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 di erent 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 speci c 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 di erent 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 e ect on the statistical estimation. This dimensionality reduction reduces the risk of over- tting. The method is used to characterize di erences in response to di erent classes of visual stimuli (white noise, natural images).
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Contributeur : Bruno Cessac <>
Soumis le : vendredi 18 décembre 2015 - 09:02:35
Dernière modification le : jeudi 11 janvier 2018 - 16:14:56


  • HAL Id : hal-01246088, version 1


Cesar Ravello, Rubén Herzog, Bruno Cessac, Maria-Jose Escobar, Adrian Palacios. Spectral dimension reduction on parametric models for spike train statistics . 12e Colloque de la Société des Neurosciences , May 2015, Montpellier, France. 〈hal-01246088〉



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