Spectral dimension reduction on parametric models for spike train statistics
Abstract
It has been shown that the neurons of visual system present correlated activity in
response to dierent stimuli. The role of these correlations is an unresolved subject. These
correlations vary according to the stimulus, specially with natural images. To uncover the
role of these correlation and characterize the population code, it is necessary to measure the
simultaneous activity of large neural populations. This has been achieved thanks to the advent
of Multi-Electrode Array technology, opening up a way to better characterize how the brain
encodes information in the concerted activity of neurons. In parallel, powerful statistical tools
have been developed to accurately characterize spatio-temporal correlations between neurons.
Methods based on Maximum Entropy Principle, where statistical entropy is maximized under
a set of constraints corresponding to specic assumptions on the relevant statistical quantities,
have been proved successfully, specially when they consider spatiotemporal correlations. [ref]
They are although limited by (i) the assumption of stationarity, (ii) the many possible
choice of constraints, and (iii) the huge number of free parameters.
In this context, focusing on (ii), (iii), we propose a method of dimensionality reduction
allowing to select a model tting data with a minimal number of parameters. This method
is based on the spectral analysis of a symmetric, positive matrix, summing up all relevant
spatial-temporal correlations, closely related to the Fisher metric in statistical analysis and
information geometry, but extended here to the spatio-temporal domain. Based on synthetic
and real data - RGC responses to dierent stimuli in a diurnal rodent- we show that the
spectrum of this matrix has a cut-o beyond which the corresponding dimensions have a
negligible eect on the statistical estimation. This dimensionality reduction reduces the risk
of over-tting. The method is used to characterize dierences in response to dierent classes
of visual stimuli (white noise, natural images).
Origin : Files produced by the author(s)