Sketching Algorithms and Lower Bounds for Ridge Regression. (arXiv:2204.06653v2 [cs.DS] UPDATED)

Web: http://arxiv.org/abs/2204.06653

We give a sketching-based iterative algorithm that computes a $1+\varepsilon$
approximate solution for the ridge regression problem $\min_x \|Ax-b\|_2^2
+\lambda\|x\|_2^2$ where $A \in R^{n \times d}$ with $d \ge n$. Our algorithm,
for a constant number of iterations (requiring a constant number of passes over
the input), improves upon earlier work (Chowdhury et al.) by requiring that the
sketching matrix only has a weaker Approximate Matrix Multiplication (AMM)
guarantee that depends on $\varepsilon$, along with a constant subspace
embedding guarantee. …

algorithms arxiv regression ridge