Titre :

On Graph Reconstruction via Empirical Risk Minimization: Fast Learning Rates and Scalability

Auteur(s) :

Papa, Guillaume [Auteur]
Laboratoire Traitement et Communication de l'Information [LTCI]
Clémençon, Stéphan [Auteur]
Laboratoire Traitement et Communication de l'Information [LTCI]
Bellet, Aurelien [Auteur]
Machine Learning in Information Networks [MAGNET]

Titre de la manifestation scientifique :

Annual Conference on Neural Information Processing Systems (NIPS 2016)

Ville :

Barcelone

Pays :

Espagne

Date de début de la manifestation scientifique :

2016-12-05

Discipline(s) HAL :

Informatique [cs]/Apprentissage [cs.LG]
Statistiques [stat]/Machine Learning [stat.ML]

Résumé en anglais : [en]

The problem of predicting connections between a set of data points finds many applications, in systems biology and social network analysis among others. This paper focuses on the \textit{graph reconstruction} problem, where ...
Lire la suite >The problem of predicting connections between a set of data points finds many applications, in systems biology and social network analysis among others. This paper focuses on the \textit{graph reconstruction} problem, where the prediction rule is obtained by minimizing the average error over all n(n-1)/2 possible pairs of the n nodes of a training graph. Our first contribution is to derive learning rates of order O(log n / n) for this problem, significantly improving upon the slow rates of order O(1/√n) established in the seminal work of Biau & Bleakley (2006). Strikingly, these fast rates are universal, in contrast to similar results known for other statistical learning problems (e.g., classification, density level set estimation, ranking, clustering) which require strong assumptions on the distribution of the data. Motivated by applications to large graphs, our second contribution deals with the computational complexity of graph reconstruction. Specifically, we investigate to which extent the learning rates can be preserved when replacing the empirical reconstruction risk by a computationally cheaper Monte-Carlo version, obtained by sampling with replacement B << n² pairs of nodes. Finally, we illustrate our theoretical results by numerical experiments on synthetic and real graphs.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL