Improved large-scale graph learning through ridge spectral sparsification

Calandriello, Daniele; Koutis, Ioannis; Lazaric, Alessandro; Valko, Michal

Document type :

Communication dans un congrès avec actes

Title :

Improved large-scale graph learning through ridge spectral sparsification

Author(s) :

Calandriello, Daniele [Auteur]
Italian Institute of Technology = Istituto Italiano di Tecnologia [IIT]
Sequential Learning [SEQUEL]
Koutis, Ioannis [Auteur]
New Jersey Institute of Technology [Newark] [NJIT]
Lazaric, Alessandro [Auteur]

Facebook AI Research [Paris] [FAIR]
Valko, Michal [Auteur]

Sequential Learning [SEQUEL]

Conference title :

International Conference on Machine Learning

City :

Stockholm

Country :

Suède

Start date of the conference :

2018-07-10

HAL domain(s) :

Statistiques [stat]/Machine Learning [stat.ML]

English abstract : [en]

The representation and learning benefits of methods based on graph Laplacians, such as Lapla-cian smoothing or harmonic function solution for semi-supervised learning (SSL), are empirically and theoretically well supported. ...
Show more >The representation and learning benefits of methods based on graph Laplacians, such as Lapla-cian smoothing or harmonic function solution for semi-supervised learning (SSL), are empirically and theoretically well supported. Nonetheless , the exact versions of these methods scale poorly with the number of nodes n of the graph. In this paper, we combine a spectral sparsifica-tion routine with Laplacian learning. Given a graph G as input, our algorithm computes a sparsi-fier in a distributed way in O(n log 3 (n)) time, O(m log 3 (n)) work and O(n log(n)) memory, using only log(n) rounds of communication. Furthermore , motivated by the regularization often employed in learning algorithms, we show that constructing sparsifiers that preserve the spectrum of the Laplacian only up to the regularization level may drastically reduce the size of the final graph. By constructing a spectrally-similar graph, we are able to bound the error induced by the sparsifica-tion for a variety of downstream tasks (e.g., SSL). We empirically validate the theoretical guarantees on Amazon co-purchase graph and compare to the state-of-the-art heuristics.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

ANR Project :

Inférence bayésienne à ressources limitées - données massives et modèles coûteux

Collections :