Weak Interventions and Instrumental Variables

Traditional experimental design has focused on experimental interventions that take full control of the distribution of treatment variables by means of randomization or clamping. The underlying motiviation, going back to R.A. Fisher, is that such interventions make the treatment variable independent of its causes, including potential latent confounders of the treatment and outcome, and therefore enable unbiased estimates of the causal effect of the treatment on the outcome. In many cases, especially in the social sciences, such “surgical” interventions (Pearl) are not possible or not feasible. However, this does not imply that discovery of the the causal structure among a set of variables is limited to passive observational data. Interventions can be weaker, influencing the conditional distribution of the intervened variable given its causes (graphical parents), without making the intervened variable independent of its normal causes. The implications for learning the causal structure under these circumstances do not revert to results available for “surgical” interventions or passive observation. Given that a weak intervention introduces a known external influence into the system under investigation, but does not destroy causal connections, under particular assumptions more can be learned faster about causal structure than with “surgical” interventions or passive observation – even if there are latent variables. That is, in fewer experiments, more details of the causal structure can be determined than when using “surgical” interventions or not intervening at all. The results rely on the assumption that the intervention is not confounded by a latent variable and not caused by any variable in the system under investigation, and that the distribution over the variables under investigation is faithful to a directed acyclic graph. The results do not depend on the model being linear or continuous.