Space lower bounds for linear prediction in the streaming model

Yuval Dagan; Gil Kur; Ohad Shamir

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arXiv · 1902.03498

Space lower bounds for linear prediction in the streaming model

Yuval Dagan·Gil Kur·Ohad Shamir

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Abstract

We show that fundamental learning tasks, such as finding an approximate linear separator or linear regression, require memory at least \emph{quadratic} in the dimension, in a natural streaming setting. This implies that such problems cannot be solved (at least in this setting) by scalable memory-efficient streaming algorithms. Our results build on a memory lower bound for a simple linear-algebraic problem -- finding orthogonal vectors -- and utilize the estimates on the packing of the Grassmannian, the manifold of all linear subspaces of fixed dimension.

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Yuval Dagan, Gil Kur, Ohad Shamir. 2019-02-09. Space lower bounds for linear prediction in the streaming model. https://arxiv.org/abs/1902.03498

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