# Binary Classification from Positive-Confidence Data

arXiv: https://arxiv.org/abs/1710.07138 · HTML: https://mlsanity.com/paper/1710.07138/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Oct 2017.

## Built on by (most cited first, 23 of 23)

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- [Learning from N-Tuple Data with M Positive Instances: Unbiased Risk Estimation and Theoretical Guarantees](https://mlsanity.com/paper/2510.18406/) (2025)
- [Sparse classification with positive-confidence data in high dimensions](https://mlsanity.com/paper/2512.24443/) (2025)
- [AUC Maximization from Biased Positive-unlabeled Data with Confidence](https://mlsanity.com/paper/2609.10928/) (2026)

## Abstract (arXiv)

Can we learn a binary classifier from only positive data, without any negative data or unlabeled data? We show that if one can equip positive data with confidence (positive-confidence), one can successfully learn a binary classifier, which we name positive-confidence (Pconf) classification. Our work is related to one-class classification which is aimed at "describing" the positive class by clustering-related methods, but one-class classification does not have the ability to tune hyper-parameters and their aim is not on "discriminating" positive and negative classes. For the Pconf classification problem, we provide a simple empirical risk minimization framework that is model-independent and optimization-independent. We theoretically establish the consistency and an estimation error bound, and demonstrate the usefulness of the proposed method for training deep neural networks through experiments.