Matt, My intention here is that there is a basic level of well-defined, "crisp" models which probabilities act upon; so in actuality the system will never be using a single model, open or closed...
(in a hurry now, more comments later) --Abram On Thu, Sep 4, 2008 at 2:47 PM, Matt Mahoney <[EMAIL PROTECTED]> wrote: > In a closed model, every statement is either true or false. In an open model, > every statement is either true or uncertain. In reality, all statements are > uncertain, but we have a means to assign them probabilities (not necessarily > accurate probabilities). > > A closed model is unrealistic, but an open model is even more unrealistic > because you lack a means of assigning likelihoods to statements like "the sun > will rise tomorrow" or "the world will end tomorrow". You absolutely must > have a means of guessing probabilities to do anything at all in the real > world. > > > -- Matt Mahoney, [EMAIL PROTECTED] > > > --- On Thu, 9/4/08, Abram Demski <[EMAIL PROTECTED]> wrote: > >> From: Abram Demski <[EMAIL PROTECTED]> >> Subject: [agi] open models, closed models, priors >> To: agi@v2.listbox.com >> Date: Thursday, September 4, 2008, 2:19 PM >> A closed model is one that is interpreted as representing >> all truths >> about that which is modeled. An open model is instead >> interpreted as >> making a specific set of assertions, and leaving the rest >> undecided. >> Formally, we might say that a closed model is interpreted >> to include >> all of the truths, so that any other statements are false. >> This is >> also known as the closed-world assumption. >> >> A typical example of an open model is a set of statements >> in predicate >> logic. This could be changed to a closed model simply by >> applying the >> closed-world assumption. A possibly more typical example of >> a >> closed-world model is a computer program that outputs the >> data so far >> (and predicts specific future output), as in Solomonoff >> induction. >> >> These two types of model are very different! One important >> difference >> is that we can simply *add* to an open model if we need to >> account for >> new data, while we must always *modify* a closed model if >> we want to >> account for more information. >> >> The key difference I want to ask about here is: a >> length-based >> bayesian prior seems to apply well to closed models, but >> not so well >> to open models. >> >> First, such priors are generally supposed to apply to >> entire joint >> states; in other words, probability theory itself (and in >> particular >> bayesian learning) is built with an assumption of an >> underlying space >> of closed models, not open ones. >> >> Second, an open model always has room for additional stuff >> somewhere >> else in the universe, unobserved by the agent. This >> suggests that, >> made probabilistic, open models would generally predict >> universes with >> infinite description length. Whatever information was >> known, there >> would be an infinite number of chances for other unknown >> things to be >> out there; so it seems as if the probability of *something* >> more being >> there would converge to 1. (This is not, however, >> mathematically >> necessary.) If so, then taking that other thing into >> account, the same >> argument would still suggest something *else* was out >> there, and so >> on; in other words, a probabilistic open-model-learner >> would seem to >> predict a universe with an infinite description length. >> This does not >> make it easy to apply the description length principle. >> >> I am not arguing that open models are a necessity for AI, >> but I am >> curious if anyone has ideas of how to handle this. I know >> that Pei >> Wang suggests abandoning standard probability in order to >> learn open >> models, for example. >> >> --Abram Demski >> > > > > ------------------------------------------- > 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/?&; > Powered by Listbox: http://www.listbox.com > ------------------------------------------- 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=111637683-c8fa51 Powered by Listbox: http://www.listbox.com
