Transductive Conformal Inference With Adaptive Scores: Proof of Corollary 4.1 | HackerNoon

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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.

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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

E Proof of Corollary 4.1

Let m0 = |H0|. We establish the following more general result.

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Now, let us prove Lemma E.1.

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