Informative Interventions

Causal discovery programs have met with considerable enthusiasm in the AI and data mining communities. Amongst philosophers they have met a more mixed response, with numerous skeptics pointing out weaknesses in their assumptions. Some criticize the reliance upon faithfulness (the idea that every causal connection will result in probabilistic dependence), since the true model may in fact be unfaithful (Cartwright, 2001). Despite a common, self-imposed restriction to observational data in causal discovery, the intervention account of causality (Pearl, 2000; Spirtes et al., 2000) suggests that the inclusion of intervention data may alleviate this concern. Korb and Nyberg (2006) established that, for linear networks, even underwhelming interventions (that never overwhelm other influences) have sufficient power to overcome unfaithfulness and go beyond the limits of observational data to identify the true model. Here we extend those results to discrete networks, which present the added difficulty that they can be unfaithful along a single path (as noted, e.g., by Hitchcock, 2001). In doing so, we illustrate both unfaithful chains and unfaithful collisions, give mathematical criteria for such interactions, make some recommendations for diagnosing unfaithfulness and designing informative interventions, and finally, demonstrate the power of both one and N − 1 underwhelming interventions.