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

TL;DR

This paper introduces a detect-then-impute conformal prediction framework to handle cellwise outliers, ensuring reliable prediction intervals even when test features are contaminated, with proven coverage guarantees and practical algorithms.

Contribution

It proposes a novel detect-then-impute approach for conformal prediction that maintains coverage guarantees under cellwise outliers, along with two practical algorithms and theoretical analysis.

Findings

Algorithms achieve robust coverage on synthetic and real data.

JDI-CP attains finite sample $1-2\alpha$ coverage guarantee.

Methods demonstrate comparable efficiency to oracle baseline.

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, PDI-CP and JDI-CP, and provide a distribution-free coverage analysis under some commonly used detection and imputation procedures. Notably, 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.