# Sensitivity analysis beyond linearity

arXiv: https://arxiv.org/abs/1901.02062 · HTML: https://mlsanity.com/paper/1901.02062/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2018.

## Built on by (most cited first, 7 of 7)

- [Context-Specific Causal Discovery for Categorical Data Using Staged Trees](https://mlsanity.com/paper/2106.04416/) (2021)
- [Staged trees and asymmetry-labeled DAGs](https://mlsanity.com/paper/2108.01994/) (2021)
- [Structural Learning of Simple Staged Trees](https://mlsanity.com/paper/2203.04390/) (2022)
- [The YODO algorithm: An efficient computational framework for sensitivity analysis in Bayesian networks](https://mlsanity.com/paper/2302.00364/) (2023)
- [Learning Staged Trees from Incomplete Data](https://mlsanity.com/paper/2405.18306/) (2024)
- [Finding an ε-close Variation of Parameters in Bayesian Networks](https://mlsanity.com/paper/2305.10051/) (2023)
- [Estimating Staged Event Tree Models via Hierarchical Clustering on the Simplex](https://mlsanity.com/paper/2603.15568/) (2026)

## Abstract (arXiv)

A wide array of graphical models can be parametrised to have atomic probabilities represented by monomial functions. Such monomial structure has proven very useful when studying robustness under the assumption of a multilinear model where all monomial 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 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.