Sensitivity analysis beyond linearity

Leonelli, M. (2019) Sensitivity analysis beyond linearity. International Journal of Approximate Reasoning, 113, pp. 106-118. (doi: 10.1016/j.ijar.2019.06.007)

Abstract

A wide array of graphical models can be parametrized to have atomic probabilities represented by monomial functions. Such a monomial structure has proven very useful when studying robustness under the assumption of a multilinear model where all monomials have either zero or one exponents. Robustness in probabilistic graphical models is usually investigated by varying some of the input probabilities and observing the effects of these on output probabilities of interest. Here the assumption of multilinearity is relaxed and a general approach for one-way sensitivity analysis in non-multilinear models is presented. It is shown that in non-multilinear models sensitivity functions have a polynomial form, conversely to multilinear models where these are simply linear. The form of various divergences and distances under different covariation schemes is also formally derived. Proportional covariation is proven to be optimal in non-multilinear models under some specific choices of varied parameters. The methodology is illustrated throughout by an educational application.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Leonelli, Dr Manuele
• Authors: Leonelli, M.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Journal Name: International Journal of Approximate Reasoning
• Publisher: Elsevier
• ISSN: 0888-613X
• ISSN (Online): 1873-4731
• Published Online: 03 July 2019
• Copyright Holders: Copyright © 2019 Elsevier Inc.
• First Published: First published in International Journal of Approximate Reasoning 113:106-118
• Publisher Policy: Reproduced in accordance with the publisher copyright policy