John Thomas Holodnak

Works (3)

Updated: July 5th, 2023 15:40

2018 article

A Probabilistic Subspace Bound with Application to Active Subspaces

Holodnak, J. T., Ipsen, I. C. F., & Smith, R. C. (2018, January 1). SIAM Journal on Matrix Analysis and Applications, Vol. 39, pp. 1208–1220.

By: J. Holodnak*, I. Ipsen*  & R. Smith* 

Contributors: J. Holodnak*, I. Ipsen*  & R. Smith* 

author keywords: positive semidefinite matrices; principal angles; eigenvalue decomposition; eigen-value gaps; matrix concentration inequality; intrinsic dimension; Monte Carlo sampling; active sub-spaces
topics (OpenAlex): Sparse and Compressive Sensing Techniques; Stochastic Gradient Optimization Techniques; Matrix Theory and Algorithms
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)
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Sources: Web Of Science, ORCID, NC State University Libraries
Added: January 7, 2019

2015 article

Conditioning of Leverage Scores and Computation by QR Decomposition

Holodnak, J. T., Ipsen, I. C. F., & Wentworth, T. A. (2015, January 1). SIAM Journal on Matrix Analysis and Applications, Vol. 36, pp. 1143–1163.

By: J. Holodnak*, I. Ipsen*  & T. Wentworth

Contributors: J. Holodnak*, I. Ipsen*  & T. Wentworth

author keywords: principal angles; stable rank; condition number; row-scaling; componentwise perturbations
topics (OpenAlex): Sparse and Compressive Sensing Techniques; Matrix Theory and Algorithms; Advanced Optimization Algorithms Research
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 article

Randomized Approximation of the Gram Matrix: Exact Computation and Probabilistic Bounds

Holodnak, J. T., & Ipsen, I. C. F. (2015, January 1). SIAM Journal on Matrix Analysis and Applications, Vol. 36, pp. 110–137.

By: J. Holodnak* & I. Ipsen* 

Contributors: J. Holodnak* & I. Ipsen* 

author keywords: leverage scores; singular value decomposition; stable rank; coherence; matrix concentration inequalities; unbiased estimator
topics (OpenAlex): Matrix Theory and Algorithms; Sparse and Compressive Sensing Techniques; Stochastic Gradient Optimization Techniques
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

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