Ben, > OK... life lesson #567: When a mathematical explanation confuses > non-math people, another mathematical explanation is not likely to > help
While I can't help with the solution, I can say that this version of your problem at last made sense to me - previous version were incomprehensible to me, this last version leaped off the page as comprehensible communication. So you're rule above holds very well. If you can teach Novamente to do what you have just done here you've made a big leap forward in human / Novamente communication. Cheers, Philip From: "Ben Goertzel" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Subject: RE: [agi] A probabilistic/algorithmic puzzle... Date sent: Thu, 20 Feb 2003 14:25:54 -0500 Send reply to: [EMAIL PROTECTED] OK... life lesson #567: When a mathematical explanation confuses non-math people, another mathematical explanation is not likely to help The basic situation can be thought of as follows. Suppose you have a large set of people, say, all the people on Earth Then you have a bunch of categories you're interested in, say: Chinese Arab fat skinny smelly female ... Then you have some absolute probabilities, e.g. P(Chinese) = .2 P(fat) = .15 etc. , which tell you how likely a randomly chosen person is to fall into each of the categories Then you have some conditional probabilities, e.g. P(fat | skinny)=0 P(smelly|male) = .62 P(fat | American) = .4 P(slow|fat) = .7 The last one, for instance, tells you that if you know someone is American, then there's a .4 chance the person is fat (i.e. 40% of Americans are fat). The problem at hand is, you're given some absolute and some conditional probabilities regarding the concepts at hand, and you want to infer a bunch of others. In localized cases this is easy, for instance using probability theory one can get evidence for P(slow|American) from the combination of P(slow|fat) and P(fat | American) Given n concepts there are n^2 conditional probabilities to look at. The most interesting ones to find are the ones for which P(A|B) is very different from P(B) just as for instance P(fat|American) is very different from P(fat) This problem is covered by elementary probability theory. Solving it in principle is no issue. The tricky problem is solving it approximately, for a large number of concepts and probabilities, in a very rapid computational way. Bayesian networks try to solve the problem by seeking a set of concepts that are arranged in an "independence hierarchy" (a directed acyclic graph with a concept at each node, so that each concept is independent of its parents conditional on its ancestors -- and no I don't feel like explaining that in nontechnical terms at the moment ;). But this can leave out a lot of information because real conceptual networks may be grossly interdependent. Of course, then one can try to learn a whole bunch of different Bayes nets and merge the probability estimates obtained from each one.... One thing that complicates the problem is that ,in some cases, as well as inferring probabilities one hasn't been given, one may want to make corrections to probabilities one HAS been given. For instance, sometimes one may be given inconsistent information, and one has to choose which information to accept. For example, if you're told P(male) = .5 P(young|male) = .4 P(young) = .1 then something's gotta give, because the first two probabilities imply P(young) >= .5*.4 = .2 Novamente's probabilistic reasoning system handles this problem pretty well, but one thing we're struggling with now is keeping this "correction of errors in the premises" under control. If you let the system revise its premises to correct errors (a necessity in an AGI context), then it can easily get carried away in cycles of revising premises based on conclusions, then revising conclusions based on the new premises, and so on in a chaotic trajectory leading to meaningless inferred probabilities. As I said before, this is a very simple incarnation of a problem that takes a lot of other forms, more complex but posing the same essential challenge. -- Ben G ------- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/?[EMAIL PROTECTED]
