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Conformal e-prediction in the presence of confounding

Vladimir Vovk, Ruodu Wang

Abstract

This note extends conformal e-prediction to cover the case where there is observed confounding between the random object $X$ and its label $Y$. We consider both the case where the observed data is IID and a case where some dependence between observations is permitted.

Conformal e-prediction in the presence of confounding

Abstract

This note extends conformal e-prediction to cover the case where there is observed confounding between the random object and its label . We consider both the case where the observed data is IID and a case where some dependence between observations is permitted.
Paper Structure (9 sections, 3 theorems, 26 equations, 2 figures)

This paper contains 9 sections, 3 theorems, 26 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The IID setting
  3. No stable stochastic mechanism for $X$
  4. Conclusion
  5. Connections with conformal prediction
  6. Simple conformal e-prediction
  7. Conditional conformal e-prediction
  8. Slack in (\ref{['eq:lem-E']})
  9. Some proofs

Key Result

Lemma 1

For each $y\in\mathbf{Y}$, it is true that

Figures (2)

  • Figure 1: The main causal graph of this note
  • Figure 2: The repeated causal graph

Theorems & Definitions (7)

  • Lemma 1
  • Corollary 2
  • proof
  • Remark 1
  • Lemma 3
  • proof : Proof of Lemma \ref{['lem:main']}
  • proof : Proof of Lemma \ref{['lem:oblivious']}