# Semiparametric conformal prediction

arXiv: https://arxiv.org/abs/2411.02114 · HTML: https://mlsanity.com/paper/2411.02114/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 86 references that are in the map.
- First posted on arXiv 4 Nov 2024.

## Builds on (most cited first, 18 of 18)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Semiparametric doubly robust targeted double machine learning: a review](https://mlsanity.com/paper/2203.06469/) (2022)
- [A Conformal Prediction Approach to Explore Functional Data](https://mlsanity.com/paper/1302.6452/) (2013)
- [Copula-based conformal prediction for Multi-Target Regression](https://mlsanity.com/paper/2101.12002/) (2021)
- [Calibrated Multiple-Output Quantile Regression with Representation Learning](https://mlsanity.com/paper/2110.00816/) (2021)
- [Conformal Uncertainty Sets for Robust Optimization](https://mlsanity.com/paper/2105.14957/) (2021)
- [Exchangeability, Conformal Prediction, and Rank Tests](https://mlsanity.com/paper/2005.06095/) (2020)
- [Visually Communicating and Teaching Intuition for Influence Functions](https://mlsanity.com/paper/1810.03260/) (2018)
- [BOtied: Multi-objective Bayesian optimization with tied multivariate ranks](https://mlsanity.com/paper/2306.00344/) (2023)
- [Nonparametric estimation of simplified vine copula models: comparison of methods](https://mlsanity.com/paper/1701.00845/) (2017)
- [Concepts and Applications of Conformal Prediction in Computational Drug Discovery](https://mlsanity.com/paper/1908.03569/) (2019)
- [Probit transformation for nonparametric kernel estimation of the copula density](https://mlsanity.com/paper/1404.4414/) (2014)
- [Probit transformation for kernel density estimation on the unit interval](https://mlsanity.com/paper/1303.4121/) (2013)
- [Nonparametric Copula Models for Multivariate, Mixed, and Missing Data](https://mlsanity.com/paper/2210.14988/) (2022)
- [Semiparametric posterior corrections](https://mlsanity.com/paper/2306.06059/) (2023)

## Built on by (most cited first, 13 of 13)

- [Multivariate Conformal Prediction using Optimal Transport](https://mlsanity.com/paper/2502.03609/) (2025)
- [Optimal Transport-based Conformal Prediction](https://mlsanity.com/paper/2501.18991/) (2025)
- [Your copula is a classifier in disguise: classification-based copula density estimation](https://mlsanity.com/paper/2411.03014/) (2024)
- [Multivariate Conformal Selection](https://mlsanity.com/paper/2505.00917/) (2025)
- [Diffusion and Flow-based Copulas: Forgetting and Remembering Dependencies](https://mlsanity.com/paper/2509.19707/) (2025)
- [Online Conformal Prediction with Adversarial Semi-bandit Feedback via Regret Minimization](https://mlsanity.com/paper/2604.17984/) (2026)
- [Beyond Uncertainty Sets: Leveraging Optimal Transport to Extend Conformal Predictive Distributions to Multivariate Settings](https://mlsanity.com/paper/2511.15146/) (2025)
- [Vine Copulas as Differentiable Computational Graphs](https://mlsanity.com/paper/2506.13318/) (2025)
- [Interpretable Multivariate Conformal Prediction with Fast Transductive Standardization](https://mlsanity.com/paper/2512.15383/) (2025)
- [Throwing Vines at the Wall: Structure Learning via Random Search](https://mlsanity.com/paper/2510.20035/) (2025)
- [Minimax Multi-Target Conformal Prediction with Applications to Imaging Inverse Problems](https://mlsanity.com/paper/2511.13533/) (2025)
- [Debiased Machine Learning for Conformal Prediction of Counterfactual Outcomes Under Runtime Confounding](https://mlsanity.com/paper/2604.03772/) (2026)
- [Multivariate conformal uncertainty propagation in multitask atomistic simulation: Successes and pitfalls](https://mlsanity.com/paper/2609.31384/) (2026)

## Abstract (arXiv)

Many risk-sensitive applications require well-calibrated prediction sets over multiple, potentially correlated target variables, for which the prediction algorithm may report correlated errors. In this work, we aim to construct the conformal prediction set accounting for the joint correlation structure of the vector-valued non-conformity scores. Drawing from the rich literature on multivariate quantiles and semiparametric statistics, we propose an algorithm to estimate the 1-α quantile of the scores, where α is the user-specified miscoverage rate. In particular, we flexibly estimate the joint cumulative distribution function (CDF) of the scores using nonparametric vine copulas and improve the asymptotic efficiency of the quantile estimate using its influence function. The vine decomposition allows our method to scale well to a large number of targets. As well as guaranteeing asymptotically exact coverage, our method yields desired coverage and competitive efficiency on a range of real-world regression problems, including those with missing-at-random labels in the calibration set.