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Mixture Proportion Estimation and Weakly-supervised Kernel Test for Conditional Independence

arXiv 2604.07191 ↗First posted 8 Apr 2026cs.LG cs.AIcited by 0

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Abstract (arXiv)

Mixture proportion estimation (MPE) aims to estimate class priors from unlabeled data. This task is a critical component in weakly supervised learning, such as PU learning, learning with label noise, and domain adaptation. Existing MPE methods rely on the textitirreducibility assumption or its variant for identifiability. In this paper, we propose novel assumptions based on conditional independence (CI) given the class label, which ensure identifiability even when irreducibility does not hold. We develop method of moments estimators under these assumptions and analyze their asymptotic properties. Furthermore, we present weakly-supervised kernel tests to validate the CI assumptions, which are of independent interest in applications such as causal discovery and fairness evaluation. Empirically, we demonstrate the improved performance of our estimators compared with existing methods and that our tests successfully control both type I and type II errors.labelkey

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References · 22

  1. 2019A Survey on Bias and Fairness in Machine Learningcited by 1,911
  2. 2018Learning from positive and unlabeled data: a surveycited by 218
  3. 2017Positive-Unlabeled Learning with Non-Negative Risk Estimatorcited by 217
  4. 2013Classification with Asymmetric Label Noise: Consistency and Maximal Denoisingcited by 67
  5. 2016Mixture Proportion Estimation via Kernel Embedding of Distributionscited by 67
  6. 2018On the Minimal Supervision for Training Any Binary Classifier from Only Unlabeled Datacited by 43
  7. 2018Classification from Pairwise Similarity and Unlabeled Datacited by 36
  8. 2022Domain Adaptation under Open Set Label Shiftcited by 32
  9. 2022Efficient Conditionally Invariant Representation Learningcited by 19
  10. 2016Unsupervised Risk Estimation Using Only Conditional Independence Structurecited by 17
  11. 2020Rethinking Class-Prior Estimation for Positive-Unlabeled Learningcited by 15
  12. 2016Nonparametric semi-supervised learning of class proportionscited by 13
10 more
  1. 2024Practical Kernel Tests of Conditional Independencecited by 13
  2. 2021Binary Classification from Multiple Unlabeled Datasets via Surrogate Set Classificationcited by 12
  3. 2021Causal Inference Despite Limited Global Confounding via Mixture Modelscited by 9
  4. 2023Mixture Proportion Estimation Beyond Irreducibilitycited by 9
  5. 2025A Practical Introduction to Kernel Discrepancies: MMD, HSIC & KSDcited by 9
  6. 2015A simpler condition for consistency of a kernel independence testcited by 8
  7. 2013Nonparametric Estimation of Multi-View Latent Variable Modelscited by 7
  8. 2013Class Proportion Estimation with Application to Multiclass Anomaly Rejectioncited by 6
  9. 2023Causal Discovery via Conditional Independence Testing with Proxy Variablescited by 3
  10. 2023Causal Discovery in Mixtures of Populationscited by 3

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