A Combinatorial Solution to Causal Compatibility
Within the field of causal inference, it is desirable to learn the structure of causal relationships holding between a system of variables from the correlations that these variables exhibit; a sub-problem of which is to certify whether or not a given causal hypothesis is compatible with the observed...
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| Format: | Article |
| Language: | English |
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De Gruyter
2020-07-01
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| Series: | Journal of Causal Inference |
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| Online Access: | https://doi.org/10.1515/jci-2019-0013 |
| _version_ | 1818582150899826688 |
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| author | Fraser Thomas C. |
| author_facet | Fraser Thomas C. |
| author_sort | Fraser Thomas C. |
| collection | DOAJ |
| description | Within the field of causal inference, it is desirable to learn the structure of causal relationships holding between a system of variables from the correlations that these variables exhibit; a sub-problem of which is to certify whether or not a given causal hypothesis is compatible with the observed correlations. A particularly challenging setting for assessing causal compatibility is in the presence of partial information; i.e. when some of the variables are hidden/latent. This paper introduces the possible worlds framework as a method for deciding causal compatibility in this difficult setting. We define a graphical object called a possible worlds diagram, which compactly depicts the set of all possible observations. From this construction, we demonstrate explicitly, using several examples, how to prove causal incompatibility. In fact, we use these constructions to prove causal incompatibility where no other techniques have been able to. Moreover, we prove that the possible worlds framework can be adapted to provide a complete solution to the possibilistic causal compatibility problem. Even more, we also discuss how to exploit graphical symmetries and cross-world consistency constraints in order to implement a hierarchy of necessary compatibility tests that we prove converges to sufficiency. |
| first_indexed | 2024-12-16T07:44:49Z |
| format | Article |
| id | doaj.art-03413a7f60374465855a3212c8062fdb |
| institution | Directory Open Access Journal |
| issn | 2193-3677 2193-3685 |
| language | English |
| last_indexed | 2024-12-16T07:44:49Z |
| publishDate | 2020-07-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Journal of Causal Inference |
| spelling | doaj.art-03413a7f60374465855a3212c8062fdb2022-12-21T22:38:59ZengDe GruyterJournal of Causal Inference2193-36772193-36852020-07-0181225310.1515/jci-2019-0013jci-2019-0013A Combinatorial Solution to Causal CompatibilityFraser Thomas C.0Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada, N2L 2Y5Within the field of causal inference, it is desirable to learn the structure of causal relationships holding between a system of variables from the correlations that these variables exhibit; a sub-problem of which is to certify whether or not a given causal hypothesis is compatible with the observed correlations. A particularly challenging setting for assessing causal compatibility is in the presence of partial information; i.e. when some of the variables are hidden/latent. This paper introduces the possible worlds framework as a method for deciding causal compatibility in this difficult setting. We define a graphical object called a possible worlds diagram, which compactly depicts the set of all possible observations. From this construction, we demonstrate explicitly, using several examples, how to prove causal incompatibility. In fact, we use these constructions to prove causal incompatibility where no other techniques have been able to. Moreover, we prove that the possible worlds framework can be adapted to provide a complete solution to the possibilistic causal compatibility problem. Even more, we also discuss how to exploit graphical symmetries and cross-world consistency constraints in order to implement a hierarchy of necessary compatibility tests that we prove converges to sufficiency.https://doi.org/10.1515/jci-2019-0013causal inferencecausal compatibilityquantum non-classicality |
| spellingShingle | Fraser Thomas C. A Combinatorial Solution to Causal Compatibility Journal of Causal Inference causal inference causal compatibility quantum non-classicality |
| title | A Combinatorial Solution to Causal Compatibility |
| title_full | A Combinatorial Solution to Causal Compatibility |
| title_fullStr | A Combinatorial Solution to Causal Compatibility |
| title_full_unstemmed | A Combinatorial Solution to Causal Compatibility |
| title_short | A Combinatorial Solution to Causal Compatibility |
| title_sort | combinatorial solution to causal compatibility |
| topic | causal inference causal compatibility quantum non-classicality |
| url | https://doi.org/10.1515/jci-2019-0013 |
| work_keys_str_mv | AT fraserthomasc acombinatorialsolutiontocausalcompatibility AT fraserthomasc combinatorialsolutiontocausalcompatibility |