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Séminaire du CMLA : Nonparametric maximum likelihood estimation for large random graphs with latent data

le 17 mai 2018
12h00 - 13h00

Séminaire animé par Sylvain Le Corff (Paris-Sud)

Sylvain_LeCorff.jpg

Sylvain_LeCorff.jpg

RÉSUMÉ :

This talk focuses on the estimation of the distribution of unobserved nodes in large random graphs from the observation of very few edges.

These graphs naturally model tournaments involving a large number of players (the nodes) where the ability to win of each player is unknown. The players are only partially observed through discrete valued scores (edges) describing the results of contests between players. In this very sparse setting, we present the first nonasymptotic risk bounds for maximum likelihood estimators (MLE) of the unknown distribution of the nodes.

The proof relies on the construction of a graphical model encoding conditional dependencies that is extremely efficient to study n-regular graphs obtained using a round-robin scheduling. This graphical model allows to prove geometric loss of memory properties and deduce the asymptotic behavior of the likelihood function. Following a classical construction in learning theory, the asymptotic likelihood is used to define a measure of performance for the MLE. Risk bounds for the MLE are finally obtained by subgaussian deviation results derived from concentration inequalities for Markov chains applied to our graphical model. Bayesian posterior concentration rates for the unknown distribution are also proposed.
Type :
Séminaires - conférences
Lieu(x) :
Bâtiment Cournot, 1er étage, salle C103

ORATEUR

Sylvain Le Corff (Institut de mathématiques, univ. Paris-Sud, Orsay)


 





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