Can we even hope for a non-tautological justification of Occam’s Razor? Can one explain, non-circularly, why the “Anti-Inductivists” are wrong?
What are the important assumptions made by Valiant’s PAC model, and how reasonable are those assumptions?
What are the relative merits of the PAC-learning and Bayesian accounts of learning?
Do the sample complexity bounds in PAC-learning theory (either the basic m=(1/ε)log(|H|/δ) bound, or the bound based on VC-dimension) go any ways toward “justifying Occam’s Razor”? What about the Bayesian account, based on a universal prior where each self-delimiting computer program P occurs with probability ~2-|P|?
Does some people’s criticism of PAC-theory—namely, that the number of bits needed to pick out an individual hypothesis h∈H need not be connected to “simplicity” in the intuitive sense—have merit? If so, what would need to be done to address that problem?