Faithful graphical representations of local independence

Søren W. Mogensen
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:2989-2997, 2024.

Abstract

Graphical models use graphs to represent conditional independence structure in the distribution of a random vector. In stochastic processes, graphs may represent so-called local independence or conditional Granger causality. Under some regularity conditions, a local independence graph implies a set of independences using a graphical criterion known as delta-separation, or using its generalization, mu-separation. This is a stochastic process analogue of d-separation in DAGs. However, there may be more independences than implied by this graph and this is a violation of so-called faithfulness. We characterize faithfulness in local independence graphs and give a method to construct a faithful graph from any local independence model such that the output equals the true graph when Markov and faithfulness assumptions hold. We discuss various assumptions that are weaker than faithfulness, and we explore different structure learning algorithms and their properties under varying assumptions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-mogensen24a, title = {Faithful graphical representations of local independence}, author = {Mogensen, S\o{}ren W.}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {2989--2997}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/mogensen24a/mogensen24a.pdf}, url = {https://proceedings.mlr.press/v238/mogensen24a.html}, abstract = {Graphical models use graphs to represent conditional independence structure in the distribution of a random vector. In stochastic processes, graphs may represent so-called local independence or conditional Granger causality. Under some regularity conditions, a local independence graph implies a set of independences using a graphical criterion known as delta-separation, or using its generalization, mu-separation. This is a stochastic process analogue of d-separation in DAGs. However, there may be more independences than implied by this graph and this is a violation of so-called faithfulness. We characterize faithfulness in local independence graphs and give a method to construct a faithful graph from any local independence model such that the output equals the true graph when Markov and faithfulness assumptions hold. We discuss various assumptions that are weaker than faithfulness, and we explore different structure learning algorithms and their properties under varying assumptions.} }
Endnote
%0 Conference Paper %T Faithful graphical representations of local independence %A Søren W. Mogensen %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-mogensen24a %I PMLR %P 2989--2997 %U https://proceedings.mlr.press/v238/mogensen24a.html %V 238 %X Graphical models use graphs to represent conditional independence structure in the distribution of a random vector. In stochastic processes, graphs may represent so-called local independence or conditional Granger causality. Under some regularity conditions, a local independence graph implies a set of independences using a graphical criterion known as delta-separation, or using its generalization, mu-separation. This is a stochastic process analogue of d-separation in DAGs. However, there may be more independences than implied by this graph and this is a violation of so-called faithfulness. We characterize faithfulness in local independence graphs and give a method to construct a faithful graph from any local independence model such that the output equals the true graph when Markov and faithfulness assumptions hold. We discuss various assumptions that are weaker than faithfulness, and we explore different structure learning algorithms and their properties under varying assumptions.
APA
Mogensen, S.W.. (2024). Faithful graphical representations of local independence. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:2989-2997 Available from https://proceedings.mlr.press/v238/mogensen24a.html.

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