# Fr'echet regression with implicit denoising and multicollinearity reduction

arXiv: https://arxiv.org/abs/2412.18247 · HTML: https://mlsanity.com/paper/2412.18247/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 10 references that are in the map.
- First posted on arXiv 24 Dec 2024.

## Builds on (most cited first, 6 of 6)

- [Fr'echet Regression for Random Objects with Euclidean Predictors](https://mlsanity.com/paper/1608.03012/) (2016)
- [A Comprehensive Analysis of Deep Regression](https://mlsanity.com/paper/1803.08450/) (2018)
- [Random Forest Weighted Local Fr'echet Regression with Random Objects](https://mlsanity.com/paper/2202.04912/) (2022)
- [Single Index Fr'echet Regression](https://mlsanity.com/paper/2108.05437/) (2021)
- [Dimension Reduction for Fr'echet Regression](https://mlsanity.com/paper/2110.00467/) (2021)
- [A Multilabel Classification Framework for Approximate Nearest Neighbor Search](https://mlsanity.com/paper/1910.08322/) (2019)

## Abstract (arXiv)

Fr'echet regression extends linear regression to model complex responses in metric spaces, making it particularly relevant for multi-label regression, where eachinstance can have multiple associated labels. However, addressing noise and dependencies among predictors within this framework remains un derexplored. In this paper, we present an extension of the Global Fr'echet re gression model that enables explicit modeling of relationships between input variables and multiple responses. To address challenges arising from noise and multicollinearity, we propose a novel framework based on implicit regu larization, which preserves the intrinsic structure of the data while effectively capturing complex dependencies. Our approach ensures accurate and efficient modeling without the biases introduced by traditional explicit regularization methods. Theoretical guarantees are provided, and the performance of the proposed method is demonstrated through numerical experiments.