Papers › Turnstile ℓₚ leverage score sampling with applications

Turnstile ℓₚ leverage score sampling with applications

1 Jun 2024arXiv:2406.00339archive 2025-07-28

Alexander Munteanu, Simon Omlor

The turnstile data stream model offers the most flexible framework where data can be manipulated dynamically, i.e., rows, columns, and even single entries of an input matrix can be added, deleted, or updated multiple times in a data stream. We develop a novel algorithm for sampling rows aᵢ of a matrix A∈ℝ^(n×d), proportional to their ℓₚ norm, when A is presented in a turnstile data stream. Our algorithm not only returns the set of sampled row indexes, it also returns slightly perturbed rows ãᵢ ≈aᵢ, and approximates their sampling probabilities up to ε relative error. When combined with preconditioning techniques, our algorithm extends to ℓₚ leverage score sampling over turnstile data streams. With these properties in place, it allows us to simulate subsampling constructions of coresets for important regression problems to operate over turnstile data streams with very little overhead compared to their respective off-line subsampling algorithms. For logistic regression, our framework yields the first algorithm that achieves a (1+ε) approximation and works in a turnstile data stream using polynomial sketch/subsample size, improving over O(1) approximations, or exp(1/ε) sketch size of previous work. We compare experimentally to plain oblivious sketching and plain leverage score sampling algorithms for ℓₚ and logistic regression.

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