Analysis of Estimating the Bayes Rule for Gaussian Mixture Models with a Specified Missing-Data Mechanism
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910282724409344 |
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| author | Lyu, Ziyang |
| author_facet | Lyu, Ziyang |
| contents | Semi-supervised learning (SSL) 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(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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_13785 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Analysis of Estimating the Bayes Rule for Gaussian Mixture Models with a Specified Missing-Data Mechanism Lyu, Ziyang Machine Learning Semi-supervised learning (SSL) 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(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. |
| title | Analysis of Estimating the Bayes Rule for Gaussian Mixture Models with a Specified Missing-Data Mechanism |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2210.13785 |