On Different Notions of Redundancy in Conditional-Independence-Based Discovery of Graphical Models

Philipp Michael Faller, Dominik Janzing
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:1027-1035, 2026.

Abstract

Conditional-independence-based discovery uses statistical tests to identify a graphical model that represents the independence structure of variables in a dataset. These test, however, can be unreliable and algorithms are sensitive to errors and violated assumptions. Often there are tests that were not used in the construction of the graph. In this work, we show that these \emph{redundant} tests have the potential to \emph{detect} or sometimes \emph{correct} errors in the learned model. But we further show that not all tests contain this additional information and that such redundant tests have to be applied with care. Precisely, we argue that the conditional (in)dependence statements that hold for every probability distribution are unlikely to detect and correct errors - in contrast to those that follow only from graphical assumptions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-faller26b, title = { On Different Notions of Redundancy in Conditional-Independence-Based Discovery of Graphical Models }, author = {Faller, Philipp Michael and Janzing, Dominik}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {1027--1035}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/faller26b/faller26b.pdf}, url = {https://proceedings.mlr.press/v300/faller26b.html}, abstract = { Conditional-independence-based discovery uses statistical tests to identify a graphical model that represents the independence structure of variables in a dataset. These test, however, can be unreliable and algorithms are sensitive to errors and violated assumptions. Often there are tests that were not used in the construction of the graph. In this work, we show that these \emph{redundant} tests have the potential to \emph{detect} or sometimes \emph{correct} errors in the learned model. But we further show that not all tests contain this additional information and that such redundant tests have to be applied with care. Precisely, we argue that the conditional (in)dependence statements that hold for every probability distribution are unlikely to detect and correct errors - in contrast to those that follow only from graphical assumptions. } }
Endnote
%0 Conference Paper %T On Different Notions of Redundancy in Conditional-Independence-Based Discovery of Graphical Models %A Philipp Michael Faller %A Dominik Janzing %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-faller26b %I PMLR %P 1027--1035 %U https://proceedings.mlr.press/v300/faller26b.html %V 300 %X Conditional-independence-based discovery uses statistical tests to identify a graphical model that represents the independence structure of variables in a dataset. These test, however, can be unreliable and algorithms are sensitive to errors and violated assumptions. Often there are tests that were not used in the construction of the graph. In this work, we show that these \emph{redundant} tests have the potential to \emph{detect} or sometimes \emph{correct} errors in the learned model. But we further show that not all tests contain this additional information and that such redundant tests have to be applied with care. Precisely, we argue that the conditional (in)dependence statements that hold for every probability distribution are unlikely to detect and correct errors - in contrast to those that follow only from graphical assumptions.
APA
Faller, P.M. & Janzing, D.. (2026). On Different Notions of Redundancy in Conditional-Independence-Based Discovery of Graphical Models . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:1027-1035 Available from https://proceedings.mlr.press/v300/faller26b.html.

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