mlsanityData to 7 Oct 2026

Conformalized Unconditional Quantile Regression

arXiv 2304.01426 ↗First posted 4 Apr 2023cs.LG stat.MEcited by 8

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Abstract (arXiv)

We develop a predictive inference procedure that combines conformal prediction (CP) with unconditional quantile regression (QR) -- a commonly used tool in econometrics that involves regressing the recentered influence function (RIF) of the quantile functional over input covariates. Unlike the more widely-known conditional QR, unconditional QR explicitly captures the impact of changes in covariate distribution on the quantiles of the marginal distribution of outcomes. Leveraging this property, our procedure issues adaptive predictive intervals with localized frequentist coverage guarantees. It operates by fitting a machine learning model for the RIFs using training data, and then applying the CP procedure for any test covariate with respect to a ``hypothetical'' covariate distribution localized around the new instance. Experiments show that our procedure is adaptive to heteroscedasticity, provides transparent coverage guarantees that are relevant to the test instance at hand, and performs competitively with existing methods in terms of efficiency.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 17 of its 34 references that are in the map. First posted on arXiv 4 Apr 2023.

Builds on

17 of 34 references.

References · 17

  1. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
  2. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,888
  3. 2016Distribution-Free Predictive Inference For Regressioncited by 657
  4. 2019Conformalized Quantile Regressioncited by 620
  5. 2015Variational Dropout and the Local Reparameterization Trickcited by 489
  6. 2019Deep Ensembles: A Loss Landscape Perspectivecited by 438
  7. 2015Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networkscited by 295
  8. 2021Localized Conformal Prediction: A Generalized Inference Framework for Conformal Predictioncited by 112
  9. 2019Distributional conformal predictioncited by 104
  10. 2019Nested conformal prediction and quantile out-of-bag ensemble methodscited by 88
  11. 2020Beyond Pinball Loss: Quantile Methods for Calibrated Uncertainty Quantificationcited by 77
  12. 2021Conformal Prediction using Conditional Histogramscited by 77
5 more
  1. 2014Regression Conformal Prediction with Nearest Neighbourscited by 59
  2. 2021Improving Conditional Coverage via Orthogonal Quantile Regressioncited by 48
  3. 2022Efficient and Differentiable Conformal Prediction with General Function Classescited by 25
  4. 2019Conformal prediction with localizationcited by 22
  5. 2017Variational Gaussian Dropout is not Bayesiancited by 13

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 2; 2025: 1; 2026: 2.

8 papers.

  1. 2024Conformal Prediction: A Data Perspectivecited by 25
  2. 2024Probabilistic Conformal Prediction with Approximate Conditional Validitycited by 23
  3. 2025Rectifying Conformity Scores for Better Conditional Coveragecited by 17
  4. 2023Efficient Conformal Prediction under Data Heterogeneitycited by 9
  5. 2023Conformalized Multimodal Uncertainty Regression and Reasoningcited by 6
  6. 2023Distribution-Free Model-Agnostic Regression Calibration via Nonparametric Methodscited by 3
  7. 2026Questioning the Coverage-Length Metric in Conformal Prediction: When Shorter Intervals Are Not Bettercited by 0
  8. 2026Generative Score Inference for Multimodal Datacited by 0