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My Wild & Crazy Idea: Causal Computational Learning Theory Scott Aaronson But first: what ever happened to my WACI from a few years ago: a Web 2.0 mathematics discussion site and conjecture/theorem repository? There now exists such a site, Mathoverflow.net, which is everything I hoped for and more. In just ~2 years, its noticeably changed the practice of mathematics. I had nothing to do with its creation.

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PAC (Probabilistically Approximately Correct) Learning Computational complexity theory meets statistics PAC-learning is a hugely successful modelbut like most statistics, it doesnt care about the distinction between correlation and cause Given a collection of labeled examples (x 1,f(x 1 )),…,(x m,f(x m )) drawn independently from some unknown distribution D, problem is to output a hypothesis h such that h(x)=f(x) for most x~D with high probability

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The result: PAC explains how banks predict who will repay their loans, but not how Einstein predicted the bending of starlight by the sun vs To predict what will happen in novel situations, you need to know something about causal mechanismswhich often requires controlled experiments (together with prior knowledge about temporal direction, autonomy of subsystems, etc.) Best theory of causality we currently have: Judea Pearls do-calculus

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My WACI Challenge for Theory Traditional statistics : PAC-learning :: Pearls do-calculus : what? Potential applications: Debugging, reconstructing gene regulatory networks… Existing work in the direction Im talking about: - PAC-learning with membership and equivalence queries - Angluin, Aspnes, Chen, Wu: Learning a circuit by injecting values, STOC2006 - Pearls IC algorithm - Leakage-resilience in cryptography

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