Conformal Prediction Under Generalized Covariate Shift with Posterior Drift (2502.17744v1)

Abstract: In many real applications of statistical learning, collecting sufficiently many training data is often expensive, time-consuming, or even unrealistic. In this case, a transfer learning approach, which aims to leverage knowledge from a related source domain to improve the learning performance in the target domain, is more beneficial. There have been many transfer learning methods developed under various distributional assumptions. In this article, we study a particular type of classification problem, called conformal prediction, under a new distributional assumption for transfer learning. Classifiers under the conformal prediction framework predict a set of plausible labels instead of one single label for each data instance, affording a more cautious and safer decision. We consider a generalization of the \textit{covariate shift with posterior drift} setting for transfer learning. Under this setting, we propose a weighted conformal classifier that leverages both the source and target samples, with a coverage guarantee in the target domain. Theoretical studies demonstrate favorable asymptotic properties. Numerical studies further illustrate the usefulness of the proposed method.

An Analysis of Conformal Prediction Under Covariate Shift with Posterior Drift

The paper "Conformal Prediction Under Generalized Covariate Shift with Posterior Drift" by Wang and Qiao addresses the complex challenge presented by distributional discrepancies between source and target domains in statistical learning. This work builds upon the framework of conformal prediction, which traditionally operates under the assumption of data exchangeability but often suffers under conditions of distribution shift.

In many real-world applications, acquiring extensive labeled data from the target distribution can be economically impractical or occasionally unfeasible. Therefore, leveraging data from a related source distribution through transfer learning becomes pivotal. This paper focuses on a novel distributional assumption: covariate shift with posterior drift (CSPD). This encompasses scenarios where both the marginal distribution of the covariates and the conditional class probabilities differ between the source and target datasets.

Investigating this intricate setup, the authors propose a method termed Weighted Conformal Classification (WCC-CSPD), which adapts the conformal prediction approach to ensure desired coverage properties even when CSPD conditions are present. The principal innovation lies in utilizing a weighted algorithmic variant of conformal prediction influenced by estimates of the likelihood ratios between source and target distributions, specifically considering both source and target samples during calibration. The proposed methodology guarantees a coverage rate for the prediction set in the target domain, which, as theoretically demonstrated, exhibits favorable asymptotic properties despite potential computational challenges in deriving weights.

The paper also introduces a generalization of the CSPD framework, referred to as $g-CSPD$, which further relaxes the monotonicity condition of the mapping between source and target posterior distributions, thus broadening the applicability of the proposed methods to more complex and realistic scenarios.

The methodological robustness of WCC-CSPD is supported by simulation and semi-synthetic data experiments that affirm its ability to maintain the intended coverage levels. Specifically, WCC-CSPD outperforms traditional Conformal Prediction (CP) and Weighted Conformal Prediction (WCP) methods under conditions of CSPD. Whereas CP falters due to limited target training data, and WCP struggles with effective sample size reduction under significant shifts, WCC-CSPD effectively harmonizes the information from both source and target datasets.

Practically, the implications of this research are significant: the ability to create prediction sets with statistical guarantees under distribution shifts enhances the reliability of models in fields where decision errors bear substantial consequence, such as in medical diagnostics or security applications. Theoretically, this work invigorates the discourse on distribution shifts in conformal prediction, paving pathways for future research into multi-source scenarios and continual exploration of broader distributional assumptions in predictive models.

The advances presented in this paper enrich the toolkit available for reliable machine learning models in non-stationary environments, signaling a promising direction for future work in distributionally robust predictive modeling. Researchers are encouraged to continue exploring the generalizations of CSPD assumptions to further bolster the robustness and versatility of predictive inference frameworks in the progressive landscape of artificial intelligence.