Instance-Dependent PU Learning by Bayesian Optimal Relabeling

TL;DR

This paper introduces a Bayesian optimal relabeling approach for positive-unlabeled learning that accounts for biased sampling of positive examples, improving label accuracy and domain correction without requiring parameter tuning.

Contribution

It proposes a novel probabilistic-gap based PU learning algorithm that automatically relabels data considering bias, with a theoretical consistency guarantee and no need for parameter tuning.

Findings

Works well on both generated and real-world datasets

Automatically relabels biased positive examples with Bayesian optimal classifier

Remedies biased domain using kernel mean matching

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.