In this paper, we dive deeper into this class of strategies.

Neural Information Processing Systems http://nips.cc/

R(h). (23) Here for simplicity, we abused the symbolD in(22)by maximizing outh0 in the originalD. In the top-left areaP,suppose only oneexample (markedbyxwith vertical coordinate1)isconfidently labeled as positive, and the rest examples are highly inconfidently labeled, hence not to contribute to the riskR. Similarly,there isonly one confidently labeled example ()inthe bottom-right area ofP, and it is negative with vertical coordinate 1. Wheneverλ > 2, the optimalhλ is in(0,1)and can be solved by a quadratic equation. In contrast,di-MDD is immune to this problem becauseRis used only to determineh, while the di-MDD value itself is solely contributed byD. Same as the scenario of largeλ, we do not change the feature distribution of source and target domains, hence keepingD(h) = 1 |h|.

Positive-Unlabeled (PU) learning aims to achieve high-accuracy binary classification with limited labeled positive examples and numerous unlabeled ones. Existing cost-sensitive-based methods often rely on strong assumptions that examples with an observed positive label were selected entirely at random. In fact, the uneven distribution of labels is prevalent in real-world PU problems, indicating that most actual positive and unlabeled data are subject to selection bias. In this paper, we propose a PU learning enhancement (PUe) algorithm based on causal inference theory, which employs normalized propensity scores and normalized inverse probability weighting (NIPW) techniques to reconstruct the loss function, thus obtaining a consistent, unbiased estimate of the classifier and enhancing the model's performance. Moreover, we investigate and propose a method for estimating propensity scores in deep learning using regularization techniques when the labeling mechanism is unknown. Our experiments on three benchmark datasets demonstrate the proposed PUe algorithm significantly improves the accuracy of classifiers on non-uniform label distribution datasets compared to advanced cost-sensitive PU methods.

In practice, γ = 1 gives good results and we mainly tuneα,β. As mentioned in Sec 2.3, I(s;x1:T),I(z1:T;x1:T) are estimated contrastively.

Given only positive examples and unlabeled examples (from both positive and negative classes), we might hope nevertheless to estimate an accurate positiveversus-negative classifier. Formally, this task is broken down into two subtasks: (i) Mixture Proportion Estimation(MPE)--determining the fraction of positive examples in the unlabeled data; and (ii)PU-learning--given such an estimate, learning the desired positive-versus-negative classifier.