IFLYSIB   05383
Unidad Ejecutora - UE
congresos y reuniones científicas
An analytically tractable model for studying beyond pairwise common input correlations
Conferencia; Second International Conference on Mathematical NeuroScience (ICMNS); 2016
Recent results from experiments involving a relatively large population of neurons have shown a signicant amountof higher-order correlations, as synchronous activity that cannot be reduced to pairwise statistics. Finding suitablemathematical models for capturing the statistical structure of ring patterns distributed across several neurons providesa challenge and a prerequisite for understanding population codes. The Dichotomized Gaussian model [1], in whichbinary patterns are thought of being generated by thresholding a multivariate Gaussian random variable, providesan appropiate statistical model to study neural correlations. In this model, correlations between neurons arise frompairwise correlations in the underlying Gaussian inputs, an analitically tractable framework for generating populationspike trains with specied mean and pairwise statistics [2]. Although inputs in the model are Gaussian distributedand therefore have no interactions beyond second order, the nonlinear threshold spiking may give rise to statisticalinteractions of all orders and can be used to construct quantitative predictions on how departures from pairwise modelsdepend on common Gaussian like neuronal inputs [3, 4]. This approach has been developed within the Central LimitTheorem context, which ensures that the probability distribution function of any measurable quantity is a normaldistribution, provided that a suciently large number of independent random variables with exactly the same meanand variance are being considered. However, the Central Limit Theorem does not hold if correlations between randomvariables cannot be neglected and, perhaps undetectable, higher-order input correlations may well have an importanteect at population level.Little is known of how correlations aect the integration and ring behavior of a population of neurons beyond thesecond order statistics. To investigate how higher-order inputs correlations can shape information coding in the brain,we developed a model which constitutes the natural extension of the Dichotomized Gaussian model, where the inputsare distributed according to deformed Gaussians (i.e. q-Gaussians) and therefore can exhibit more complex inputinteractions [5]. Furthermore, q-Gaussians are often favored for their heavy tails in comparison to Gaussians, allowingfor better tting of deviations in amplitude distributions of local eld potentials. This Dichotomized q-Gaussian modelarises due to the Extended Central Limit Theorem [6], in which the independence constraint for the independent andidentically distributed variables is relaxed to an extent dened by the q parameter, and converges to the DichotomizedGaussian model when we consider the limit of the Central Limit Theorem framework (that is, q ! 1). This approachallows for generating binary spike trains with beyond second order input correlations, and so it provides a means forfurther studying higher-order correlations in neuronal populations.References[1] S. Amari, H. Nakahara, S. Wu, Y. Sakai. Synchronous ring and higher-order interactions in neuron pool, NeuralComputation 15 pp. 127-142, 2003.[2] J. H. Macke, P. Berens, A. S. Ecker, A. S. Tolias, M. Bethge. Generating spike trains with specied correlationcoecients, Neural Computation 21 pp. 397-423, 2009.[3] S. Yu, H. Yang, H. Nakahara, G.S. Santos, D. Nikolic, D. Plenz. Higher-order interactions characterized in corticalactivity, The Journal of Neuroscience 31 (48) pp. 1751417526, 2011.[4] J. H. Macke, M. Opper, M. Bethge. Common input explains higher-order correlations and entropy in a simplemodel of neural population activity, Phys. Rev. Lett. 106 pp. 208102, 2011.[5] L. Montangie, F. Montani. Quantifying higher-order correlations in a neuronal pool, Physica A 421 pp. 388-400,2015.[6] C. Vignat and A. Plastino. Central limit theorem and deformed exponentials, J. Phys. A: Math. Theor. 40 pp.969-978, 2007.