Monday, February 11, 2008

NFL Theorems (Part II)

Now, I will show what Dr. Dembski and Marks state. If you don’t agree with what they write, you’ll have to show me that their conclusions are inconsistent with and/or not built upon the NFL Theorems. Here’s what they say in a nutshell:

“active information ... measures the contribution of problem-specific information for successfully finding a target. This paper develops a methodology based on these information measures to gauge the effectiveness with which problem-specific information facilitates successful search.”

“Active information captures numerically the problem-specific information that assists a search in reaching a target. We therefore find it convenient to use the term “active information” in two equivalent ways:
1) as the specific information about target location and search-space structure incorporated into a search algorithm that guides a search to a solution.
2) as the numerical measure for this information and defined as the difference between endogenous and exogenous information.”

From ActiveInfo “Conclusions:”

“If any search algorithm is to perform better than random search, active information must be resident in it. If the active information is inaccurate, the search can perform worse than random (which, numerically, comes out as negative active information) ... Accordingly, attempts to characterize evolutionary algorithms as “creators of novel information” are inappropriate. To have integrity, all search algorithms, especially computer simulations of evolutionary search, should make explicit (1) a numerical measure of the difficulty of the problem to be solved, i.e., the endogenous information, and (2) a numerical measure of the amount of problem-specific information resident in the search algorithm, i.e., the active information.”

Conservation of Information in Search: Measuring the Cost of Success:

“Search algorithms, including evolutionary searches, do not generate free information. Instead, they consume information, incurring it as a cost. Over 50 years ago, Leon Brillouin, a pioneer in information theory, made this very point: “The [computing] machine does not create any new information, but it performs a very valuable transformation of known information” [3] When Brillouin’s insight is applied to search algorithms that do not employ specific information about the problem being addressed, one finds that no search performs consistently better than any other. Accordingly, there is no magic-bullet search algorithm that successfully resolves all problems [7], [32].”

Thus ...

A. Problem specific information about search space and target must be incorporated into the behavior of evolutionary algorithms in order for them to produce better than chance results.

B. Active information gives a numerical measurement in information theoretic terms, of the amount of problem specific information incorporated into an algorithm to cause it to perform efficiently.

C. Evolutionary algorithms do not create new information. They operate off of previously inputted, correct information about target location and search structure which is then used to find and transform the previously existing information.

No comments: