# Copula-based conformal prediction for Multi-Target Regression

arXiv: https://arxiv.org/abs/2101.12002 · HTML: https://mlsanity.com/paper/2101.12002/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 51 references that are in the map.
- First posted on arXiv 28 Jan 2021.

## Builds on (most cited first, 6 of 6)

- [An Overview of Multi-Task Learning in Deep Neural Networks](https://mlsanity.com/paper/1706.05098/) (2017)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Learning by Transduction](https://mlsanity.com/paper/1301.7375/) (2013)
- [Regression Conformal Prediction with Nearest Neighbours](https://mlsanity.com/paper/1401.3880/) (2014)
- [CLTune: A Generic Auto-Tuner for OpenCL Kernels](https://mlsanity.com/paper/1703.06503/) (2017)
- [Training conformal predictors](https://mlsanity.com/paper/2005.07037/) (2020)

## Built on by (most cited first, 30 of 53)

- [Conformal Uncertainty Sets for Robust Optimization](https://mlsanity.com/paper/2105.14957/) (2021)
- [Probabilistic Conformal Prediction Using Conditional Random Samples](https://mlsanity.com/paper/2206.06584/) (2022)
- [Conformal prediction for multi-dimensional time series by ellipsoidal sets](https://mlsanity.com/paper/2403.03850/) (2024)
- [Copula Conformal Prediction for Multi-step Time Series Forecasting](https://mlsanity.com/paper/2212.03281/) (2022)
- [Minimum Volume Conformal Sets for Multivariate Regression](https://mlsanity.com/paper/2503.19068/) (2025)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Adaptive Bounding Box Uncertainties via Two-Step Conformal Prediction](https://mlsanity.com/paper/2403.07263/) (2024)
- [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)
- [MAPIE: an open-source library for distribution-free uncertainty quantification](https://mlsanity.com/paper/2207.12274/) (2022)
- [Rectifying Conformity Scores for Better Conditional Coverage](https://mlsanity.com/paper/2502.16336/) (2025)
- [Semiparametric conformal prediction](https://mlsanity.com/paper/2411.02114/) (2024)
- [Conformal Methods for Quantifying Uncertainty in Spatiotemporal Data: A Survey](https://mlsanity.com/paper/2209.03580/) (2022)
- [Uncertainty Quantification of Surrogate Models using Conformal Prediction](https://mlsanity.com/paper/2408.09881/) (2024)
- [Your copula is a classifier in disguise: classification-based copula density estimation](https://mlsanity.com/paper/2411.03014/) (2024)
- [Conditional Coverage Diagnostics for Conformal Prediction](https://mlsanity.com/paper/2512.11779/) (2025)
- [Exact and Approximate Conformal Inference for Multi-Output Regression](https://mlsanity.com/paper/2210.17405/) (2022)
- [Max-Rank: Efficient Multiple Testing for Conformal Prediction](https://mlsanity.com/paper/2311.10900/) (2023)
- [Guaranteed prediction sets for functional surrogate models](https://mlsanity.com/paper/2501.18426/) (2025)
- [Volume-Sorted Prediction Set: Efficient Conformal Prediction for Multi-Target Regression](https://mlsanity.com/paper/2503.02205/) (2025)
- [Document Summarization with Conformal Importance Guarantees](https://mlsanity.com/paper/2509.20461/) (2025)
- [Conformal Prediction for Hierarchical Data](https://mlsanity.com/paper/2411.13479/) (2024)
- [Flow-based Conformal Prediction for Multi-dimensional Time Series](https://mlsanity.com/paper/2502.05709/) (2025)
- [Powerful batch conformal prediction for classification](https://mlsanity.com/paper/2411.02239/) (2024)
- [JAPAN: Joint Adaptive Prediction Areas with Normalising-Flows](https://mlsanity.com/paper/2505.23196/) (2025)
- [Calibrating Decision Robustness via Inverse Conformal Risk Control](https://mlsanity.com/paper/2510.07750/) (2025)
- [Conformal Loss-Controlling Prediction](https://mlsanity.com/paper/2301.02424/) (2023)
- [Uncertainty quantification in automated valuation models with spatially weighted conformal prediction](https://mlsanity.com/paper/2312.06531/) (2023)
- [JANET: Joint Adaptive predictioN-region Estimation for Time-series](https://mlsanity.com/paper/2407.06390/) (2024)
- [Topology-Aware Conformal Prediction for Stream Networks](https://mlsanity.com/paper/2503.04981/) (2025)

## Abstract (arXiv)

There are relatively few works dealing with conformal prediction for multi-task learning issues, and this is particularly true for multi-target regression. This paper focuses on the problem of providing valid (i.e., frequency calibrated) multi-variate predictions. To do so, we propose to use copula functions applied to deep neural networks for inductive conformal prediction. We show that the proposed method ensures efficiency and validity for multi-target regression problems on various data sets.