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Randomly Pivoted Partial Cholesky: Random How?
April 18, 2024, 4:43 a.m. | Stefan Steinerberger
stat.ML updates on arXiv.org arxiv.org
Abstract: We consider the problem of finding good low rank approximations of symmetric, positive-definite $A \in \mathbb{R}^{n \times n}$. Chen-Epperly-Tropp-Webber showed, among many other things, that the randomly pivoted partial Cholesky algorithm that chooses the $i-$th row with probability proportional to the diagonal entry $A_{ii}$ leads to a universal contraction of the trace norm (the Schatten 1-norm) in expectation for each step. We show that if one chooses the $i-$th row with likelihood proportional to $A_{ii}^2$ …
abstract algorithm arxiv chen cs.na good leads low math.na positive probability random stat.ml type universal
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