mlsanityData to 7 Oct 2026

Estimating the class prior and posterior from noisy positives and unlabeled data

arXiv 1606.08561 ↗First posted 28 Jun 2016stat.ML cs.LGcited by 25

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Abstract (arXiv)

We develop a classification algorithm for estimating posterior distributions from positive-unlabeled data, that is robust to noise in the positive labels and effective for high-dimensional data. In recent years, several algorithms have been proposed to learn from positive-unlabeled data; however, many of these contributions remain theoretical, performing poorly on real high-dimensional data that is typically contaminated with noise. We build on this previous work to develop two practical classification algorithms that explicitly model the noise in the positive labels and utilize univariate transforms built on discriminative classifiers. We prove that these univariate transforms preserve the class prior, enabling estimation in the univariate space and avoiding kernel density estimation for high-dimensional data. The theoretical development and both parametric and nonparametric algorithms proposed here constitutes an important step towards wide-spread use of robust classification algorithms for positive-unlabeled data.

Key facts. Cited by 25 papers in the map (data through 7 Oct 2026). First posted on arXiv 28 Jun 2016.

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Citing papers per year: 2021: 4; 2022: 6; 2023: 4; 2024: 2; 2025: 6; 2026: 3.

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  1. 2022A Self-supervised Riemannian GNN with Time Varying Curvature for Temporal Graph Learningcited by 24
  2. 2022Distantly Supervised Named Entity Recognition via Confidence-Based Multi-Class Positive and Unlabeled Learningcited by 21
  3. 2021Binary Classification from Multiple Unlabeled Datasets via Surrogate Set Classificationcited by 12
  4. 2021Learning Graph Neural Networks with Positive and Unlabeled Nodescited by 11
  5. 2021Quantifying disparities in intimate partner violence: a machine learning method to correct for underreportingcited by 8
  6. 2023When Less is Enough: Positive and Unlabeled Learning Model for Vulnerability Detectioncited by 8
  7. 2022One-Class Risk Estimation for One-Class Hyperspectral Image Classificationcited by 6
  8. 2025Learning from positive and unlabeled examples -Finite size sample boundscited by 6
  9. 2022Double logistic regression approach to biased positive-unlabeled datacited by 3
  10. 2023Leveraging Contaminated Datasets to Learn Clean-Data Distribution with Purified Generative Adversarial Networkscited by 2
  11. 2023Noisy Positive-Unlabeled Learning with Self-Training for Speculative Knowledge Graph Reasoningcited by 2
  12. 2024Deep Positive-Unlabeled Anomaly Detection for Contaminated Unlabeled Datacited by 2
13 more
  1. 2025Positive-Unlabeled Diffusion Models for Preventing Sensitive Data Generationcited by 2
  2. 2021A Novel Perspective for Positive-Unlabeled Learning via Noisy Labelscited by 1
  3. 2024Verifying the Selected Completely at Random Assumption in Positive-Unlabeled Learningcited by 1
  4. 2026Value Bonuses using Ensemble Errors for Exploration in Reinforcement Learningcited by 1
  5. 2022Risk bounds for PU learning under Selected At Random assumptioncited by 0
  6. 2022A Boosting Algorithm for Positive-Unlabeled Learningcited by 0
  7. 2023Regression with Sensor Data Containing Incomplete Observationscited by 0
  8. 2025Learning from Ambiguous Data with Hard Labelscited by 0
  9. 2025Prior shift estimation for positive unlabeled data through the lens of kernel embeddingcited by 0
  10. 2025Skill-based Safe Reinforcement Learning with Risk Planningcited by 0
  11. 2025Semiparametric Learning from Open-Set Label Shift Datacited by 0
  12. 2026AUCp: Pseudo-AUC for Inference Model Selection with Unlabeled Validation Data in Abnormality Detectioncited by 0
  13. 2026Importance Weighting for Unlabeled-unlabeled Learning under Distribution Shiftcited by 0