Adjoint Differentiation for generic matrix functions
Computational Finance
2021-09-13 v1 Symbolic Computation
Risk Management
Abstract
We derive a formula for the adjoint of a square-matrix operation of the form , where is holomorphic in the neighborhood of each eigenvalue. We then apply the formula to derive closed-form expressions in particular cases of interest such as the case when we have a spectral decomposition , the spectrum cut-off and the Nearest Correlation Matrix routine. Finally, we explain how to simplify the computation of adjoints for regularized linear regression coefficients.
Cite
@article{arxiv.2109.04913,
title = {Adjoint Differentiation for generic matrix functions},
author = {Andrei Goloubentsev and Dmitri Goloubentsev and Evgeny Lakshtanov},
journal= {arXiv preprint arXiv:2109.04913},
year = {2021}
}