On metric choice in dimension reduction for Fréchet regression
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913558974955520 |
|---|---|
| author | Soale, Abdul-Nasah Ma, Congli Chen, Siyu Koomson, Obed |
| author_facet | Soale, Abdul-Nasah Ma, Congli Chen, Siyu Koomson, Obed |
| contents | Fréchet regression is becoming a mainstay in modern data analysis for analyzing non-traditional data types belonging to general metric spaces. This novel regression method is especially useful in the analysis of complex health data such as continuous monitoring and imaging data. Fréchet regression utilizes the pairwise distances between the random objects, which makes the choice of metric crucial in the estimation. In this paper, existing dimension reduction methods for Fréchet regression are reviewed, and the effect of metric choice on the estimation of the dimension reduction subspace is explored for the regression between random responses and Euclidean predictors. Extensive numerical studies illustrate how different metrics affect the central and central mean space estimators. Two real applications involving analysis of brain connectivity networks of subjects with and without Parkinson's disease and an analysis of the distributions of glycaemia based on continuous glucose monitoring data are provided, to demonstrate how metric choice can influence findings in real applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01783 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On metric choice in dimension reduction for Fréchet regression Soale, Abdul-Nasah Ma, Congli Chen, Siyu Koomson, Obed Methodology Applications Computation Machine Learning Fréchet regression is becoming a mainstay in modern data analysis for analyzing non-traditional data types belonging to general metric spaces. This novel regression method is especially useful in the analysis of complex health data such as continuous monitoring and imaging data. Fréchet regression utilizes the pairwise distances between the random objects, which makes the choice of metric crucial in the estimation. In this paper, existing dimension reduction methods for Fréchet regression are reviewed, and the effect of metric choice on the estimation of the dimension reduction subspace is explored for the regression between random responses and Euclidean predictors. Extensive numerical studies illustrate how different metrics affect the central and central mean space estimators. Two real applications involving analysis of brain connectivity networks of subjects with and without Parkinson's disease and an analysis of the distributions of glycaemia based on continuous glucose monitoring data are provided, to demonstrate how metric choice can influence findings in real applications. |
| title | On metric choice in dimension reduction for Fréchet regression |
| topic | Methodology Applications Computation Machine Learning |
| url | https://arxiv.org/abs/2410.01783 |