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, suitably defined. Furthermore, local independence has been suggested as a useful independence concept for stochastic dynamical systems. There is, however, no well-developed theoretical framework for causal learning based on this notion of independence. We study independence models induced by directed graphs (DGs) and provide abstract graphoid properties 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 system, directed mixed graphs (DMGs) represent the marginalized local independence model, and we develop, under a faithfulness assumption, a sound and complete learning algorithm of the directed mixed equivalence graph (DMEG) as a summary of all Markov equivalent 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, suitably defined. Furthermore, local independence has been suggested as a useful independence concept for stochastic dynamical systems. There is, however, no well-developed theoretical framework for causal learning based on this notion of independence. We study independence models induced by directed graphs (DGs) and provide abstract graphoid properties 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 system, directed mixed graphs (DMGs) represent the marginalized local independence model, and we develop, under a faithfulness assumption, a sound and complete learning algorithm of the directed mixed equivalence graph (DMEG) as a summary of all Markov equivalent 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, suitably defined. Furthermore, local independence has been suggested as a useful independence concept for stochastic dynamical systems. There is, however, no well-developed theoretical framework for causal learning based on this notion of independence. We study independence models induced by directed graphs (DGs) and provide abstract graphoid properties 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 system, directed mixed graphs (DMGs) represent the marginalized local independence model, and we develop, under a faithfulness assumption, a sound and complete learning algorithm of the directed mixed equivalence graph (DMEG) as a summary of all Markov equivalent 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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