Stochastic tensor space feature theory with applications to robust machine learning
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2021
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| author | Castrillon-Candas, Julio Enrique Shi, Kaili Liu, Dingning Yang, Sicheng Zhang, Xiaoling Kon, Mark Initiative, the Alzheimer's Disease Neuroimaging |
| author_facet | Castrillon-Candas, Julio Enrique Shi, Kaili Liu, Dingning Yang, Sicheng Zhang, Xiaoling Kon, Mark Initiative, the Alzheimer's Disease Neuroimaging |
| contents | In this paper we develop a Multilevel Orthogonal Subspace (MOS) Karhunen-Loeve feature theory based on stochastic tensor spaces, for the construction of robust machine learning features. Training data are treated as instances of a random field within a relevant Bochner space. Our key observation is that separate machine learning classes can reside predominantly in mostly distinct subspaces. Using the Karhunen-Loeve expansion and a hierarchical expansion of the first (nominal) class, a MOS is constructed to detect anomalous signal components, treating the second class as an outlier of the first. The projection coefficients of the input data into these subspaces are then used to train a Machine Learning (ML) classifier. These coefficients become new features from which much clearer separation surfaces can arise for the underlying classes. Tests in the blood plasma dataset (Alzheimer's Disease Neuroimaging Initiative) show dramatic increases in accuracy. This contrast to popular ML methods such as Gradient Boosting, RUS Boost, Random Forest and Neural Networks. We show that with a non-invasive blood test, high-accuracy results can be obtained for predicting AD stages such as cognitive normal, mild cognitive impairment and dementia. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_01729 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Stochastic tensor space feature theory with applications to robust machine learning Castrillon-Candas, Julio Enrique Shi, Kaili Liu, Dingning Yang, Sicheng Zhang, Xiaoling Kon, Mark Initiative, the Alzheimer's Disease Neuroimaging Machine Learning 62R10, 60G35, 62-08, 60G60, 65F25, 46B09 In this paper we develop a Multilevel Orthogonal Subspace (MOS) Karhunen-Loeve feature theory based on stochastic tensor spaces, for the construction of robust machine learning features. Training data are treated as instances of a random field within a relevant Bochner space. Our key observation is that separate machine learning classes can reside predominantly in mostly distinct subspaces. Using the Karhunen-Loeve expansion and a hierarchical expansion of the first (nominal) class, a MOS is constructed to detect anomalous signal components, treating the second class as an outlier of the first. The projection coefficients of the input data into these subspaces are then used to train a Machine Learning (ML) classifier. These coefficients become new features from which much clearer separation surfaces can arise for the underlying classes. Tests in the blood plasma dataset (Alzheimer's Disease Neuroimaging Initiative) show dramatic increases in accuracy. This contrast to popular ML methods such as Gradient Boosting, RUS Boost, Random Forest and Neural Networks. We show that with a non-invasive blood test, high-accuracy results can be obtained for predicting AD stages such as cognitive normal, mild cognitive impairment and dementia. |
| title | Stochastic tensor space feature theory with applications to robust machine learning |
| topic | Machine Learning 62R10, 60G35, 62-08, 60G60, 65F25, 46B09 |
| url | https://arxiv.org/abs/2110.01729 |