Modelling positive and unlabelled data with a generalized additive density ratio model
Authors
Paper Information
-
Journal:
Journal of the Royal Statistical Society Series B -
DOI:
10.1093/jrsssb/qkag130 -
Published:
October 05, 2026 -
Added to Tracker:
Oct 06, 2026
Abstract
Abstract This paper focuses on learning from positive and unlabelled (PU) data, where only some positives are labelled and the rest are mixed with negatives. Classical exponential tilting models guarantee identifiability by imposing a linear structure, but they can be severely misspecified when the true relationships are nonlinear. We propose a generalized additive density-ratio framework that retains identifiability while allowing nonlinear and feature-specific effects. The approach comes with a practical fitting algorithm and supporting theory that enable estimation and inference for the mixture proportion and other quantities of interest. In simulations and analyses of real datasets, the proposed method matches the standard exponential tilting method when the linear model is correct and delivers clear gains when it is not. Overall, the framework strikes a useful balance between flexibility and interpretability for PU data and provides principled tools for estimation, prediction, and uncertainty assessment.
Author Details
Peijun Sang
AuthorDonglin Zeng
AuthorQinglong Tian
AuthorPengfei Li
AuthorYifan Sun
AuthorCitation Information
APA Format
Peijun Sang
,
Donglin Zeng
,
Qinglong Tian
,
Pengfei Li
&
Yifan Sun
(2026)
.
Modelling positive and unlabelled data with a generalized additive density ratio model.
Journal of the Royal Statistical Society Series B
, 10.1093/jrsssb/qkag130.
BibTeX Format
@article{paper1734,
title = { Modelling positive and unlabelled data with a generalized additive density ratio model },
author = {
Peijun Sang
and Donglin Zeng
and Qinglong Tian
and Pengfei Li
and Yifan Sun
},
journal = { Journal of the Royal Statistical Society Series B },
year = { 2026 },
doi = { 10.1093/jrsssb/qkag130 },
url = { https://doi.org/10.1093/jrsssb/qkag130 }
}