Causal Graph Factored Joint Distribution Age

The literature on causal discovery has focused on interventions that involve randomly assigning values to a single variable. But such a randomized intervention is not the only possibility, nor is it always optimal. In some cases it is impossible or it would be unethical to perform such an intervention. We provide an account of “hard” and “soft” interventions, and discuss what they can contribute to causal discovery. We also describe how the choice of the optimal intervention(s) depends heavily on the particular experimental set-up and the assumptions that can be made. Introduction Interventions have taken a prominent role in recent philosophical literature on causation, in particular in work by James Woodward (2003), Christopher Hitchcock (2005), Nancy Cartwright (2006, 2002) and Dan Hausman and James Woodward (1999, 2004). Their work builds on a graphical representation of causal systems developed by computer scientists, philosophers and statisticians called “Causal Bayes Nets” (Pearl, 2000; Spirtes, Glymour, Scheines (hereafter SGS), 2000). The framework makes interventions explicit, and introduces two assumptions to connect qualitative causal structure to sets of probability distributions: the Causal Markov and Faithfulness assumptions. In his recent book, Making Things Happen (2003), Woodward attempts to build a full theory of causation on top of a theory of interventions. In Woodward’s theory, roughly, one variable X is a direct cause of another variable Y if there exists an intervention on X such that if all other variables are held fixed at some value, X and Y are associated. Such an account assumes a lot about the sort of intervention needed, however, and Woodward goes to great lengths to make the idea clear. For example, the intervention must make its target independent of its other causes, and it must directly influence only its target, both of which are ideas difficult to make clear without resorting to the notion of direct causation. Statisticians have long relied on intervention to ground causal inference. In The Design of Experiments (1935), Sir Ronald Fisher considers one treatment variable (the purported cause) and one or more effect variables (the purported effects). This approach has since been extended to include multiple treatment and effect variables in experimental designs such as Latin and Graeco-Latin squares and Factor experiments. In all such cases, however, one must designate certain variables as potential causes (the treatment variables) and others as potential effects (the outcome variables), and inference begins with a randomized assignment (intervention) of the potential cause. Similarly, the 1 The first author is supported by the Causal Learning Collaborative Initiative supported by the James S. McDonnell Foundation. Many aspects of this paper were inspired by discussions with members of the collaborative.