The Advantages of Fresh Sketching for Ridge Regression

תקציר מקורי באנגליתarXiv:2609.38565v1 Announce Type: new Abstract: Over the past 25 years, sketching and sampling have become widely used tools for accelerating large-scale regression. In iterative randomized solvers, a basic design choice is whether to $\textit{reuse}$ the same sketch or draw $\textit{fresh}$ randomness at every step. For (under-constrained) iterative ridge regression with column sampling, whether fresh sketches offer provable advantages has remained open: $\textit{We show that they do.}$ Fresh sketching lets us analyze error only along the current residual solution, rather than uniformly over the entire Gram matrix. This directional view yields sharper convergence guarantees for leverage score and ridge leverage score sampling and, more importantly, leads to residual-aware sampling rules.