A Deterministic Streaming Sketch for Ridge Regression

Apr 14, 2021

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We provide a deterministic space-efficient algorithm for estimating ridge regression. For n data points with d features and a large enough regularization parameter, we provide a solution within eps L_2 error using only O(d/eps) space. This is the first o(d^2) space deterministic streaming algorithm with guaranteed solution error and risk bound for this classic problem. The algorithm sketches the covariance matrix by variants of Frequent Directions, which implies it can operate in insertion-only streams and a variety of distributed data settings. In comparisons to randomized sketching algorithms on synthetic and real-world datasets, our algorithm has less empirical error using less space and similar time.

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The 24th International Conference on Artificial Intelligence and Statistics was held virtually from Tuesday, 13 April 2021 to Thursday, 15 April 2021.

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