  The number of neurons that can be simultaneously recorded doubles every seven
years. This ever increasing number of recorded neurons opens up the possibility
to address new questions and extract higher dimensional stimuli from the
recordings. Modeling neural spike trains as point processes, this task of
extracting dynamical signals from spike trains is commonly set in the context
of nonlinear filtering theory. Particle filter methods relying on importance
weights are generic algorithms that solve the filtering task numerically, but
exhibit a serious drawback when the problem dimensionality is high: they are
known to suffer from the 'curse of dimensionality' (COD), i.e. the number of
particles required for a certain performance scales exponentially with the
observable dimensions. Here, we first briefly review the theory on filtering
with point process observations in continuous time. Based on this theory, we
investigate both analytically and numerically the reason for the COD of
weighted particle filtering approaches: Similarly to particle filtering with
continuous-time observations, the COD with point-process observations is due to
the decay of effective number of particles, an effect that is stronger when the
number of observable dimensions increases. Given the success of unweighted
particle filtering approaches in overcoming the COD for continuous- time
observations, we introduce an unweighted particle filter for point-process
observations, the spike-based Neural Particle Filter (sNPF), and show that it
exhibits a similar favorable scaling as the number of dimensions grows.
Further, we derive rules for the parameters of the sNPF from a maximum
likelihood approach learning. We finally employ a simple decoding task to
illustrate the capabilities of the sNPF and to highlight one possible future
application of our inference and learning algorithm.
