Summary
The paper proposes a novel variable selection method for multi-label Fréchet regression, which employs implicit regularization to capture nonlinear interactions between predictors and responses while promoting model sparsity.
Highlights
- The proposed method extends the Global Fréchet regression model to accommodate multi-label settings.
- It uses implicit regularization instead of traditional explicit regularization approaches.
- The method effectively captures nonlinear interactions between predictors and responses.
- It promotes model sparsity and reduces dimensionality.
- The approach is particularly well-suited for high-dimensional datasets.
- Theoretical results demonstrate selection consistency and asymptotic normality.
- Numerical examples illustrate the performance of the proposed approach.
Key Insights
- The proposed variable selection method addresses the limitations of traditional explicit regularization approaches, which can introduce bias and compromise the model's ability to capture complex relationships.
- By employing implicit regularization, the method transforms the variable selection problem into a smoother one, better adapted to multidimensional data.
- The approach is particularly effective in high-dimensional datasets, where capturing subtle interactions between variables becomes increasingly challenging.
- The use of implicit regularization enables the method to reduce dimensionality without compromising the model's ability to capture complex relationships.
- Theoretical results demonstrate the consistency and asymptotic normality of the proposed estimator, ensuring its reliability and accuracy.
- The proposed method has significant implications for fields such as bioinformatics and image analysis, where multi-label problems are common and dimensionality reduction is crucial.
- The approach provides a novel solution for addressing the challenges of multi-label Fréchet regression, offering a more efficient and effective alternative to traditional methods.
Mindmap
Citation
Mansouri, D. E. K., Benkabou, S.-E., & Benabdeslem, K. (2024). Fréchet regression for multi-label feature selection with implicit regularization (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.18247