Complex-to-Real Sketches for Tensor Products with Applications to the Polynomial Kernel - 3IA Côte d’Azur – Interdisciplinary Institute for Artificial Intelligence Accéder directement au contenu
Article Dans Une Revue Proceedings of Machine Learning Research Année : 2023

Complex-to-Real Sketches for Tensor Products with Applications to the Polynomial Kernel

Ruben Ohana
  • Fonction : Auteur
Maurizio Filippone
  • Fonction : Auteur
  • PersonId : 1021042

Résumé

Randomized sketches of a tensor product of p vectors follow a tradeoff between statistical efficiency and computational acceleration. Commonly used approaches avoid computing the high-dimensional tensor product explicitly, resulting in a suboptimal dependence of O(3 p) in the embedding dimension. We propose a simple Complex-to-Real (CtR) modification of wellknown sketches that replaces real random projections by complex ones, incurring a lower O(2 p) factor in the embedding dimension. The output of our sketches is real-valued, which renders their downstream use straightforward. In particular, we apply our sketches to p-fold self-tensored inputs corresponding to the feature maps of the polynomial kernel. We show that our method achieves state-of-the-art performance in terms of accuracy and speed compared to other randomized approximations from the literature.
Fichier principal
Vignette du fichier
wacker23a.pdf (1.23 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04076375 , version 1 (20-04-2023)

Identifiants

  • HAL Id : hal-04076375 , version 1

Citer

Jonas Wacker, Ruben Ohana, Maurizio Filippone. Complex-to-Real Sketches for Tensor Products with Applications to the Polynomial Kernel. Proceedings of Machine Learning Research, inPress. ⟨hal-04076375⟩
15 Consultations
9 Téléchargements

Partager

Gmail Facebook X LinkedIn More