2021 journal article
Multiplicative perturbation bounds for multivariate multiple linear regression in Schatten p-norms
Linear Algebra Appl., 624, 87–102.
author keywords: Projector Multiplicative perturbations; Moore Penrose inverse; Schatten p-norms; Multivariate multiple linear; regression
TL;DR:
This work extends recent MLR analyses to sketched MMLR in general Schatten $p-norms by interpreting the sketched problem as a multiplicative perturbation, and derives expressions for the exact and perturbed solutions in terms of projectors for easy geometric interpretation.
(via Semantic Scholar)
open access via arxiv.org (repository)
Source: ORCID
Added: May 1, 2021
Multivariate multiple linear regression (MMLR), which occurs in a number of practical applications, generalizes traditional least squares (multivariate linear regression) to multiple right-hand sides. We extend recent MLR analyses to sketched MMLR in general Schatten p-norms by interpreting the sketched problem as a multiplicative perturbation. Our work represents an extension of Maher's results on Schatten p-norms. We derive expressions for the exact and perturbed solutions in terms of projectors for easy geometric interpretation. We also present a geometric interpretation of the action of the sketching matrix in terms of relevant subspaces. We show that a key term in assessing the accuracy of the sketched MMLR solution can be viewed as a tangent of a largest principal angle between subspaces under some assumptions. Our results enable additional interpretation of the difference between an orthogonal and oblique projector with the same range.