HOW VALUABLE IS SOLMONONOFF INDUCTION FOR REAL WORLD AGI? Through some AGIRI links I stumbled on the Shane Legg's "Friendly AI is bunk" page. I was impressed. I read more of his related web pages and became very impressed.
Then I read his paper "Solmononoff Induction." (http://www.vetta.org/documents/disSol.pdf ) It left me confused. I don't have a sufficient math background to understand all its notation, so I know I may well be wrong (I mean totally wrong), but to me Solmononoff Induction, as described in the paper seemed to be missing something big, at least if it were to be used for a general purpose AGI that was to learn from perception in the real world. I understand the basic idea that if you are seeking a prior likelihood for the occurrence of an event and you have no data about the frequency of its occurrence -- absent any other knowledge -- some notion of the complexity, in information-theory terms, of the event might help you make a better guess. This makes sense because reality is a big computer, and complexity -- in terms of the number of combined events required to make reality cough up a given event , and the complexity of the space in which those events are to be combined -- should to some extent be related to the event's probability. I can understand how such complexity could be approximated by the length of code required in some a theoretical Universal computer to model such real world event-occurrence complexity. But it seems to me there are factors other than the complexity of representing or computing a match against a hypothesis that -- in the an AGI sensing and acting in a real world -- might be much more important and functional for estimating probabilities. For example, although humans are not good at accurately estimating certain types of probabilities, we have an innate ability to guess probabilities in a context sensitive way and by using knowledge about similar yet different things. (As shown in the example quoted below from the Kemp paper below.) It would seem to me that the complexity of the computation required to understand what is the appropriate context is not, itself, necessarily related to the complexity of an event occurring in that context once the context has been determined. Similarly, it does not seem to me that the complexity of determining what is similar to what, in which ways, for purpose of determining the extent to which probabilities from something similar might provide an appropriate prior for something never-before-seen, are not necessarily related to the probability of the thing never-before-seen occurring, itself. For example, the complexity of perception is not directly related to the complexity of occurrence. For example, complexity of perception can be greatly affected by changes in light, shape, and view which might not have anything to do with the probability or complexity of occurrence. So what I am saying is, for example, that if you are receiving a sequence of bytes from a video camera, much of the complexity in the input stream might not be related to complexity-of-event-creation- or Occam's-razor-type issues, but rather to complexity of perception, or similarity understanding, or of appropriate context selection, factors which are not themselves necessarily related to complexity of occurrence. Furthermore, I am saying that for an AGI it seems to me it would make much more sense to attempt to derive priors from notions of similarity, of probabilities of similar things, events, and contexts, and from things like causal models for similar or generalized classes. There is usually much from reality that we do know that we can, and do, use when learning about things we don't know. A very good paper on this subject is one by Charles Kemp et al., "Learning overhypotheses with hierarchical Bayesian models" at http://www.mit.edu/~perfors/KempPTDevSci.pdf . It give a very good example of the power of this type of reasoning -- power that it appears to me Solomonoff Induction totally lacks "participants were asked to imagine that they were exploring an island in the Southeastern Pacific, that they had encountered a single member of the Barratos tribe, and that this tribesman was brown and obese. Based on this single example, participants concluded that most Barratos were brown, but gave a much lower estimate of the proportion of obese Barratos (Figure 4). When asked to justify their responses, participants often said that tribespeople were homogeneous with respect to color but heterogeneous with respect to body weight (Nisbett et al., 1983)." Perhaps I am totally missing something, which is very possible, and if so, I would like to have it pointed out to me, but I think the type of overhypothesis reasoning described in this Kemp paper is a much more powerful and useful source for deriving priors to be used in Bayesian reasoning in AGIs that are expected to learn in the "real world" than Solomonoff Induction. Since I expect Shane Legg is much more knowledgable than I am on the subject, I am expecting to be told that I am really off track, either by him or someone else on this list. If so, please inform me how. Ed Porter 24 String Bridge S12 Exeter, NH 03833 (617) 494-1722 Fax (617) 494-1822 [EMAIL PROTECTED] ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244&id_secret=62743443-5258c6
