# The gradient complexity of linear regression

6 Nov 2019  ·  , , , ·

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.

PDF Abstract

## Code Add Remove Mark official

No code implementations yet. Submit your code now

## Datasets

Add Datasets introduced or used in this paper

## Results from the Paper Edit

Submit results from this paper to get state-of-the-art GitHub badges and help the community compare results to other papers.