@inproceedings{1931823d486c4b71a052525aa894d4f8,
title = "The Complexity of Dynamic Least-Squares Regression",
abstract = "We settle the complexity of dynamic least-squares regression (LSR), where rows and labels (A(t), b(t)) can be adaptively inserted and/or deleted, and the goal is to efficiently maintain an ϵ-approximate solution to minx(t)||A(t) x(t)-b(t)||_2 for all t ∈[T]. We prove sharp separations (d2-o(1). vs. .∼ d) between the amortized update time of: (i) Fully vs. Partially dynamic 0.01-LSR; (ii) High vs. low-accuracy LSR in the partially-dynamic (insertion-only) setting.Our lower bounds follow from a gap-amplification reduction-reminiscent of iterative refinement-from the exact version of the Online Matrix Vector Conjecture (OMv) [HKNS15], to constant approximate OMv over the reals, where the i-th online product Hv(i) only needs to be computed to 0.1 -relative error. All previous fine-grained reductions from OMv to its approximate versions only show hardness for inverse polynomial approximation ϵ= n-Ω(1) (additive or multiplicative). This result is of independent interest in fine-grained complexity and for the investigation of the OMv Conjecture, which is still widely open.",
keywords = "Numerical linear algebra, dynamic algorithms, fine-grained complexity",
author = "Shunhua Jiang and Binghui Peng and Omri Weinstein",
note = "Publisher Copyright: {\textcopyright} 2023 IEEE.; 64th IEEE Annual Symposium on Foundations of Computer Science, FOCS 2023 ; Conference date: 06-11-2023 Through 09-11-2023",
year = "2023",
doi = "https://doi.org/10.1109/FOCS57990.2023.00097",
language = "الإنجليزيّة",
series = "Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS",
publisher = "IEEE Computer Society",
pages = "1605--1627",
booktitle = "Proceedings - 2023 IEEE 64th Annual Symposium on Foundations of Computer Science, FOCS 2023",
address = "الولايات المتّحدة",
}