Benwei Shi, Aditya Bhaskara, Wai Ming Tai et al.
We show that a constant-size constant-error coreset for polytope distance is simple to maintain under merges of coresets. However, increasing the size cannot improve the error bound significantly beyond that constant.
Benwei Shi, Jeff M. Phillips
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 $\varepsilon$ L$_2$ error using only $O(d/\varepsilon)$ 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.