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

Jan Mielniczuk, Wojciech Rejchel, Paweł Teisseyre
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:640-648, 2026.

Abstract

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 the 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 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-mielniczuk26a, title = { Prior shift estimation for positive unlabeled data through the lens of kernel embedding }, author = {Mielniczuk, Jan and Rejchel, Wojciech and Teisseyre, Pawe{\l}}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {640--648}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/mielniczuk26a/mielniczuk26a.pdf}, url = {https://proceedings.mlr.press/v300/mielniczuk26a.html}, abstract = { 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 the 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 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. } }
Endnote
%0 Conference Paper %T Prior shift estimation for positive unlabeled data through the lens of kernel embedding %A Jan Mielniczuk %A Wojciech Rejchel %A Paweł Teisseyre %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-mielniczuk26a %I PMLR %P 640--648 %U https://proceedings.mlr.press/v300/mielniczuk26a.html %V 300 %X 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 the 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 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.
APA
Mielniczuk, J., Rejchel, W. & Teisseyre, P.. (2026). Prior shift estimation for positive unlabeled data through the lens of kernel embedding . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:640-648 Available from https://proceedings.mlr.press/v300/mielniczuk26a.html.

Related Material