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Analysis of estimating the Bayes rule for Gaussian mixture models with a specified missing-data mechanism

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  • Ziyang Lyu

    (University of New South Wales)

Abstract

Semi-supervised learning approaches have been successfully applied in a wide range of engineering and scientific fields. This paper investigates the generative model framework with a missingness mechanism for unclassified observations, as introduced by Ahfock and McLachlan (Stat Comput 30:1–12, 2020). We show that in a partially classified sample, a classifier using Bayes’ rule of allocation with a missing-data mechanism can surpass a fully supervised classifier in a two-class normal homoscedastic model, especially with moderate to low overlap and proportion of missing class labels, or with large overlap but few missing labels. It also outperforms a classifier with no missing-data mechanism regardless of the overlap region or the proportion of missing class labels. Our exploration of two- and three-component normal mixture models with unequal covariances through simulations further corroborates our findings. Finally, we illustrate the use of the proposed classifier with a missing-data mechanism on interneuronal and skin lesion datasets.

Suggested Citation

  • Ziyang Lyu, 2024. "Analysis of estimating the Bayes rule for Gaussian mixture models with a specified missing-data mechanism," Computational Statistics, Springer, vol. 39(7), pages 3727-3751, December.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:7:d:10.1007_s00180-023-01447-0
    DOI: 10.1007/s00180-023-01447-0
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    References listed on IDEAS

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    1. Fabrizia Mealli & Donald B. Rubin, 2015. "Clarifying missing at random and related definitions, and implications when coupled with exchangeability," Biometrika, Biometrika Trust, vol. 102(4), pages 995-1000.
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