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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.06383 |
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| _version_ | 1866909164691783680 |
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| author | Wang, Lijun Fan, Xiaodan Zhao, Hongyu Liu, Jun S. |
| author_facet | Wang, Lijun Fan, Xiaodan Zhao, Hongyu Liu, Jun S. |
| contents | A univariate continuous function can always be decomposed as the sum of a non-increasing function and a non-decreasing one. Based on this property, we propose a non-parametric regression method that combines two spline-fitted monotone curves. We demonstrate by extensive simulations that, compared to standard spline-fitting methods, the proposed approach is particularly advantageous in high-noise scenarios. Several theoretical guarantees are established for the proposed approach. Additionally, we present statistics to test the monotonicity of a function based on monotone decomposition, which can better control Type I error and achieve comparable (if not always higher) power compared to existing methods. Finally, we apply the proposed fitting and testing approaches to analyze the single-cell pseudotime trajectory datasets, identifying significant biological insights for non-monotonically expressed genes through Gene Ontology enrichment analysis. The source code implementing the methodology and producing all results is accessible at https://github.com/szcf-weiya/MonotoneDecomposition.jl. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06383 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Decomposition with Monotone B-splines: Fitting and Testing Wang, Lijun Fan, Xiaodan Zhao, Hongyu Liu, Jun S. Methodology A univariate continuous function can always be decomposed as the sum of a non-increasing function and a non-decreasing one. Based on this property, we propose a non-parametric regression method that combines two spline-fitted monotone curves. We demonstrate by extensive simulations that, compared to standard spline-fitting methods, the proposed approach is particularly advantageous in high-noise scenarios. Several theoretical guarantees are established for the proposed approach. Additionally, we present statistics to test the monotonicity of a function based on monotone decomposition, which can better control Type I error and achieve comparable (if not always higher) power compared to existing methods. Finally, we apply the proposed fitting and testing approaches to analyze the single-cell pseudotime trajectory datasets, identifying significant biological insights for non-monotonically expressed genes through Gene Ontology enrichment analysis. The source code implementing the methodology and producing all results is accessible at https://github.com/szcf-weiya/MonotoneDecomposition.jl. |
| title | Decomposition with Monotone B-splines: Fitting and Testing |
| topic | Methodology |
| url | https://arxiv.org/abs/2401.06383 |