Syracuse

Spectral dimension reduction on parametric models for spike train statistics

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Ravello, Cesar | Herzog, Rubén | Cessac, Bruno | Escobar, Maria-Jose | Palacios, Adrian

Edité par CCSD -

International audience. It has been shown that the neurons of visual system present correlated activity inresponse to dierent stimuli. The role of these correlations is an unresolved subject. Thesecorrelations vary according to the stimulus, specially with natural images. To uncover therole of these correlation and characterize the population code, it is necessary to measure thesimultaneous activity of large neural populations. This has been achieved thanks to the adventof Multi-Electrode Array technology, opening up a way to better characterize how the brainencodes information in the concerted activity of neurons. In parallel, powerful statistical toolshave been developed to accurately characterize spatio-temporal correlations between neurons.Methods based on Maximum Entropy Principle, where statistical entropy is maximized undera 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 possiblechoice of constraints, and (iii) the huge number of free parameters.In this context, focusing on (ii), (iii), we propose a method of dimensionality reductionallowing to select a model tting data with a minimal number of parameters. This methodis based on the spectral analysis of a symmetric, positive matrix, summing up all relevantspatial-temporal correlations, closely related to the Fisher metric in statistical analysis andinformation geometry, but extended here to the spatio-temporal domain. Based on syntheticand real data - RGC responses to dierent stimuli in a diurnal rodent- we show that thespectrum of this matrix has a cut-o beyond which the corresponding dimensions have anegligible eect on the statistical estimation. This dimensionality reduction reduces the riskof over-tting. The method is used to characterize dierences in response to dierent classesof visual stimuli (white noise, natural images).

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