Distributed adaptive sampling for kernel matrix approximation

Calandriello, Daniele; Lazaric, Alessandro; Valko, Michal

Document type :

Communication dans un congrès avec actes

Title :

Distributed adaptive sampling for kernel matrix approximation

Author(s) :

Calandriello, Daniele [Auteur]
Sequential Learning [SEQUEL]
Lazaric, Alessandro [Auteur]

Sequential Learning [SEQUEL]
Valko, Michal [Auteur]

Sequential Learning [SEQUEL]

Conference title :

International Conference on Artificial Intelligence and Statistics

City :

Fort Lauderdale

Country :

Etats-Unis d'Amérique

Start date of the conference :

2017

HAL domain(s) :

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

English abstract : [en]

Most kernel-based methods, such as kernel or Gaussian process regression, kernel PCA, ICA, or $k$-means clustering, do not scale to large datasets, because constructing and storing the kernel matrix $\mathbf{K}_n$ requires ...
Show more >Most kernel-based methods, such as kernel or Gaussian process regression, kernel PCA, ICA, or $k$-means clustering, do not scale to large datasets, because constructing and storing the kernel matrix $\mathbf{K}_n$ requires at least $\mathcal{O}(n^2)$ time and space for $n$ samples. Recent works show that sampling points with replacement according to their ridge leverage scores (RLS) generates small dictionaries of relevant points with strong spectral approximation guarantees for $\mathbf{K}_n$. The drawback of RLS-based methods is that computing exact RLS requires constructing and storing the whole kernel matrix. In this paper, we introduce SQUEAK, a new algorithm for kernel approximation based on RLS sampling that sequentially processes the dataset, storing a dictionary which creates accurate kernel matrix approximations with a number of points that only depends on the effective dimension $d_{eff}(\gamma)$ of the dataset. Moreover since all the RLS estimations are efficiently performed using only the small dictionary, SQUEAK is the first RLS sampling algorithm that never constructs the whole matrix $\mathbf{K}_n$, runs in linear time $\widetilde{\mathcal{O}}(nd_{eff}(\gamma)^3)$ w.r.t. $n$, and requires only a single pass over the dataset. We also propose a parallel and distributed version of SQUEAK that linearly scales across multiple machines, achieving similar accuracy in as little as $\widetilde{\mathcal{O}}(\log(n)d_{eff}(\gamma)^3)$ time.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
Extraction et transfert de connaissances dans l'apprentissage par renforcement

Collections :

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

Source :

Harvested from HAL

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calandriello2017distributed.pdf
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1803.10172
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