Adaptive Geometric Regression for High-Dimensional Structured Data
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| author | Gajer, Pawel Ravel, Jacques |
| author_facet | Gajer, Pawel Ravel, Jacques |
| contents | We present a geometric framework for regression on structured high-dimensional
data that shifts the analysis from the ambient space to a geometric object
capturing the data's intrinsic structure. The method addresses a fundamental
challenge in analyzing datasets with high ambient dimension but low intrinsic
dimension, such as microbiome compositions, where traditional approaches fail
to capture the underlying geometric structure. Starting from a k-nearest
neighbor covering of the feature space, the geometry evolves iteratively
through heat diffusion and response-coherence modulation, concentrating mass
within regions where the response varies smoothly while creating diffusion
barriers where the response changes rapidly. This iterative refinement
produces conditional expectation estimates that respect both the intrinsic
geometry of the feature space and the structure of the response. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03817 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adaptive Geometric Regression for High-Dimensional Structured Data Gajer, Pawel Ravel, Jacques Methodology Statistics Theory 62G08, 62G20, 05C50, 58J35 We present a geometric framework for regression on structured high-dimensional data that shifts the analysis from the ambient space to a geometric object capturing the data's intrinsic structure. The method addresses a fundamental challenge in analyzing datasets with high ambient dimension but low intrinsic dimension, such as microbiome compositions, where traditional approaches fail to capture the underlying geometric structure. Starting from a k-nearest neighbor covering of the feature space, the geometry evolves iteratively through heat diffusion and response-coherence modulation, concentrating mass within regions where the response varies smoothly while creating diffusion barriers where the response changes rapidly. This iterative refinement produces conditional expectation estimates that respect both the intrinsic geometry of the feature space and the structure of the response. |
| title | Adaptive Geometric Regression for High-Dimensional Structured Data |
| topic | Methodology Statistics Theory 62G08, 62G20, 05C50, 58J35 |
| url | https://arxiv.org/abs/2511.03817 |