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65th Annual Meeting of the German Association for Medical Informatics, Biometry and Epidemiology (GMDS), Meeting of the Central European Network (CEN: German Region, Austro-Swiss Region and Polish Region) of the International Biometric Society (IBS)

06.09. - 09.09.2020, Berlin (online conference)

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The hardness of conditional independence testing

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  • Jonas Peters - University of Copenhagen, Copenhagen, Denmark
  • Rajen Shah - University of Cambridge, Cambridge, United Kingdom

Deutsche Gesellschaft für Medizinische Informatik, Biometrie und Epidemiologie. 65th Annual Meeting of the German Association for Medical Informatics, Biometry and Epidemiology (GMDS), Meeting of the Central European Network (CEN: German Region, Austro-Swiss Region and Polish Region) of the International Biometric Society (IBS). Berlin, 06.-09.09.2020. Düsseldorf: German Medical Science GMS Publishing House; 2021. DocAbstr. 17

doi: 10.3205/20gmds051, urn:nbn:de:0183-20gmds0512

Published: February 26, 2021

© 2021 Peters et al.
This is an Open Access article distributed under the terms of the Creative Commons Attribution 4.0 License. See license information at http://creativecommons.org/licenses/by/4.0/.

Outline

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It is a common saying that testing for conditional independence, i.e., testing whether two random vectors X and Y are independent, given Z, is a hard statistical problem if Z is a continuous random variable (or vector). In this work, we prove that conditional independence is indeed a particularly difficult hypothesis to test for and is fundamentally harder than testing for unconditional independence, for example. Solving it requires carefully chosen assumptions on the data generating process. We also provide a conditional independence test, the generalised covariance measure (GCM), that is explicit about such assumptions.

The authors declare that they have no competing interests.

The authors declare that an ethics committee vote is not required.

Outline

References

1.
Shah R, Peters J. “The Hardness of Conditional Independence Testing and the Generalised Covariance Measure”. Annals of Statistics. Forthcoming.