Adjoint Differentiation for generic matrix functions

Andrei Goloubentsev, Dmitri Goloubentsev and Evgeny Lakshtanov

Papers from arXiv.org

Abstract: We derive a formula for the adjoint $\overline{A}$ of a square-matrix operation of the form $C=f(A)$, where $f$ 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 $A=UDU^{-1}$, the spectrum cut-off $C=A_+$ and the Nearest Correlation Matrix routine. Finally, we explain how to simplify the computation of adjoints for regularized linear regression coefficients.

Date: 2021-09
New Economics Papers: this item is included in nep-isf
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