Instance-Dependent PU Learning by Bayesian Optimal Relabeling
This addresses a limitation in PU learning for real-world applications where positive examples are biasedly sampled, offering a model-free solution, but it appears incremental as it builds on existing assumptions and techniques.
The paper tackles the problem of learning from positive and unlabelled data by addressing the assumption that positive observations are randomly sampled, proposing a probabilistic-gap based algorithm that automatically relabels examples with a consistency guarantee and remedies bias using kernel mean matching. Experimental results show it works well on generated and real-world datasets, though no concrete numbers are provided.
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.