal density. We also use the SMC-PPFs algorithm to track the temporal evolution of a spatial receptive field of a rat hippocampal neuron recorded while the animal foraged in an open environment. Our results suggest an approach for constructing point process adaptive filters using SMC methods.