Instance-Dependent PU Learning by Bayesian Optimal Relabeling

Abstract

When learning from positive and unlabelled data, it is a strong assumption that the positive observations are randomly sampled from the distribution of $X$ conditional on $Y=1$, where X stands for the feature and Y the label. Most existing algorithms are optimally designed under the assumption. However, for many real-world applications, the observed positive examples are dependent on the conditional probability $P(Y=1|X)$ and should be sampled biasedly. In this paper, we assume that a positive example with a higher $P(Y=1|X)$ is more likely to be labelled and propose a probabilistic-gap based PU learning algorithms. Specifically, by treating the unlabelled data as noisy negative examples, we could automatically label a group positive and negative examples whose labels are identical to the ones assigned by a Bayesian optimal classifier with a consistency guarantee. The relabelled examples have a biased domain, which is remedied by the kernel mean matching technique. The proposed algorithm is model-free and thus do not have any parameters to tune. Experimental results demonstrate that our method works well on both generated and real-world datasets.

References in corpus (5)

• Distributed Representations of Sentences and Documents
• Learning from Complementary Labels
• Transfer Learning with Label Noise
• Learning with Bounded Instance- and Label-dependent Label Noise
• Learning with Biased Complementary Labels

Cited by in corpus (5)

• Generalized Out-of-Distribution Detection: A Survey
• Alleviating Structural Distribution Shift in Graph Anomaly Detection
• Positive-Unlabeled Learning with Adversarial Data Augmentation for Knowledge Graph Completion
• Fairness Evaluation in Presence of Biased Noisy Labels
• Fairness-aware Model-agnostic Positive and Unlabeled Learning