Um, I hate to keep disagreeing with Kathryn, but I'm afraid her statement
here is provably (i.e., mathematically) wrong. It amounts to the claim
that cross-validation can establish the legitimacy of cross-validation,
i.e., that a learning algorithm can establish its own legitimacy. This is
circular reasoning.
The relevant theorems establish this with complete mathematical rigor.
Again, the formal proofs of all this, underscoring all the subtleties,
relating the results to "something for nothing" results in the COLT
community, etc., can be found in the papers I mentioned in my previous
posting.
David Wolpert
On Tue, 29 Jun 1999, Kathryn Blackmond Laskey wrote:
> Robert,
>
> Hume and others were right. Induction can't be proven because it's not
> universally true. However, induction works in universes in which induction
> works. We appear to be in the process of establishing by induction that
> ours is such a universe. That we exist and have invented science is, of
> course, strong evidence for this claim, assuming that our prior puts
> nonzero weight on our being in a universe in which induction works.
>
