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Main Authors: Wang, Lijun, Fan, Xiaodan, Zhao, Hongyu, Liu, Jun S.
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2401.06383
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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