My Wild & Crazy Idea: Causal Computational Learning Theory

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

2. “Computational complexity theory meets statistics” PAC(Probabilistically Approximately Correct)Learning Given a collection of labeled examples (x1,f(x1)),…,(xm,f(xm)) 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 PAC-learning is a hugely successful model—but like most statistics, it doesn’t care about the distinction between correlation and cause

3. 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 mechanisms—which often requires controlled experiments (together with prior knowledge about temporal direction, autonomy of subsystems, etc.) Best theory of causality we currently have: Judea Pearl’s “do-calculus”

4. My WACI Challenge for Theory Traditional statistics : PAC-learning :: Pearl’s do-calculus : what? Potential applications: Debugging, reconstructing gene regulatory networks… Existing work in the direction I’m talking about: - PAC-learning with membership and equivalence queries - Angluin, Aspnes, Chen, Wu: “Learning a circuit by injecting values,” STOC’2006 - Pearl’s IC algorithm - Leakage-resilience in cryptography