Since inductive reasoning in one way or another is a key ingredient in most AI systems, and the induction problem is a long-standing (supposedly open) philosophical problem, the following (survey-like) paper may be interesting to some list members:
The title of the posting is intentionally provocative, since the paper I would like to discuss is too. The paper considers a range of philosophical and statistical problems around induction; more precisely problems that the well-known approaches to induction have. The paper then shows how a specific single known (but not too well-known) theory S has none of these problems, hence concludes that the induction problem is solved. The problems discussed include: Confirmation of (universal) hypotheses in general, and the classical Black ravens paradox in particular (Maher's approach does not solve the problem). Reparametrization invariance: How to extend the symmetry principle from finite hypothesis classes (all hypotheses are equally likely) to infinite hypothesis classes (Jeffrey's prior does not always work). Old-evidence problem / Ad-hoc hypotheses: How can old evidence confirm a theory developed thereafter? How can we spot ad-hoc hypotheses, just tailored towards the past data? Updating problem: A Bayesian needs to choose the hypothesis/model class before seeing the data, which seldomly reflects scientific practice. Many other issues are discussed: Error bounds, magic numbers, Carnap's confirmation theory, Laplace rule, and many more. I would like to encourage the interested list members to read and reflect on the paper, and then ideally start a critical discussion (here or offline). Marcus Hutter, On Universal Prediction and Bayesian Confirmation Theoretical Computer Science (2007) http://dx.doi.org/10.1016/j.tcs.2007.05.016 http://www.hutter1.net/ai/uspx.pdf Short version (very dense, not recommended): Marcus Hutter, On the Foundations of Universal Sequence Prediction Proc. 3rd Annual Conference on Theory and Applications of Models of Computation (TAMC 2006) http://arxiv.org/abs/cs.LG/0605009 Best regards, Marcus ______________________ Marcus Hutter, Assoc. Prof. RSISE, Room B259, Building 115 Australian National University Corner of North and Daley Road Canberra ACT 0200, Australia Phone: +61(0)2 612 51605 Fax: +61(0)2 612 58651 Email: [EMAIL PROTECTED] http://rsise.anu.edu.au/~marcus _______________________________________________ uai mailing list uai@ENGR.ORST.EDU https://secure.engr.oregonstate.edu/mailman/listinfo/uai
