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Metainduction over Unboundedly Many Prediction Methods: A Reply to Arnold and Sterkenburg

Published online by Cambridge University Press:  01 January 2022

Gerhard Schurz
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Abstract

The universal optimality theorem for metainduction works for epistemic agents faced with a choice among finitely many prediction methods. Eckhart Arnold and Tom Sterkenburg objected that it breaks down for infinite or unboundedly growing sets of methods. In this article the metainductive approach is defended against this challenge by extending the optimality theorem (i) to unboundedly growing sets of methods whose number grows less than exponentially in time, (ii) to sequences of methods with an application to Goodman's problem, and (iii) to infinite sets of methods whose number of predictive equivalence classes grows less than linearly in time.

Type
Research Article
Information
Philosophy of Science , Volume 88 , Issue 2 , April 2021 , pp. 320 - 340
Copyright
Copyright © The Philosophy of Science Association

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References

Arnold, Eckhart. 2010. “Can the Best-Alternative-Justification Solve Hume’s Problem?” Philosophy of Science 77:584–93.CrossRefGoogle Scholar
Cesa-Bianchi, Nicolo, and Lugosi, Gabor. 2006. Prediction, Learning, and Games. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Chernov, Alexey, and Vovk, Vladimir. 2009. “Prediction with Expert Evaluator’s Advice.” In Algorithmic Learning Theory: 20th International Conference, ALT 2009, Porto, Portugal, October 3–5, 2009, ed. Gavaldà, Ricard, Zilles, Sandra, Lugosi, Gábor, and Zeugmann, Thomas, 8–22. Berlin: Springer.CrossRefGoogle Scholar
Cover, Thomas M., and Thomas, Joy A.. 1991. Elements of Information Theory. New York: Wiley.CrossRefGoogle Scholar
Goodman, Nelson. 1946. “A Query on Confirmation.” Journal of Philosophy 44:383–85.Google Scholar
Kelly, Kevin T. 1996. The Logic of Reliable Inquiry. New York: Oxford University Press.Google Scholar
Mourtada, Jaouad, and Maillard, Odalric-Ambrym. 2017. “Efficient Tracking of a Growing Number of Experts.” Journal of Machine Learning Research 76:1–23.Google Scholar
Reichenbach, Hans. 1949. The Theory of Probability. Berkeley: University of California Press.Google Scholar
Schurz, Gerhard. 2008. “The Meta-inductivist’s Winning Strategy in the Prediction Game: A New Approach to Hume’s Problem.” Philosophy of Science 75:278–305.CrossRefGoogle Scholar
Schurz, Gerhard. 2017. “No Free Lunch Theorem, Inductive Skepticism, and the Optimality of Meta-induction.” Philosophy of Science 84:825–39.CrossRefGoogle Scholar
Schurz, Gerhard. 2019. Hume’s Problem Solved: The Optimality of Meta-induction. Cambridge, MA: MIT Press.CrossRefGoogle Scholar
Schurz, Gerhard, and Thorn, Paul. 2016. “The Revenge of Ecological Rationality: Strategy-Selection by Meta-induction.” Minds and Machines 26 (1): 31–59.CrossRefGoogle Scholar
Schurz, Gerhard, and Thorn, Paul. 2017. “A Priori Advantages of Meta-induction and the No Free Lunch Theorem: A Contradiction?” In Advances in Artificial Intelligence, 236–48. Lecture Notes in Computer Science 10505. Cham: Springer.Google Scholar
Shalev-Shwartz, Shai, and Ben-David, Shai. 2014. Understanding Machine Learning: From Theory to Algorithms. New York: Cambridge University Press.CrossRefGoogle Scholar
Sterkenburg, Tom F. 2019. “The Meta-inductive Justification of Induction: The Pool of Strategies.” Philosophy of Science 86:981–92.CrossRefGoogle Scholar
Wolpert, David H. 1996. “The Lack of A Priori Distinctions between Learning Algorithms.” Neural Computation 8:1341–90.Google Scholar