On computations with causal compositional models. (English) Zbl 1340.65011

Summary: The knowledge of causal relations provides a possibility to perform predictions and helps to decide about the most reasonable actions aiming at the desired objectives. Although the causal reasoning appears to be natural for the human thinking, most of the traditional statistical methods fail to address this issue. One of the well-known methodologies correctly representing the relations of cause and effect is Pearl’s causality approach. The paper brings an alternative, purely algebraic methodology of causal compositional models. It presents the properties of operator of composition, on which a general methodology is based that makes it possible to evaluate the causal effects of some external action. The proposed methodology is applied to four illustrative examples. They illustrate that the effect of intervention can in some cases be evaluated even when the model contains latent (unobservable) variables.


65C50 Other computational problems in probability (MSC2010)
60G25 Prediction theory (aspects of stochastic processes)


Full Text: DOI Link


[1] Detwarasiti, A., Shachter, R. D.: Influence diagrams for team decision analysis. Decision Analysis 2 (2005), 4, 207-228. · doi:10.1287/deca.1050.0047
[2] Hagmayer, Y., Sloman, S., Lagnado, D., Waldmann, M. R.: Causal reasoning through intervention. Causal Learning: Psychology, Philosophy, and Computation (A. Gopnik and L. Schulz, Oxford University Press 2007, pp. 86-101. · doi:10.1093/acprof:oso/9780195176803.003.0007
[3] Jiroušek, R.: Foundations of compositional model theory. Int. J. Gen. Syst. 40 (2011), 6, 623-678. · Zbl 1252.68285 · doi:10.1080/03081079.2011.562627
[4] Jiroušek, R.: On causal compositional models: Simple examples. Proc. 15th Int. Conf. on Inf. Processing and Management of Uncertainty - Part I. Springer 2014, pp. 517-526. · doi:10.1007/978-3-319-08795-5_53
[5] Malvestuto, F. M.: Equivalence of compositional expressions and independence relations in compositional models. Kybernetika 50 (2014), 3, 322-362. · Zbl 1366.62103 · doi:10.14736/kyb-2014-3-0322
[6] Malvestuto, F. M.: Marginalization in models generated by compositional expressions. To appear in Kybernetika 51 (2015), 4. · Zbl 1363.05246
[7] Pearl, J.: Causality: Models, Reasoning, and Inference. Cambridge University Press, NY 2009. · Zbl 1188.68291 · doi:10.1017/cbo9780511803161
[8] Ryall, M., Bramson, A.: Inference and Intervention: Causal Models for Business Analysis. Routledge, NY 2013. · doi:10.4324/9780203076835
[9] Shachter, R.: Evaluating influence diagrams. Oper. Res. 34 (1986), 6, 871-882. · doi:10.1287/opre.34.6.871
[10] Spirtes, P., Glymour, C., Scheines, R.: Causation, Prediction and Search. Springer Lecture Notes in Statistics, New York 1993. · Zbl 0981.62001 · doi:10.1007/978-1-4612-2748-9
[11] Tucci, R. R.: Introduction to Judea Pearl’s Do-Calculus. arXiv:1305.5506v1 [cs.AI] (2013).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.