Variable Selection for Additive Global Fréchet Regression
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914041733054464 |
|---|---|
| author | Yang, Haoyi Bhattacharjee, Satarupa Xue, Lingzhou Li, Bing |
| author_facet | Yang, Haoyi Bhattacharjee, Satarupa Xue, Lingzhou Li, Bing |
| contents | We present a novel framework for variable selection in Fréchet regression with responses in general metric spaces, a setting increasingly relevant for analyzing non-Euclidean data such as probability distributions and covariance matrices. Building on the concept of (weak) Fréchet conditional means, we develop an additive regression model that represents the metric-based discrepancy of the response as a sum of covariate-specific nonlinear functions in reproducing kernel Hilbert spaces (RKHS). To address the absence of linear structure in the response space, we transform the response via squared distances, enabling an interpretable and tractable additive decomposition. Variable selection is performed using Elastic Net regularization, extended to the RKHS setting, and further refined through a local linear approximation scheme that incorporates folded concave penalties such as the SCAD. We establish theoretical guarantees, including variable selection consistency and the strong oracle property, under minimal assumptions tailored to metric-space-valued responses. Simulations and applications to distributional and matrix-valued data demonstrate the scalability, interpretability, and practical effectiveness of the proposed approach. This work provides a principled foundation for statistical learning with random object data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13685 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variable Selection for Additive Global Fréchet Regression Yang, Haoyi Bhattacharjee, Satarupa Xue, Lingzhou Li, Bing Statistics Theory Methodology 62G05, 62J02, 62G08, 62J99 We present a novel framework for variable selection in Fréchet regression with responses in general metric spaces, a setting increasingly relevant for analyzing non-Euclidean data such as probability distributions and covariance matrices. Building on the concept of (weak) Fréchet conditional means, we develop an additive regression model that represents the metric-based discrepancy of the response as a sum of covariate-specific nonlinear functions in reproducing kernel Hilbert spaces (RKHS). To address the absence of linear structure in the response space, we transform the response via squared distances, enabling an interpretable and tractable additive decomposition. Variable selection is performed using Elastic Net regularization, extended to the RKHS setting, and further refined through a local linear approximation scheme that incorporates folded concave penalties such as the SCAD. We establish theoretical guarantees, including variable selection consistency and the strong oracle property, under minimal assumptions tailored to metric-space-valued responses. Simulations and applications to distributional and matrix-valued data demonstrate the scalability, interpretability, and practical effectiveness of the proposed approach. This work provides a principled foundation for statistical learning with random object data. |
| title | Variable Selection for Additive Global Fréchet Regression |
| topic | Statistics Theory Methodology 62G05, 62J02, 62G08, 62J99 |
| url | https://arxiv.org/abs/2509.13685 |