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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
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Maurizio Filippone
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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.
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Dates et versions

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

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  • HAL Id : hal-04076375 , version 1

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