Causal Learning for Partially Observed Stochastic Dynamical Systems

Søren Wengel Mogensen, Daniel Malinsky, Niels Richard Hansen
Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, PMLR R16:349-359, 2018.

Abstract

Many models of dynamical systems have causal interpretations that support reasoning about the consequences of interventions, suita- bly defined. Furthermore, local independence has been suggested as a useful independence concept for stochastic dynamical systems. There is, however, no well-developed theore- tical framework for causal learning based on this notion of independence. We study inde- pendence models induced by directed graphs (DGs) and provide abstract graphoid proper- ties that guarantee that an independence model has the global Markov property w.r.t. a DG. We apply these results to It\^{}o diffusions and event processes. For a partially observed sys- tem, directed mixed graphs (DMGs) represent the marginalized local independence model, and we develop, under a faithfulness assump- tion, a sound and complete learning algo- rithm of the directed mixed equivalence graph (DMEG) as a summary of all Markov equiva- lent DMGs.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR16-mogensen18a, title = {Causal Learning for Partially Observed Stochastic Dynamical Systems}, author = {Mogensen, S{\o}ren Wengel and Malinsky, Daniel and Hansen, Niels Richard}, booktitle = {Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence}, pages = {349--359}, year = {2018}, editor = {Globerson, Amir and Silva, Ricardo}, volume = {R16}, series = {Proceedings of Machine Learning Research}, month = {06--10 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r16/main/assets/mogensen18a/mogensen18a.pdf}, url = {https://proceedings.mlr.press/r16/mogensen18a.html}, abstract = {Many models of dynamical systems have causal interpretations that support reasoning about the consequences of interventions, suita- bly defined. Furthermore, local independence has been suggested as a useful independence concept for stochastic dynamical systems. There is, however, no well-developed theore- tical framework for causal learning based on this notion of independence. We study inde- pendence models induced by directed graphs (DGs) and provide abstract graphoid proper- ties that guarantee that an independence model has the global Markov property w.r.t. a DG. We apply these results to It\^{}o diffusions and event processes. For a partially observed sys- tem, directed mixed graphs (DMGs) represent the marginalized local independence model, and we develop, under a faithfulness assump- tion, a sound and complete learning algo- rithm of the directed mixed equivalence graph (DMEG) as a summary of all Markov equiva- lent DMGs.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Causal Learning for Partially Observed Stochastic Dynamical Systems %A Søren Wengel Mogensen %A Daniel Malinsky %A Niels Richard Hansen %B Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2018 %E Amir Globerson %E Ricardo Silva %F pmlr-vR16-mogensen18a %I PMLR %P 349--359 %U https://proceedings.mlr.press/r16/mogensen18a.html %V R16 %X Many models of dynamical systems have causal interpretations that support reasoning about the consequences of interventions, suita- bly defined. Furthermore, local independence has been suggested as a useful independence concept for stochastic dynamical systems. There is, however, no well-developed theore- tical framework for causal learning based on this notion of independence. We study inde- pendence models induced by directed graphs (DGs) and provide abstract graphoid proper- ties that guarantee that an independence model has the global Markov property w.r.t. a DG. We apply these results to It\^{}o diffusions and event processes. For a partially observed sys- tem, directed mixed graphs (DMGs) represent the marginalized local independence model, and we develop, under a faithfulness assump- tion, a sound and complete learning algo- rithm of the directed mixed equivalence graph (DMEG) as a summary of all Markov equiva- lent DMGs. %Z Reissued by PMLR on 04 October 2026.
APA
Mogensen, S.W., Malinsky, D. & Hansen, N.R.. (2018). Causal Learning for Partially Observed Stochastic Dynamical Systems. Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R16:349-359 Available from https://proceedings.mlr.press/r16/mogensen18a.html. Reissued by PMLR on 04 October 2026.

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