The three faces of faithfulness
Causal inference, Bayes nets, Faithfulness, Graphical models
In the causal inference framework of Spirtes, Glymour, and Scheines (SGS), inferences about causal relationships are made from samples from probability distributions and a number of assumptions relating causal relations to probability distributions. The most controversial of these assumptions is the Causal Faithfulness Assumption, which roughly states that if a conditional independence statement is true of a probability distribution generated by a causal structure, it is entailed by the causal structure and not just for particular parameter values. In this paper we show that the addition of the Causal Faithfulness Assumption plays three quite different roles in the SGS framework: (i) it reduces the degree of underdetermination of causal structure by probability distribution; (ii) computationally, it justifies reliable (constraint-based) causal inference algorithms that would otherwise have to be slower in order to be reliable; and (iii) statistically, it implies that those algorithms reliably obtain the correct answer at smaller sample sizes than would otherwise be the case. We also consider a number of variations on the Causal Faithfulness Assumption, and show how they affect each of these three roles.
The research of J. Zhang was supported in part by the Research Grants Council of Hong Kong under the General Research Fund LU342213.
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Zhang, J., & Spirtes, P. (2015). The three faces of faithfulness. Synthese. 193(4), 1011-1027. doi: 10.1007/s11229-015-0673-9