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4 March 2009

Follow-up on Robins' Talk ("A Bold Vision of Artificial Intelligence and Philosophy")

A few blog readers asked for more information about Jamie Robins' talk today and the "pinch of magic and miracle" he promised in the abstract. I wanted to offer my non-expert report on the presentation, particularly because Jamie and his coauthors don't yet have a paper to circulate.

Jamie organized the talk around a research scenario in which five variables are measured in trillions of independent experiments and the task is to uncover the causal process relating the variables. (His example involved gene expression.) He led us through an algorithm that he claimed could accomplish this feat (in some circumstances) with no outside, substantive input. The algorithm involves looking for conditional independencies in the data, not just in its original form but also under various transformations in which one or more independencies are induced by inverse probability weighting and we check whether others exist. For some data generating processes, this algorithm will hit on conditional independencies such that (under a key assumption, which he was coy about until the end of the talk) the causal model will be revealed -- the ordering and all of the effect sizes.

The key assumption is "faithfulness," which states that when two variables are found to be conditionally independent in the data, we can conclude that there is no causal arrow between them (i.e. we can rule out that there is an arrow between them that is perfectly offset by other effects). Without that assumption we can't infer the causal model from a joint density, but with it we can -- and the point of Jamie's talk was that, in the "star worlds" in which independencies have been induced by reweighting, even more information can be gleaned from the joint density than has been recognized.

All of this may seem surprising to people who have followed the debates over causal modeling and "causal discovery," much of which has centered around the work of Spirtes, Glymour, and Sheines. In these debates, Jamie has been (by his own admission) a consistent critic of the faithfulness assumption and has insisted that substantive knowledge, not conditional independence in sampled data, is the way to draw causal models. Rest assured, he has not changed his position. (I think he described the embrace of the faithfulness assumption by mainstream statistics as "probably insane" at one point in the talk.) The point of the talk was not to defend faithfulness, but rather to show that it implies a lot more than was realized by researchers who currently employ it to uncover causal structure from joint densities.

Anyone else who wants to fill in or correct my account, please chime in.

Posted by Andy Eggers at March 4, 2009 10:19 PM