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arXiv · 1911.02212

The gradient complexity of linear regression

Mark Braverman·Elad Hazan·Max Simchowitz·Blake Woodworth
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Abstract

We investigate the computational complexity of several basic linear algebra primitives, including largest eigenvector computation and linear regression, in the computational model that allows access to the data via a matrix-vector product oracle. We show that for polynomial accuracy, $\Theta(d)$ calls to the oracle are necessary and sufficient even for a randomized algorithm. Our lower bound is based on a reduction to estimating the least eigenvalue of a random Wishart matrix. This simple distribution enables a concise proof, leveraging a few key properties of the random Wishart ensemble.

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Mark Braverman, Elad Hazan, Max Simchowitz, Blake Woodworth. 2019-11-06. The gradient complexity of linear regression. https://arxiv.org/abs/1911.02212

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