Questioning Information Cost
|July 12, 2013||Posted by Winston Ewert under Intelligent Design|
Di.. Eb.., or Dieb, on the blog DiEbLog, has posted a number of questions, relating to the paper A General Theory of Information Cost Incurred by Successful Search. He raises a number of questions and objections to the paper.
Firstly, Dieb objects that the quasi-Bayesian calculation on Page 56 is incorrect, although it obtains the correct result. However, the calculation is called a quasi-Bayesian calculation because it engages in hand-waving rather than presenting a rigorous proof. The text in question is shortly after a theorem and is intended to explicate the consequences of that theorem rather than rigorously prove its result. The calculation is not incorrect, but rather deliberately oversimplified.
Secondly, Dieb objects that many quite different searches can be constructed which are represented by the same probability measure. However, if searches were represented as a mapping from the previously visited points to a new point (as in Wolpert and Macready’s original formulation), algorithms which derive the same queries in different ways will be represented the same way. Giving multiple searches the same representation is neither avoidable nor inherently problematic.
Thirdly, Dieb objects that a search will be biased by the discriminator towards selecting elements in the target, not a uniform distribution. However, Dieb’s logic depends on assuming that we have a good discriminator. As the paper states, we do not assume this to be the case. If choosing a random search, we cannot assume that we have a good discriminator (or any other component). The search for the search assumes that we have no prior information, not even the ability to identify points in the target.
Fourthly, Dieb doesn’t see the point in the navigator’s output as it is can be seen as just the next element of the search path. However, the navigator produces information like a distance to the target. The distance will be helpful in determining where to query, but it does not determine the next element of the search path. So it cannot be seen as just the next element of the search path.
Fifthly, Dieb objects that the inspector is treated inconsistently. However, the output of the inspector is not inconsistent but rather general. The information extracted by the inspector is the information relevant to whether or not a point is in the target. That information will take different forms depending on the search, it may be a fitness value, a probability, a yes/no answer, etc.
The authors of the paper conclude that Dieb’s objections derive from misunderstanding our paper. Despite five blog posts related to this paper, we find that Dieb has failed to raise any useful or interesting questions. Should Dieb be inclined to disagree with our assessment, we suggest that he organize his ideas and publish them as a journal article or in a similar venue.