# Prior shift estimation for positive unlabeled data through the lens of kernel embedding

arXiv: https://arxiv.org/abs/2502.21194 · HTML: https://mlsanity.com/paper/2502.21194/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 50 references that are in the map.
- First posted on arXiv 28 Feb 2025.

## Builds on (most cited first, 16 of 16)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [Detecting and Correcting for Label Shift with Black Box Predictors](https://mlsanity.com/paper/1802.03916/) (2018)
- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [Learning from positive and unlabeled data: a survey](https://mlsanity.com/paper/1811.04820/) (2018)
- [A Unified View of Label Shift Estimation](https://mlsanity.com/paper/2003.07554/) (2020)
- [Mixture Proportion Estimation via Kernel Embedding of Distributions](https://mlsanity.com/paper/1603.02501/) (2016)
- [Self-PU: Self Boosted and Calibrated Positive-Unlabeled Training](https://mlsanity.com/paper/2006.11280/) (2020)
- [Dist-PU: Positive-Unlabeled Learning from a Label Distribution Perspective](https://mlsanity.com/paper/2212.02801/) (2022)
- [Efficient Aggregated Kernel Tests using Incomplete U-statistics](https://mlsanity.com/paper/2206.09194/) (2022)
- [Estimating the class prior and posterior from noisy positives and unlabeled data](https://mlsanity.com/paper/1606.08561/) (2016)
- [Learning from Positive and Unlabeled Data with Arbitrary Positive Shift](https://mlsanity.com/paper/2002.10261/) (2020)
- [Quantification under prior probability shift: the ratio estimator and its extensions](https://mlsanity.com/paper/1807.03929/) (2018)
- [Positive-Unlabeled Classification under Class-Prior Shift: A Prior-invariant Approach Based on Density Ratio Estimation](https://mlsanity.com/paper/2107.05045/) (2021)
- [Label Shift Quantification with Robustness Guarantees via Distribution Feature Matching](https://mlsanity.com/paper/2306.04376/) (2023)
- [Single-sample versus case-control sampling scheme for Positive Unlabeled data: the story of two scenarios](https://mlsanity.com/paper/2312.02095/) (2023)

## Built on by (most cited first, 1 of 1)

- [Identifiability and Estimation for Unlabeled Finite Mixtures under Marginal Independence](https://mlsanity.com/paper/2606.07914/) (2026)

## Abstract (arXiv)

We study estimation of a class prior for unlabeled target samples which possibly differs from that of source population. Moreover, it is assumed that the source data is partially observable: only samples from the positive class and from the whole population are available (PU learning scenario). We introduce a novel direct estimator of a class prior which avoids estimation of posterior probabilities in both populations and has a simple geometric interpretation. It is based on a distribution matching technique together with kernel embedding in a Reproducing Kernel Hilbert Space and is obtained as an explicit solution to an optimisation task. We establish its asymptotic consistency as well as an explicit non-asymptotic bound on its deviation from the unknown prior, which is calculable in practice. We study finite sample behaviour for synthetic and real data and show that the proposal works consistently on par or better than its competitors.