In this paper, we focus on the problem of conformal prediction with conditional guarantees. Prior work has shown that it is impossible to construct nontrivial prediction sets with full conditional coverage guarantees. A wealth of research has considered relaxations of full conditional guarantees, relying on some predefined uncertainty structures. Departing from this line of thinking, we propose Partition Learning Conformal Prediction (PLCP), a framework to improve conditional validity of prediction sets through learning uncertainty-guided features from the calibration data. We implement PLCP efficiently with alternating gradient descent, utilizing off-the-shelf machine learning models. We further analyze PLCP theoretically and provide conditional guarantees for infinite and finite sample sizes. Finally, our experimental results over four real-world and synthetic datasets show the superior performance of PLCP compared to state-of-the-art methods in terms of coverage and length in both classification and regression scenarios.

In partial label learning (PLL), each instance is associated with a set of candidate labels among which only one is ground-truth. The majority of the existing works focuses on constructing robust classifiers to estimate the labeling confidence of candidate labels in order to identify the correct one. However, these methods usually struggle to rectify mislabeled samples. To help existing PLL methods identify and rectify mislabeled samples, in this paper, we introduce a novel partner classifier and propose a novel ``mutual supervision'' paradigm. Specifically, we instantiate the partner classifier predicated on the implicit fact that non-candidate labels of a sample should not be assigned to it, which is inherently accurate and has not been fully investigated in PLL. Furthermore, a novel collaborative term is formulated to link the base classifier and the partner one. During each stage of mutual supervision, both classifiers will blur each other's predictions through a blurring mechanism to prevent overconfidence in a specific label. Extensive experiments demonstrate that the performance and disambiguation ability of several well-established stand-alone and deep-learning based PLL approaches can be significantly improved by coupling with this learning paradigm.