In this work, we discuss the Automatic Adjoint Differentiation (AAD) for functions of the form [Formula: see text], which often appear in the calibration of stochastic models. We demonstrate that it allows a perfect SIMD a parallelization and provides its relative computational cost. In addition, we demonstrate that this theoretical result is in concordance with numerical experiments. a Single Input Multiple Data.
We derive a formula for the adjoint 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 = U DU −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.
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