Works (3)
Updated: July 5th, 2023 15:40
2018 journal article
A PROBABILISTIC SUBSPACE BOUND WITH APPLICATION TO ACTIVE SUBSPACES
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 39(3), 1208–1220.
Contributors: *, I. Ipsen n & R. Smith n
author keywords: positive semidefinite matrices; principal angles; eigenvalue decomposition; eigen-value gaps; matrix concentration inequality; intrinsic dimension; Monte Carlo sampling; active sub-spaces
TL;DR:
This work presents a bound on the number of samples so that with high probability the angle between the dominant subspaces of E and S is less than a user-specified tolerance, and suggests that Monte Carlo sampling can be efficient in the presence of many parameters, as long as the underlying function f is sufficiently smooth.
(via Semantic Scholar)
open access via arxiv.org (repository)
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Sources: Web Of Science, ORCID, NC State University Libraries
Added: January 7, 2019
2015 journal article
CONDITIONING OF LEVERAGE SCORES AND COMPUTATION BY QR DECOMPOSITION
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 36(3), 1143–1163.
Contributors: n, I. Ipsen n & T. Wentworth*
author keywords: principal angles; stable rank; condition number; row-scaling; componentwise perturbations
TL;DR:
The leverage scores of a full-column rank matrix A are the squared row norms of any orthonormal basis for range(A) and it is shown that corresponding leverage Scores of two matrices A and A + \Delta A are close in the relative sense, if they have large magnitude and if all principal angles between the column spaces of A & A are small.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2015 journal article
RANDOMIZED APPROXIMATION OF THE GRAM MATRIX: EXACT COMPUTATION AND PROBABILISTIC BOUNDS
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 36(1), 110–137.
Contributors: n & I. Ipsen n
author keywords: leverage scores; singular value decomposition; stable rank; coherence; matrix concentration inequalities; unbiased estimator
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
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