Useful Compact Representations for Data-Fitting

• URL: http://arxiv.org/abs/2403.12206v2
• Date: Sat, 18 Jan 2025 06:39:40 GMT
• Title: Useful Compact Representations for Data-Fitting
• Authors: Johannes J. Brust,
• Abstract summary: We develop new compact representations that are parameterized by a choice of vectors and that reduce to existing well known formulas for special choices. We demonstrate effectiveness of the compact representations for large eigenvalue computations, tensor factorizations and nonlinear regressions.
• Score: 0.0
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• Abstract: For minimization problems without 2nd derivative information, methods that estimate Hessian matrices can be very effective. However, conventional techniques generate dense matrices that are prohibitive for large problems. Limited-memory compact representations express the dense arrays in terms of a low rank representation and have become the state-of-the-art for software implementations on large deterministic problems. We develop new compact representations that are parameterized by a choice of vectors and that reduce to existing well known formulas for special choices. We demonstrate effectiveness of the compact representations for large eigenvalue computations, tensor factorizations and nonlinear regressions.

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