# A geometric characterisation of sensitivity analysis in monomial models

arXiv: https://arxiv.org/abs/1901.02058 · HTML: https://mlsanity.com/paper/1901.02058/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2018.

## Built on by (most cited first, 6 of 6)

- [Sensitivity and robustness analysis in Bayesian networks with the bnmonitor R package](https://mlsanity.com/paper/2107.11785/) (2021)
- [You Only Derive Once (YODO): Automatic Differentiation for Efficient Sensitivity Analysis in Bayesian Networks](https://mlsanity.com/paper/2206.08687/) (2022)
- [The YODO algorithm: An efficient computational framework for sensitivity analysis in Bayesian networks](https://mlsanity.com/paper/2302.00364/) (2023)
- [Global Sensitivity Analysis of Uncertain Parameters in Bayesian Networks](https://mlsanity.com/paper/2406.05764/) (2024)
- [The diameter of a stochastic matrix: A new measure for sensitivity analysis in Bayesian networks](https://mlsanity.com/paper/2407.04667/) (2024)
- [Global sensitivity analysis in probabilistic graphical models](https://mlsanity.com/paper/2110.03749/) (2021)

## Abstract (arXiv)

Sensitivity analysis in probabilistic discrete graphical models is usually conducted by varying one probability value at a time and observing how this affects output probabilities of interest. When one probability is varied then others are proportionally covaried to respect the sum-to-one condition of probability laws. The choice of proportional covariation is justified by a variety of optimality conditions, under which the original and the varied distributions are as close as possible under different measures of closeness. For variations of more than one parameter at a time proportional covariation is justified in some special cases only. In this work, for the large class of discrete statistical models entertaining a regular monomial parametrisation, we demonstrate the optimality of newly defined proportional multi-way schemes with respect to an optimality criterion based on the notion of I-divergence. We demonstrate that there are varying parameters choices for which proportional covariation is not optimal and identify the sub-family of model distributions where the distance between the original distribution and the one where probabilities are covaried proportionally is minimum. This is shown by adopting a new formal, geometric characterization of sensitivity analysis in monomial models, which include a wide array of probabilistic graphical models. We also demonstrate the optimality of proportional covariation for multi-way analyses in Naive Bayes classifiers.