Parametric Estimation of spike train statistics
Identifieur interne : 003C54 ( Main/Exploration ); précédent : 003C53; suivant : 003C55Parametric Estimation of spike train statistics
Auteurs : Bruno Cessac [France] ; Juan Carlos Vasquez [France] ; Thierry Viéville [France]Source :
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Abstract
We consider the evolution of a network of neurons, focusing on the asymptotic behavior of spikes dynamics instead of membrane potential dynamics. The spike response is not sought as a deterministic response in this context, but as a conditional probability: "Reading the code" consists in inferring such a probability. This probability is computed from empirical raster plots, by using the framework of thermodynamic formalism in ergodic theory. This provides us a parametric statistical model where the probability has the form of a Gibbs distribution. In this respect, this approach generalizes the seminal and profound work of Schneidman and collaborators . A minimal presentation of the formalism is reviewed here, while a general algorithmic estimation method is proposed, minimizing the relative entropy, yielding fast convergent implementations. It is also made explicit how several spike observables (entropy, rate, synchronizations, correlations) are given in closed-form from the parametric estimation. This paradigm does not only allow us to estimate the spike statistics, given a design choice, but also to compare different models, thus answering comparative questions about the neural code such as : are correlations (or time synchrony or a given set of spike patterns, ..) significant with respect to rate coding ? A numerical validation of the method is proposed and the perspectives regarding spike-train code analysis are also discussed.
Url:
Affiliations:
- France
- Grand Est, Lorraine (région), Provence-Alpes-Côte d'Azur
- Nancy, Nice
- Institut national polytechnique de Lorraine, Université Nancy 2, Université Nice Sophia Antipolis, Université de Lorraine
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Le document en format XML
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BP 10578153 Le Chesnay Cedex</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/en/</ref></desc></org></tutelle><tutelle active="#struct-300291" type="indirect"><org type="institution" xml:id="struct-300291" status="OLD"><orgName>Université Henri Poincaré - Nancy 1</orgName><orgName type="acronym">UHP</orgName><date type="end">2011-12-31</date><desc><address><addrLine>24-30 rue Lionnois, BP 60120, 54 003 NANCY cedex, France</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300292" type="indirect"><org type="institution" xml:id="struct-300292" status="OLD"><orgName>Université Nancy 2</orgName><date type="end">2011-12-31</date><desc><address><addrLine>91 avenue de la Libération, BP 454, 54001 Nancy cedex</addrLine><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-300293" type="indirect"><org type="institution" xml:id="struct-300293" status="OLD"><orgName>Institut National Polytechnique de Lorraine</orgName><orgName type="acronym">INPL</orgName><date type="end">2011-12-31</date><desc><address><country key="FR"></country></address></desc></org></tutelle><tutelle active="#struct-2496" type="direct"><org type="laboratory" xml:id="struct-2496" status="OLD"><orgName>INRIA Lorraine</orgName><desc><address><addrLine>615 rue du Jardin Botanique 54600 Villers-lès-Nancy</addrLine><country key="FR"></country></address><ref type="url">http://www.inria.fr/centre-de-recherche-inria/nancy-grand-est</ref></desc><listRelation><relation active="#struct-300009" type="direct"></relation></listRelation></org></tutelle></tutelles></hal:affiliation><country>France</country><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Université Nancy 2</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName><placeName><settlement type="city">Nancy</settlement><region type="region" nuts="2">Grand Est</region><region type="old region" nuts="2">Lorraine (région)</region></placeName><orgName type="university">Institut national polytechnique de Lorraine</orgName><orgName type="institution" wicri:auto="newGroup">Université de Lorraine</orgName></affiliation></author></analytic></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>Gibbs distributions</term><term>Neurons dynamics</term><term>Spike coding</term><term>Statistical physics</term><term>Thermodynamic formalism</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">We consider the evolution of a network of neurons, focusing on the asymptotic behavior of spikes dynamics instead of membrane potential dynamics. The spike response is not sought as a deterministic response in this context, but as a conditional probability: "Reading the code" consists in inferring such a probability. This probability is computed from empirical raster plots, by using the framework of thermodynamic formalism in ergodic theory. This provides us a parametric statistical model where the probability has the form of a Gibbs distribution. In this respect, this approach generalizes the seminal and profound work of Schneidman and collaborators . A minimal presentation of the formalism is reviewed here, while a general algorithmic estimation method is proposed, minimizing the relative entropy, yielding fast convergent implementations. It is also made explicit how several spike observables (entropy, rate, synchronizations, correlations) are given in closed-form from the parametric estimation. This paradigm does not only allow us to estimate the spike statistics, given a design choice, but also to compare different models, thus answering comparative questions about the neural code such as : are correlations (or time synchrony or a given set of spike patterns, ..) significant with respect to rate coding ? A numerical validation of the method is proposed and the perspectives regarding spike-train code analysis are also discussed.</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Grand Est</li><li>Lorraine (région)</li><li>Provence-Alpes-Côte d'Azur</li></region><settlement><li>Nancy</li><li>Nice</li></settlement><orgName><li>Institut national polytechnique de Lorraine</li><li>Université Nancy 2</li><li>Université Nice Sophia Antipolis</li><li>Université de Lorraine</li></orgName></list><tree><country name="France"><region name="Provence-Alpes-Côte d'Azur"><name sortKey="Cessac, Bruno" sort="Cessac, Bruno" uniqKey="Cessac B" first="Bruno" last="Cessac">Bruno Cessac</name></region><name sortKey="Vasquez, Juan Carlos" sort="Vasquez, Juan Carlos" uniqKey="Vasquez J" first="Juan Carlos" last="Vasquez">Juan Carlos Vasquez</name><name sortKey="Vieville, Thierry" sort="Vieville, Thierry" uniqKey="Vieville T" first="Thierry" last="Viéville">Thierry Viéville</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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