928 research outputs found
Particle-filtering approaches for nonlinear Bayesian decoding of neuronal spike trains
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
Fast non-negative deconvolution for spike train inference from population calcium imaging
Calcium imaging for observing spiking activity from large populations of
neurons are quickly gaining popularity. While the raw data are fluorescence
movies, the underlying spike trains are of interest. This work presents a fast
non-negative deconvolution filter to infer the approximately most likely spike
train for each neuron, given the fluorescence observations. This algorithm
outperforms optimal linear deconvolution (Wiener filtering) on both simulated
and biological data. The performance gains come from restricting the inferred
spike trains to be positive (using an interior-point method), unlike the Wiener
filter. The algorithm is fast enough that even when imaging over 100 neurons,
inference can be performed on the set of all observed traces faster than
real-time. Performing optimal spatial filtering on the images further refines
the estimates. Importantly, all the parameters required to perform the
inference can be estimated using only the fluorescence data, obviating the need
to perform joint electrophysiological and imaging calibration experiments.Comment: 22 pages, 10 figure
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