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Second-order induction in prediction problems.

Rossella Argenziano1, Itzhak Gilboa2,3

  • 1Department of Economics, University of Essex, Colchester CO4 3SQ, United Kingdom.

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Summary
This summary is machine-generated.

Rational agents learn similarity functions for predictions. Uniqueness of the empirically optimal similarity function (EOSF) depends on data: unique with many observations and few variables, but non-unique and hard to find otherwise.

Keywords:
belief formationempirically optimal similarity functiongeneralized context modelkernel estimationlearning

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Area of Science:

  • Decision theory
  • Machine learning
  • Cognitive science

Background:

  • Agents often predict outcomes using past similar cases.
  • Learning involves determining attribute importance for similarity judgments.

Purpose of the Study:

  • Investigate the uniqueness of the empirically optimal similarity function (EOSF).
  • Determine the computational difficulty of finding the EOSF.

Main Methods:

  • Theoretical analysis of similarity function learning.
  • Examination of conditions for uniqueness and computational complexity.

Main Results:

  • EOSF uniqueness is guaranteed with abundant observations and few relevant variables.
  • Non-uniqueness prevails when variables outnumber observations, posing computational challenges.

Conclusions:

  • Identifies conditions for convergent predictions among rational agents with shared data.
  • Highlights scenarios where differing probabilistic beliefs may arise due to non-unique EOSFs.