Mike Dougherty said in the below email. >Mike Dougherty #######> "Admittedly, I do not have a quantitative grasp of Bayesian methods (naive or otherwise) but if I understand qualitatively it is about attempting to reach a conclusion based on complete knowledge based on a confidence of available knowledge to the unknown. If I'm already wrong, please school me. "
Ed Porter #######> I am not an expert on it either, but it don't think it is really that mystical. It take the frequency based approach to probability, but modifies it by addresses some of the major lackings of a pure frequency based approach, such by (a) focusing on the issue of what to do when you don't have that much frequency data (it tries to use some sort of educated guess to pick a prior probability distribution); (b) how to update a prior probability as you obtain more data; and (c) how to estimate which of multiple different possible probability distributions is the one you are actually sampling with the data you are receiving. It also does provide formulas for calculating the impact of various probabilities on other probabilities. I don't understand what you were saying about chaos. It would seem to me that as a general rule considerations of chaos usually come into play when considering systems at a higher level of complexity than those at which one is usually doing normally sees individual Bayesian equations. But of course one could have a complex system in which many nodes were interacting with each other in a probabilistic manner (as would be the case in a Novamente type machine), and in which the probabilities would be an essential part of the complex computation contributing to the complexity, stability, and/or chaos the system. I don't know to what extent one needs a new type of math to deal with this. It seems to me that one of the things Wolfram was saying when he talked about "irreducibility", is that for many chaotic some systems much of their behavior cannot be described by simplifying generalizations, but instead has to be computed. That does not mean that simplifying generalizations have no applicability to chaotic systems, but it often means that the percent of the systems behavior we might care about that is described or can be predicted by such simplifications is often substantially less. So net-net maybe we just have to compute a lot of complex probabilistic interactions of the type that are useful for the types of AGI's we want to build and see what happens. After doing so we will be in a better position to see what sort of simplifying generalizations can be made and what sort of math best describes it. I am confident that there will be multiple tuning parameters that can be used to determine how stable or chaotic or on the boarder line between the two such systems will be. This is not that unlike some of the things Richard Loosemore has been saying. But unlike him, I don't think we need to undertake some grand exploration of the space of complex systems to find the important generalizations (particularly since that space is infinite), instead I think we should focus on the space of such systems that is relevant to the types of AGIs we thing we want to build. Ed Porter -----Original Message----- From: Mike Dougherty [mailto:[EMAIL PROTECTED] Sent: Monday, February 25, 2008 10:48 PM To: [email protected] Subject: Re: [agi] A possible less ass-backward way of computing naive bayesian conditional probabilities On Mon, Feb 25, 2008 at 2:51 PM, Ed Porter <[EMAIL PROTECTED]> wrote: > But that does stop people from modeling systems in a simplified manner by > acting as if these limitations were met. Naïve Bayesian methods are > commonly used. I have read multiple papers saying that in many cases it > proves surprisingly accurate (considering what a gross hack it is) and, of > course, it greatly simplifies computation. Admittedly, I do not have a quantitative grasp of Bayesian methods (naive or otherwise) but if I understand qualitatively it is about attempting to reach a conclusion based on complete knowledge based on a confidence of available knowledge to the unknown. If I'm already wrong, please school me. While walking the dog tonight I was considering the application of knowledge across different domains. In this light, I considered the unknown (or unknowable) part of the problem to be similar to some amount of chaos in a system that displays a gross-level order. Increasing the precision of the measurement of the ordered part can increase the instability of the chaotic part. Is it possible that a different kind of math is required to model the chaotic part of a complex system like this? Something as fundamental as the discovery of irrational numbers perhaps? This would have been yet another fleeting thought if I hadn't returned to this thread about Bayesian (thinking?) and I was curious what insight the list could offer... ------------------------------------------- agi Archives: http://www.listbox.com/member/archive/303/=now RSS Feed: http://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: http://www.listbox.com/member/?&; Powered by Listbox: http://www.listbox.com ------------------------------------------- agi Archives: http://www.listbox.com/member/archive/303/=now RSS Feed: http://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: http://www.listbox.com/member/?member_id=8660244&id_secret=95818715-a78a9b Powered by Listbox: http://www.listbox.com
