- Date de réalisation : 1 Juillet 2019
- Lieu de réalisation : École Normale Supérieure, Paris.
- Durée du programme : 40 min
- Classification Dewey : Probabilités, Statistiques mathématiques, Mathématiques appliquées
- Auteur(s) : Klopp Olga
- producteur : Lehec Joseph, Boyer Claire, Chafaï Djalil
Dans la même collectionTropp 9/9 - Random matrix theory and computational linear algebra Tropp 8/9 - Random matrix theory and computational linear algebra Carpentier - Introduction to some problems of composite and minimax hypothesis testing Tropp 7/9 - Random matrix theory and computational linear algebra Tropp 6/9 - Random matrix theory and computational linear algebra Bubeck 9/9 - Some geometric aspects of randomized online decision making
Klopp - Sparse Network Estimation
Inhomogeneous random graph models encompass many network models such as stochastic block models and latent position models. We consider the problem of the statistical estimation of the matrix of connection probabilities based on the observations of the adjacency matrix of the network. We will also discuss the problem of graphon estimation when the probability matrix is sampled according to the graphon model. For these two problems, the minimax optimal rates of convergence in Frobenius norm are achieved by the least squares estimator which is known to be NP-hard. In this talk we will present two alternatives to the least squares: the hard thresholding estimator and the maximum likelihood estimator. We will provide new results for these two methods. We will also discuss the problem of link prediction commonly encountered in applications.