My Wild

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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
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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.)
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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