# Alternate Estimation of a Classifier and the Class-Prior from Positive and Unlabeled Data

arXiv: https://arxiv.org/abs/1809.05710 · HTML: https://mlsanity.com/paper/1809.05710/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2018.

## Built on by (most cited first, 2 of 2)

- [A Positive/Unlabeled Approach for the Segmentation of Medical Sequences using Point-Wise Supervision](https://mlsanity.com/paper/2107.08394/) (2021)
- [Learning from Double Positive and Unlabeled Data for Potential-Customer Identification](https://mlsanity.com/paper/2506.00436/) (2025)

## Abstract (arXiv)

We consider a problem of learning a binary classifier only from positive data and unlabeled data (PU learning) and estimating the class-prior in unlabeled data under the case-control scenario. Most of the recent methods of PU learning require an estimate of the class-prior probability in unlabeled data, and it is estimated in advance with another method. However, such a two-step approach which first estimates the class prior and then trains a classifier may not be the optimal approach since the estimation error of the class-prior is not taken into account when a classifier is trained. In this paper, we propose a novel unified approach to estimating the class-prior and training a classifier alternately. Our proposed method is simple to implement and computationally efficient. Through experiments, we demonstrate the practical usefulness of the proposed method.