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Tensor Sketch: Fast and Scalable Polynomial Kernel Approximation

Year: 2025

Type: preprint

Abstract: Approximation of non-linear kernels using random feature maps has become a powerful technique for scaling kernel methods to large datasets. We propose $\textit{Tensor Sketch}$, an efficient random feature map for approximating polynomial kernels. Given $n$ training samples in $\mathbb{R}^d$ Tensor Sketch computes low-dimensional embeddings in $\mathbb{R}^D$ in time $\mathcal{O}\left( n(d+D \log{D}) \right)$ making it well-suited for high-dimensional and large-scale settings. We provide theoretical guarantees on the approximation error, ensuring the fidelity of the resulting kernel function estimates. We also discuss extensions and highlight applications where Tensor Sketch serves as a central computational tool.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2505.08146

Authors: Pham, Ninh, Pagh, Rasmus

Institutions: University of Auckland, Auckland University of Technology, University of Copenhagen, University College Copenhagen, IT University of Copenhagen

Language: English

Topic: Stochastic Gradient Optimization Techniques

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W6910797168

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