This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Ulysse Gazin, Universit´e Paris Cit´e and Sorbonne Universit´e, CNRS, Laboratoire de Probabilit´es, Statistique et Mod´elisation,
(2) Gilles Blanchard, Universit´e Paris Saclay, Institut Math´ematique d’Orsay,
(3) Etienne Roquain, Sorbonne Universit´e and Universit´e Paris Cit´e, CNRS, Laboratoire de Probabilit´es, Statistique et Mod´elisation.
Table of Links
- Abstract & Introduction
- Main results
- Application to prediction intervals
- Application to novelty detection
- Conclusion, Acknowledgements and References
- Appendix A: Exact formulas for Pn,m
- Appendix B: Numerical bounds and templates
- Appendix C: Proof
- Appendix D: Explicit control of (16) for α=0
- Appendix E: Proof of Corollary 4.1
- Appendix F: The Simes inequality
- Appendix G: Uniform FDP bound for AdaDetect
- Appendix H: Additional experiments
A Exact formulas for Pn,m
Theorem A.1 (ii) provides the exact dependency structure between the p-values: for instance, M(j)! = 1 when the coordinates of j = (j1, . . . , jm) are all distinct, while M(j)! = m! when the coordinates of j = (j1, . . . , jm) are the same. This means that the distribution slightly favors the j with repeated entries. This shows that the conformal p-values are not i.i.d. but have a positive structure of dependency. This is in accordance with the specific positive dependence property (called PRDS) already shown by Bates et al. (2023); Marandon et al. (2022).
