# Binary Classification from Positive Data with Skewed Confidence

arXiv: https://arxiv.org/abs/2001.10642 · HTML: https://mlsanity.com/paper/2001.10642/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jan 2020.

## Built on by (most cited first, 8 of 8)

- ["This is my unicorn, Fluffy": Personalizing frozen vision-language representations](https://mlsanity.com/paper/2204.01694/) (2022)
- [Is the Performance of My Deep Network Too Good to Be True? A Direct Approach to Estimating the Bayes Error in Binary Classification](https://mlsanity.com/paper/2202.00395/) (2022)
- [Binary Classification with Confidence Difference](https://mlsanity.com/paper/2310.05632/) (2023)
- [Multi-Class Classification from Single-Class Data with Confidences](https://mlsanity.com/paper/2106.08864/) (2021)
- [Classification from Positive and Biased Negative Data with Skewed Labeled Posterior Probability](https://mlsanity.com/paper/2203.05749/) (2022)
- [Learning from N-Tuple Data with M Positive Instances: Unbiased Risk Estimation and Theoretical Guarantees](https://mlsanity.com/paper/2510.18406/) (2025)
- [Recent advances in weakly supervised learning: New supervision paradigms, assumption relaxations, and practical solutions](https://mlsanity.com/paper/2608.06896/) (2026)
- [AUC Maximization from Biased Positive-unlabeled Data with Confidence](https://mlsanity.com/paper/2609.10928/) (2026)

## Abstract (arXiv)

Positive-confidence (Pconf) classification [Ishida et al., 2018] is a promising weakly-supervised learning method which trains a binary classifier only from positive data equipped with confidence. However, in practice, the confidence may be skewed by bias arising in an annotation process. The Pconf classifier cannot be properly learned with skewed confidence, and consequently, the classification performance might be deteriorated. In this paper, we introduce the parameterized model of the skewed confidence, and propose the method for selecting the hyperparameter which cancels out the negative impact of skewed confidence under the assumption that we have the misclassification rate of positive samples as a prior knowledge. We demonstrate the effectiveness of the proposed method through a synthetic experiment with simple linear models and benchmark problems with neural network models. We also apply our method to drivers' drowsiness prediction to show that it works well with a real-world problem where confidence is obtained based on manual annotation.