no code implementations • 15 Jul 2022 • Arvind V. Mahankali, David P. Woodruff, Ziyu Zhang
Our key technique is a method for obtaining subspace embeddings with a number of rows polynomial in $q$ for a matrix which is the flattening of a tensor train of $q$ tensors.
no code implementations • 1 Jan 2021 • Shuli Jiang, Dongyu Li, Irene Mengze Li, Arvind V. Mahankali, David Woodruff
We give a distributed protocol with nearly-optimal communication and number of rounds for Column Subset Selection with respect to the entrywise {$\ell_1$} norm ($k$-CSS$_1$), and more generally, for the $\ell_p$-norm with $1 \leq p < 2$.
no code implementations • 20 Jul 2020 • Arvind V. Mahankali, David P. Woodruff
We give the first polynomial time column subset selection-based $\ell_1$ low rank approximation algorithm sampling $\tilde{O}(k)$ columns and achieving an $\tilde{O}(k^{1/2})$-approximation for any $k$, improving upon the previous best $\tilde{O}(k)$-approximation and matching a prior lower bound for column subset selection-based $\ell_1$-low rank approximation which holds for any $\text{poly}(k)$ number of columns.