Useful Compact Representations for Data-Fitting
<|reference_start|>Useful Compact Representations for Data-Fitting: 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.<|reference_end|>
@article{brust2024useful,
    title={Useful Compact Representations for Data-Fitting},
    author={Johannes J. Brust},
    journal={arXiv preprint arXiv:2403.12206},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.12206},
    primaryClass={math.OC cs.LG cs.NA math.NA stat.CO}
}