A comparison of some conformal quantile regression methods

By Matteo Sesia, E.J. Candes. Stat, 2019

140 citations recorded by the source corpus.

We compare two recent methods that combine conformal inference with quantile regression to produce locally adaptive and marginally valid prediction intervals under sample exchangeability (Romano, Patterson, & Candès, 2019, arXiv:1905.03222; Kivaranovic, Johnson, & Leeb, 2019, arXiv:1905.10634). First, we prove that these two approaches are asymptotically efficient in large samples, under some additional assumptions. Then we compare them empirically on simulated and real data. Our results demonstrate that the method of Romano et al. typically yields tighter prediction intervals in finite samples. Finally, we discuss how to tune these procedures by fixing the relative proportions of observations used for training and conformalization. Our empirical results suggest that using between 70% and 90% of the data for training often achieves a good balance between minimizing the average width of the predictions intervals and the variability in their practical coverage.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/14759c1a3b35a2ca545bf075c434689a5c4a688c

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Citations in the corpus

Knowing what you know: valid confidence sets in multiclass and multilabel prediction (2020, methodology): “We additionally have that This is item (ii) in the proof of Theorem 1 of Sesia and Cand`es [29] (see Appendix A of their paper), which proves the convergence (25) of the marginal quantile of the error precisely when (cid:98) q σα and (cid:98) s are L 2 -consistent in probability (when the…”
Localized Conformal Prediction: A Generalized Inference Framework for Conformal Prediction (2021, background): “Another line of related work aims to construct better score functions (Lei et al., 2018; Romano et al., 2019; Kivaranovic et al., 2019; Sesia and Candès, 2020; Izbicki et al., 2019a; Chernozhukov et al., 2019).”
Classification with Valid and Adaptive Coverage (2020, methodology): “This statement could be made rigorous under some additional technical assumptions besides the consistency of the black box [20].”