Conformal Prediction with Cellwise Outliers: A Detect-then-Impute Approach

Qian Peng, Yajie Bao, Haojie Ren, Zhaojun Wang, Changliang Zou
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:48808-48831, 2025.

Abstract

Conformal prediction is a powerful tool for constructing prediction intervals for black-box models, providing a finite sample coverage guarantee for exchangeable data. However, this exchangeability is compromised when some entries of the test feature are contaminated, such as in the case of cellwise outliers. To address this issue, this paper introduces a novel framework called detect-then-impute conformal prediction. This framework first employs an outlier detection procedure on the test feature and then utilizes an imputation method to fill in those cells identified as outliers. To quantify the uncertainty in the processed test feature, we adaptively apply the detection and imputation procedures to the calibration set, thereby constructing exchangeable features for the conformal prediction interval of the test label. We develop two practical algorithms, $\texttt{PDI-CP}$ and $\texttt{JDI-CP}$, and provide a distribution-free coverage analysis under some commonly used detection and imputation procedures. Notably, $\texttt{JDI-CP}$ achieves a finite sample $1-2\alpha$ coverage guarantee. Numerical experiments on both synthetic and real datasets demonstrate that our proposed algorithms exhibit robust coverage properties and comparable efficiency to the oracle baseline.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-peng25b, title = {Conformal Prediction with Cellwise Outliers: A Detect-then-Impute Approach}, author = {Peng, Qian and Bao, Yajie and Ren, Haojie and Wang, Zhaojun and Zou, Changliang}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {48808--48831}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/peng25b/peng25b.pdf}, url = {https://proceedings.mlr.press/v267/peng25b.html}, abstract = {Conformal prediction is a powerful tool for constructing prediction intervals for black-box models, providing a finite sample coverage guarantee for exchangeable data. However, this exchangeability is compromised when some entries of the test feature are contaminated, such as in the case of cellwise outliers. To address this issue, this paper introduces a novel framework called detect-then-impute conformal prediction. This framework first employs an outlier detection procedure on the test feature and then utilizes an imputation method to fill in those cells identified as outliers. To quantify the uncertainty in the processed test feature, we adaptively apply the detection and imputation procedures to the calibration set, thereby constructing exchangeable features for the conformal prediction interval of the test label. We develop two practical algorithms, $\texttt{PDI-CP}$ and $\texttt{JDI-CP}$, and provide a distribution-free coverage analysis under some commonly used detection and imputation procedures. Notably, $\texttt{JDI-CP}$ achieves a finite sample $1-2\alpha$ coverage guarantee. Numerical experiments on both synthetic and real datasets demonstrate that our proposed algorithms exhibit robust coverage properties and comparable efficiency to the oracle baseline.} }
Endnote
%0 Conference Paper %T Conformal Prediction with Cellwise Outliers: A Detect-then-Impute Approach %A Qian Peng %A Yajie Bao %A Haojie Ren %A Zhaojun Wang %A Changliang Zou %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-peng25b %I PMLR %P 48808--48831 %U https://proceedings.mlr.press/v267/peng25b.html %V 267 %X Conformal prediction is a powerful tool for constructing prediction intervals for black-box models, providing a finite sample coverage guarantee for exchangeable data. However, this exchangeability is compromised when some entries of the test feature are contaminated, such as in the case of cellwise outliers. To address this issue, this paper introduces a novel framework called detect-then-impute conformal prediction. This framework first employs an outlier detection procedure on the test feature and then utilizes an imputation method to fill in those cells identified as outliers. To quantify the uncertainty in the processed test feature, we adaptively apply the detection and imputation procedures to the calibration set, thereby constructing exchangeable features for the conformal prediction interval of the test label. We develop two practical algorithms, $\texttt{PDI-CP}$ and $\texttt{JDI-CP}$, and provide a distribution-free coverage analysis under some commonly used detection and imputation procedures. Notably, $\texttt{JDI-CP}$ achieves a finite sample $1-2\alpha$ coverage guarantee. Numerical experiments on both synthetic and real datasets demonstrate that our proposed algorithms exhibit robust coverage properties and comparable efficiency to the oracle baseline.
APA
Peng, Q., Bao, Y., Ren, H., Wang, Z. & Zou, C.. (2025). Conformal Prediction with Cellwise Outliers: A Detect-then-Impute Approach. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:48808-48831 Available from https://proceedings.mlr.press/v267/peng25b.html.

Related Material