Advertisement

Brief Introduction to Causal Compositional Models

  • Radim JiroušekEmail author
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 622)

Abstract

When applying probabilistic models to support decision making processes, the users have to strictly distinguish whether the impact of their decision changes the considered situation or not. In the former case it means that they are planing to make an intervention, and its respective impact cannot be estimated from a usual stochastic model but one has to use a causal model. The present paper thoroughly explains the difference between conditioning, which can be computed from both usual stochastic model and a causal model, and computing the effect of intervention, which can only be computed from a causal model. In the paper a new type of causal models, so called compositional causal models are introduced. Its great advantage is that both conditioning and the result of intervention are computed in very similar ways in these models. On an example, the paper illustrates that like in Pearl’s causal networks, also in the described compositional models one can consider models with hidden variables.

Keywords

Bayesian Network Causal Relation Conditional Distribution Causal Model Hide Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This work was supported in part by the National Science Foundation of the Czech Republic by grant no. GACR 15-00215S.

References

  1. 1.
    Bína, V., Jiroušek, R.: Marginalization in multidimensional compositional models. Kybernetika 42(4), 405–422 (2006)Google Scholar
  2. 2.
    Bína, V., Jiroušek, R.: On computations with causal compositional models. Kybernetika 51(3), 525–539 (2015)MathSciNetGoogle Scholar
  3. 3.
    Dempster, A.P.: Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Stat. 38(2), 325–339 (1967)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Dubois, D., Prade, H.: Possibility Theory: An Approach to Computerized Processing of Uncertainty. Plenum Press, New York (1988)zbMATHCrossRefGoogle Scholar
  5. 5.
    Hagmayer, Y., Sloman, S., Lagnado, D., Waldmann, M.R.: Causal reasoning through intervention. In: Gopnik, A., Schulz, L. (eds.) Causal Learning: Psychology, Philosophy, and Computation, pp. 86–101. Oxford University Press, Oxford (2002)Google Scholar
  6. 6.
    Jensen, F.V.: Bayesian Networks and Decision Graphs. IEEE Computer Society Press, New York (2001)zbMATHCrossRefGoogle Scholar
  7. 7.
    Jiroušek, R.: Foundations of compositional model theory. Int. J. Gen. Syst. 40(6), 623–678 (2011)zbMATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Jiroušek, R.: Brief introduction to probabilistic compositional models. Uncertainty analusis in econometrics with applications. In: Huynh, V.N., Kreinovich, V., Sriboonchita, S., Suriya, K. (eds.) AISC 200, pp. 49–60. Springer, Berlin (2013)Google Scholar
  9. 9.
    Jiroušek, R.: On causal compositional models: simple examples. In: Laurent, A. et al. (eds.) Proceedings of the 15th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems. Part I, CCIS 442, Springer International Publishing, Switzerland, pp. 517–526 (2014)Google Scholar
  10. 10.
    Jiroušek, R., Kratochvíl, V.: Foundations of Compositional Models: structural properties. Int. J. Gen. Syst. 44(1), 2–25 (2015)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Jiroušek, R., Shenoy, P.P.: Compositional models in valuation-based systems. Int. J. Approx. Reason. 55(1), 277–293 (2014)CrossRefGoogle Scholar
  12. 12.
    Jiroušek, R., Vejnarová, J., Daniel, M.: Compositional models of belief functions. In: de Cooman, G., Vejnarová, J., Zaffalon, M. (eds.) Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications, Praha, pp. 243–252 (2007)Google Scholar
  13. 13.
    Lauritzen, S.L.: Graphical Models. Oxford University Press, Oxford (1996)Google Scholar
  14. 14.
    Malvestuto, F.M.: Equivalence of compositional expressions and independence relations in compositional models. Kybernetika 50(3), 322–362 (2014)zbMATHMathSciNetGoogle Scholar
  15. 15.
    Malvestuto, F.M.: Marginalization in models generated by compositional expressions. Kybernetika 51(4), 541–570 (2015)MathSciNetGoogle Scholar
  16. 16.
    Pearl, J.: Causality: Models, Reasoning, and Inference, Second Edition. Cambridge University Press, Cambridge (2009)Google Scholar
  17. 17.
    Ryall, M., Bramson, A.: Inference and Intervention: Causal Models for Business Analysis. Routledge, New York (2013)Google Scholar
  18. 18.
    Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)zbMATHGoogle Scholar
  19. 19.
    Shenoy, P.P.: A valuation-based language for expert systems. Int. J. Approx. Reason. 3(5), 383–411 (1989)CrossRefGoogle Scholar
  20. 20.
    Tucci, R.R.: Introduction to Judea Pearl’s Do-Calculus (2013). arXiv:1305.5506v1 [cs.AI]
  21. 21.
    Vejnarová, J.: Composition of possibility measures on finite spaces: preliminary results. In: Bouchon-Meunier, B., Yager, R.R. (eds.) Proceedings of 7th International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems IPMU’98, Editions E.D.K. Paris, pp. 25–30 (1998)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Faculty of managementUniversity of Economics, PragueJindřichův HradecCzech Republic

Personalised recommendations