This work gives the first sublinear time classical algorithms for eigenvector approximation with additive error $\epsilon \|A\|_F$ and presents an alternative approach, based on a truncated Nystrom method, that achieves near optimal sample complexity for general symmetric matrices, and improved bounds for positive semi...
CAST (Canonical Approximate Schur Tree) is introduced, which replaces this clique with a weighted random spanning tree sampled directly from it, and it is proved that its leverage-score marginals minimize the largest normalized reweighted-edge contribution among unbiased inverse-marginal one-tree estimators.
Meher Chaitanya, Cameron Musco, A. Gionis· 1 citation
It is proved that sketching dimension m = O(k^{3/2}/\epsilon^2) suffices for subspace embedding with a Khatri-Rao sketching matrix with any fixed order $d$.
We describe a simple rejection-sampling-based algorithm to perform length-squared sampling on an $n \times n$ positive-semidefinite (psd) matrix: that is, to sample a column with probability proportional to its squared $\ell_2$-norm. The algorithm runs in just $O(n)$ expected time, which is significantly sublinear in t...
Rajarshi Bhattacharjee, Ethan N. Epperly, Cameron Musco et al.· 0 citations
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