Parameter Sensitivity Analysis in Mixtures of Polynomials

Ángel Tomás Sáez-Ruiz, Rafael Rumı́, Ana D. Maldonado
Proceedings of the 13th International Conference on Probabilistic Graphical Models, PMLR 343:797-817, 2026.

Abstract

Parameter sensitivity analysis examines how a model is affected when some of its parameters are changed. In this study, we consider Mixtures of Polynomial (MoP) models to represent the probability distributions of continuous variables in Bayesian networks (BN). The objective of this study is to analyse the difference between a MoP density function and its perturbed versions, and how these perturbations propagate to other variables in the BN. A sensitivity measure, which is based on $L^1$ distance, is defined to compare the original distribution and the obtained distribution after perturbation. The theoretical results indicate that the sensitivity measure of a marginal distribution is at most the same as the sensitivity measure of the perturbed density. Overall, perturbations in local distributions of MoP Bayesian networks propagate to marginal distributions with decreasing intensity —meaning that their effect on marginal distributions of descendant variables becomes progressively weaker— which suggests that sensitivity analysis should primarily focus on local components.

Cite this Paper

BibTeX
@InProceedings{pmlr-v343-saez-ruiz26a, title = {Parameter Sensitivity Analysis in Mixtures of Polynomials}, author = {S{\'a}ez-Ruiz, {\'A}ngel Tom{\'a}s and Rum{\'\i}, Rafael and Maldonado, Ana D.}, booktitle = {Proceedings of the 13th International Conference on Probabilistic Graphical Models}, pages = {797--817}, year = {2026}, editor = {Camps-Valls, Gustau and Leonelli, Manuele and Varando, Gherardo}, volume = {343}, series = {Proceedings of Machine Learning Research}, month = {09--11 Sep}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v343/main/assets/saez-ruiz26a/saez-ruiz26a.pdf}, url = {https://proceedings.mlr.press/v343/saez-ruiz26a.html}, abstract = {Parameter sensitivity analysis examines how a model is affected when some of its parameters are changed. In this study, we consider Mixtures of Polynomial (MoP) models to represent the probability distributions of continuous variables in Bayesian networks (BN). The objective of this study is to analyse the difference between a MoP density function and its perturbed versions, and how these perturbations propagate to other variables in the BN. A sensitivity measure, which is based on $L^1$ distance, is defined to compare the original distribution and the obtained distribution after perturbation. The theoretical results indicate that the sensitivity measure of a marginal distribution is at most the same as the sensitivity measure of the perturbed density. Overall, perturbations in local distributions of MoP Bayesian networks propagate to marginal distributions with decreasing intensity —meaning that their effect on marginal distributions of descendant variables becomes progressively weaker— which suggests that sensitivity analysis should primarily focus on local components.} }
Endnote
%0 Conference Paper %T Parameter Sensitivity Analysis in Mixtures of Polynomials %A Ángel Tomás Sáez-Ruiz %A Rafael Rumı́ %A Ana D. Maldonado %B Proceedings of the 13th International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2026 %E Gustau Camps-Valls %E Manuele Leonelli %E Gherardo Varando %F pmlr-v343-saez-ruiz26a %I PMLR %P 797--817 %U https://proceedings.mlr.press/v343/saez-ruiz26a.html %V 343 %X Parameter sensitivity analysis examines how a model is affected when some of its parameters are changed. In this study, we consider Mixtures of Polynomial (MoP) models to represent the probability distributions of continuous variables in Bayesian networks (BN). The objective of this study is to analyse the difference between a MoP density function and its perturbed versions, and how these perturbations propagate to other variables in the BN. A sensitivity measure, which is based on $L^1$ distance, is defined to compare the original distribution and the obtained distribution after perturbation. The theoretical results indicate that the sensitivity measure of a marginal distribution is at most the same as the sensitivity measure of the perturbed density. Overall, perturbations in local distributions of MoP Bayesian networks propagate to marginal distributions with decreasing intensity —meaning that their effect on marginal distributions of descendant variables becomes progressively weaker— which suggests that sensitivity analysis should primarily focus on local components.
APA
Sáez-Ruiz, Á.T., Rumı́, R. & Maldonado, A.D.. (2026). Parameter Sensitivity Analysis in Mixtures of Polynomials. Proceedings of the 13th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 343:797-817 Available from https://proceedings.mlr.press/v343/saez-ruiz26a.html.

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