Sharper Bounds for ℓ_p Sensitivity Sampling
ICML 2023(2023)
摘要
In large scale machine learning, random sampling is a popular way to
approximate datasets by a small representative subset of examples. In
particular, sensitivity sampling is an intensely studied technique which
provides provable guarantees on the quality of approximation, while reducing
the number of examples to the product of the VC dimension d and the total
sensitivity 𝔖 in remarkably general settings. However, guarantees
going beyond this general bound of 𝔖 d are known in perhaps only
one setting, for ℓ_2 subspace embeddings, despite intense study of
sensitivity sampling in prior work. In this work, we show the first bounds for
sensitivity sampling for ℓ_p subspace embeddings for p > 2 that improve
over the general 𝔖 d bound, achieving a bound of roughly 𝔖^2-2/p for 2
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