Revisiting the general identifiability problem

Yaroslav Kivva, Ehsan Mokhtarian, Jalal Etesami, Negar Kiyavash
Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, PMLR 180:1022-1030, 2022.

Abstract

We revisit the problem of general identifiability originally introduced in [Lee et al., 2019] for causal inference and note that it is necessary to add positivity assumption of observational distribution to the original definition of the problem. We show that without such an assumption the rules of do-calculus and consequently the proposed algorithm in [Lee et al., 2019] are not sound. Moreover, adding the assumption will cause the completeness proof in [Lee et al., 2019] to fail. Under positivity assumption, we present a new algorithm that is provably both sound and complete. A nice property of this new algorithm is that it establishes a connection between general identifiability and classical identifiability by Pearl [1995] through decomposing the general identifiability problem into a series of classical identifiability sub-problems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v180-kivva22a, title = {Revisiting the general identifiability problem}, author = {Kivva, Yaroslav and Mokhtarian, Ehsan and Etesami, Jalal and Kiyavash, Negar}, booktitle = {Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence}, pages = {1022--1030}, year = {2022}, editor = {Cussens, James and Zhang, Kun}, volume = {180}, series = {Proceedings of Machine Learning Research}, month = {01--05 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v180/kivva22a/kivva22a.pdf}, url = {https://proceedings.mlr.press/v180/kivva22a.html}, abstract = {We revisit the problem of general identifiability originally introduced in [Lee et al., 2019] for causal inference and note that it is necessary to add positivity assumption of observational distribution to the original definition of the problem. We show that without such an assumption the rules of do-calculus and consequently the proposed algorithm in [Lee et al., 2019] are not sound. Moreover, adding the assumption will cause the completeness proof in [Lee et al., 2019] to fail. Under positivity assumption, we present a new algorithm that is provably both sound and complete. A nice property of this new algorithm is that it establishes a connection between general identifiability and classical identifiability by Pearl [1995] through decomposing the general identifiability problem into a series of classical identifiability sub-problems.} }
Endnote
%0 Conference Paper %T Revisiting the general identifiability problem %A Yaroslav Kivva %A Ehsan Mokhtarian %A Jalal Etesami %A Negar Kiyavash %B Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2022 %E James Cussens %E Kun Zhang %F pmlr-v180-kivva22a %I PMLR %P 1022--1030 %U https://proceedings.mlr.press/v180/kivva22a.html %V 180 %X We revisit the problem of general identifiability originally introduced in [Lee et al., 2019] for causal inference and note that it is necessary to add positivity assumption of observational distribution to the original definition of the problem. We show that without such an assumption the rules of do-calculus and consequently the proposed algorithm in [Lee et al., 2019] are not sound. Moreover, adding the assumption will cause the completeness proof in [Lee et al., 2019] to fail. Under positivity assumption, we present a new algorithm that is provably both sound and complete. A nice property of this new algorithm is that it establishes a connection between general identifiability and classical identifiability by Pearl [1995] through decomposing the general identifiability problem into a series of classical identifiability sub-problems.
APA
Kivva, Y., Mokhtarian, E., Etesami, J. & Kiyavash, N.. (2022). Revisiting the general identifiability problem. Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 180:1022-1030 Available from https://proceedings.mlr.press/v180/kivva22a.html.

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