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Testing Exchangeability

In: Algorithmic Learning in a Random World

Author

Listed:
  • Vladimir Vovk

    (University of London, Royal Holloway)

  • Alexander Gammerman

    (University of London, Royal Holloway)

  • Glenn Shafer

    (Rutgers University)

Abstract

In Chaps. 2 – 7 we assumed that all examples output by Reality are exchangeable. This is a strong assumption, but it is standard in machine learning (where the even stronger assumption of randomness is usually made). We start this chapter (in Sect. 8.1) by discussing how to test this assumption in the online mode: at each point in time we would like to have a valid measure of the amount of evidence found against the hypothesis of exchangeability. Conformal prediction is a valuable tool for designing such online testing methods, and can also be adapted for detecting different kinds of deviations from exchangeability (Sect. 8.2). Such methods of conformal testing can be applied in multistage testing, when the task is to raise an alarm soon after the assumption of exchangeability becomes violated (Sect. 8.3), and in deciding when a machine learning algorithm depending on the exchangeability assumption should be retrained (Sect. 8.4).

Suggested Citation

  • Vladimir Vovk & Alexander Gammerman & Glenn Shafer, 2022. "Testing Exchangeability," Springer Books, in: Algorithmic Learning in a Random World, edition 2, chapter 0, pages 227-263, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-06649-8_8
    DOI: 10.1007/978-3-031-06649-8_8
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