
What is important about the No Free Lunch theorems?
The No Free Lunch theorems prove that under a uniform distribution over ...
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Induction and Skolemization in saturation theorem proving
We consider a typical integration of induction in saturationbased theor...
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Automation of Mathematical Induction as part of the History of Logic
We review the history of the automation of mathematical induction...
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(Deep) Induction Rules for GADTs
Deep data types are those that are defined in terms of other such data t...
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Interpolating Strong Induction
The principle of strong induction, also known as kinduction is one of t...
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Induction, Popper, and machine learning
Francis Bacon popularized the idea that science is based on a process of...
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Induction, of and by Probability
This paper examines some methods and ideas underlying the author's succe...
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The Implications of the NoFreeLunch Theorems for Metainduction
The important recent book by G. Schurz appreciates that the nofreelunch theorems (NFL) have major implications for the problem of (meta) induction. Here I review the NFL theorems, emphasizing that they do not only concern the case where there is a uniform prior – they prove that there are “as many priors” (loosely speaking) for which any induction algorithm A outgeneralizes some induction algorithm B as viceversa. Importantly though, in addition to the NFL theorems, there are many free lunch theorems. In particular, the NFL theorems can only be used to compare the marginal expected performance of an induction algorithm A with the marginal expected performance of an induction algorithm B. There is a rich set of free lunches which instead concern the statistical correlations among the generalization errors of induction algorithms. As I describe, the metainduction algorithms that Schurz advocate as a “solution to Hume's problem” are just an example of such a free lunch based on correlations among the generalization errors of induction algorithms. I end by pointing out that the prior that Schurz advocates, which is uniform over bit frequencies rather than bit patterns, is contradicted by thousands of experiments in statistical physics and by the great success of the maximum entropy procedure in inductive inference.
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