A 'propagative' approach to sensitivity analysis

It is shown that the computational cost of traditional approaches to sensitivity analysis is logically unnecessary and can be largely avoided by propagating and combining sensitivities during a computation, rather than recomputing them.

Abstract

It is shown that the computational cost of traditional approaches to sensitivity analysis is logically unnecessary and can be largely avoided by propagating and combining sensitivities during a computation, rather than recomputing them. This propagative approach to sensitivity analysis is described and the algorithm implemented to explore its potential is presented. Initial results indicate that this approach has tremendous potential, reducing a combinatorial process to a linear one. In addition, it is noted that the approach has implications beyond sensitivity analysis: it suggests a novel computational paradigm in which functions replace themselves by approximations when they are first called and these approximations are used for the remainder of a computation, e.g. to improve performance. Sensitivity analysis is simply one instance of this approach, using linear approximations based on partial derivatives; however, the approach and the computational environment implemented allow arbitrary approximations to be used.>