"Problem Statement: What are the optimal functions, derived from real-world observations of past events, the timings of their comings and goings, and perhaps their physical association, to extract each successive parameter containing the maximum amount of information (in a Shannon sense) usable in reconstructing the observed inputs."
I see it now! It is typically very useful to decompose a problem into sub-problems that can be solved either independently or with simple well-defined interaction. What you are proposing is such a decomposition, for the very general problem of compression. "Find an encoding scheme for the data in dataset X that minimizes the number of bits we need" can be split into subproblems of the form "find a meaning for the next N bits of an encoding that maximizes the information they carry". The general problem can be solved by applying a solution to the simpler problem until the data is completely compressed. "However, it still fails to consider temporal clues, unless of course you just consider these to be another dimension." Why does this not count as a working solution? On Tue, Jul 22, 2008 at 1:48 PM, Steve Richfield <[EMAIL PROTECTED]> wrote: > Ben, > On 7/22/08, Benjamin Johnston <[EMAIL PROTECTED]> wrote: >>> >>> You are confusing what PCA now is, and what it might become. I am more >>> interested in the dream than in the present reality. >> >> That is like claiming that multiplication of two numbers is the answer to >> AGI, and then telling any critics that they're confusing what multiplication >> is now with what multiplication may become. > > > Restating (not copying) my original posting, the challenge of effective > unstructured learning is to utilize every clue and NOT just go with static > clusters, etc. This includes temporal as well as positional clues, > information content, etc. PCA does some but certainly not all of this, but > considering that we were talking about clustering here just a couple of > weeks ago, ratcheting up to PCA seems to be at least a step out of the > basement. > > I think that perhaps I mis-stated or was misunderstood in my "position". No > one has "the answer" yet, but given recent work, I think that perhaps the > problem can now be stated. Given a problem statement, it (hopefully) should > be "just some math" to zero in on the solution. OK... > > Problem Statement: What are the optimal functions, derived from real-world > observations of past events, the timings of their comings and goings, and > perhaps their physical association, to extract each successive parameter > containing the maximum amount of information (in a Shannon sense) usable in > reconstructing the observed inputs. IMHO these same functions will be > exactly what you need to recognize what is happening in the world, what you > need to act upon, which actions will have the most effect on the world, etc. > PCA is clearly NOT there (e.g. it lacks temporal consideration), but seems > to be a step closer than anything else on the horizon. Hopefully, given the > "hint" of PCA, we can follow the path. > > You should find an explanation of PCA in any elementary linear algebra or > statistics textbook. It has a range of applications (like any transform), > but it might be best regarded as an/the elementary algorithm for > unsupervised dimension reduction. > > Bingo! However, it still fails to consider temporal clues, unless of course > you just consider these to be another dimension. > > When PCA works, it is more likely to be interpreted as a comment on the > underlying simplicity of the original dataset, rather than the power of PCA > itself. > > Agreed, but so far, I haven't seen any solid evidence that the world is NOT > simple, though it appears pretty complex until you understand it. > > Thanks for making me clarify my thoughts. > > Steve Richfield > > ________________________________ > agi | Archives | Modify Your Subscription ------------------------------------------- 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=108809214-a0d121 Powered by Listbox: http://www.listbox.com
