Well I guess I misunderstood what you said. But, you did say, "The question of whether the function would be useful for the "sorts of things we keep talking about" ... well, I think the best argument that I can give is that MDL is strongly supported by both theory and practice for many *subsets* of the full program space. The concern might be that, so far, it is only supported by *theory* for the full program space-- and since approximations have very bad error-bound properties, it may never be supported in practice. My reply to this would be that it still appears useful to approximate Solomonoff induction, since most successful predictors can be viewed as approximations to Solomonoff induction. "It approximates solomonoff induction" appears to be a good _explanation_ for the success of many systems."
Saying that something "approximates Solomonoff Induction" doesn't have any meaning since we don't know what Solomonoff Induction actually represents. And does talk about the "full program space," merit mentioning? I can see how some of the kinds of things that you have talked about (to use my own phrase in order to avoid having to list all the kinds of claims that I think have been made about this subject) could be produced from finite sets, but I don't understand why you think they are important. I think we both believe that there must be some major breakthrough in computational theory waiting to be discovered, but I don't see how that could be based on anything other than Boolean Satisfiability. Can you give me a simple example and explanation of the kind of thing you have in mind, and why you think it is important? Jim Bromer On Fri, Jul 16, 2010 at 12:40 AM, Abram Demski <[email protected]>wrote: > Jim, > > The statements about bounds are mathematically provable... furthermore, I > was just agreeing with what you said, and pointing out that the statement > could be proven. So what is your issue? I am confused at your response. Is > it because I didn't include the proofs in my email? > > --Abram ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=8660244-6e7fb59c Powered by Listbox: http://www.listbox.com
