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Cybernetics and Systems Analysis

, Volume 55, Issue 2, pp 174–185 | Cite as

Upper Bound on the Sum of Correlations of Three Indicators Under the Absence of a Common Factor

  • O. S. BalabanovEmail author
Article
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Abstract

It is shown that, in a linear model with three indicator variables where each pair of indicators has a separate hidden “paired” factor, and the sum of three correlations is upper bounded. A violation of an established inequality constraint testifies that the causal structure of a generative model differs from the supposed one. When such a constraint is violated, it is arguable that there is a common cause of these three indicators or that one of them causally influences another. An inequality constraint can be efficiently used even under incomplete observability (in particular, when only two indicator variables are observed).

Keywords

correlation inequality constraint cycle with three colliders hidden common cause linear structural equation model 

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References

  1. 1.
    Ch. Kang and J. Tian, “Inequality constraints in causal models with hidden variables,” in: Proc. 22nd Conf. on Uncertainty in Artificial Intelligence (UAI-06), AUAI Press (2006), pp. 233–240.Google Scholar
  2. 2.
    G. V. Steeg and A. Galstyan, “A sequence of relaxations constraining hidden variable models,” in: Proc. 27th Conf. on Uncertainty in Artif. Intel. (UAI-11), AUAI Press (2011), pp. 717–726.Google Scholar
  3. 3.
    B. Steudel and N. Ay, “Information-theoretic inference of common ancestors,” Entropy, Vol. 17, 2304–2327 (2015).MathSciNetCrossRefGoogle Scholar
  4. 4.
    B. Chen, J. Tian, and J. Pearl, “Testable implications of linear structural equation models,” in: Proc. 28th AAAI Conf. on Artif. Intel. (AAAI’14), AAAI Press Quebec, Canada (2014), pp. 2424–2430.Google Scholar
  5. 5.
    T. van Ommen and J. M. Mooij, “Algebraic equivalence class selection for linear structural equation models,” in: Proc. 33rd Conf. on Uncertainty in Artif. Intel. (UAI-17), Vol. 1, Curran Associates, Inc. (2017), pp. 763–773.Google Scholar
  6. 6.
    P. Spirtes and T. Richardson, “Ancestral graph Markov models,” Ann. Statist., Vol. 30, No. 4, 962–1030 (2002).Google Scholar
  7. 7.
    O. S. Balabanov, “Structurally determined inequality constraints on correlations in the cycle of linear dependencies,” Cybernetics and Systems Analysis, Vol. 54, No 2, 173–184 (2018).Google Scholar
  8. 8.
    R. D. Gill, “Statistics, causality and Bell’s theorem,” Statistical Science, Vol. 29, No. 4, 512–528 (2014).MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    P. Suppes, J. A. de Barros, and G. Oas, “A collection of probabilistic hidden-variable theorems and counterexamples,” In: R. Pratesi and E. Ronchi (eds.), Waves, Information and Foundations of Physics, Conf. Proceeding, Vol. 60, Società Italiana Di Fisica, Bologna (1998), pp. 267–291 (arXiv:quant-ph/9610010).Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Software SystemsNational Academy of Sciences of UkraineKyivUkraine

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