# Errors-in-variables Fr'echet Regression with Low-rank Covariate Approximation

arXiv: https://arxiv.org/abs/2305.09282 · HTML: https://mlsanity.com/paper/2305.09282/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 60 references that are in the map.
- First posted on arXiv 16 May 2023.

## Builds on (most cited first, 10 of 10)

- [Fr'echet Regression for Random Objects with Euclidean Predictors](https://mlsanity.com/paper/1608.03012/) (2016)
- [On Robustness of Principal Component Regression](https://mlsanity.com/paper/1902.10920/) (2019)
- [Fr'echet Means and Procrustes Analysis in Wasserstein Space](https://mlsanity.com/paper/1701.06876/) (2017)
- [Fr'echet random forests for metric space valued regression with non euclidean predictors](https://mlsanity.com/paper/1906.01741/) (2019)
- [Functional Models for Time-Varying Random Objects](https://mlsanity.com/paper/1907.10829/) (2019)
- [Total Variation Regularized Fr'echet Regression for Metric-Space Valued Data](https://mlsanity.com/paper/1904.09647/) (2019)
- [Matrix-Variate Regressions and Envelope Models](https://mlsanity.com/paper/1605.01485/) (2016)
- [Fr'echet single index models for object response regression](https://mlsanity.com/paper/2108.06058/) (2021)
- [Robust functional regression based on principal components](https://mlsanity.com/paper/1807.00135/) (2018)
- [Nonparametric covariate-adjusted regression](https://mlsanity.com/paper/1601.02739/) (2016)

## Built on by (most cited first, 5 of 5)

- [End-to-End Deep Learning for Predicting Metric Space-Valued Outputs](https://mlsanity.com/paper/2509.23544/) (2025)
- [DFNN: A Deep Fr'echet Neural Network Framework for Learning Metric-Space-Valued Responses](https://mlsanity.com/paper/2510.17072/) (2025)
- [Fr'echet Geodesic Boosting](https://mlsanity.com/paper/2509.18013/) (2025)
- [Wasserstein-type Gaussian Process Regressions for Input Measurement Uncertainty](https://mlsanity.com/paper/2603.17271/) (2026)
- [Deep Single-Index Fr'echet Regression](https://mlsanity.com/paper/2606.06957/) (2026)

## Abstract (arXiv)

Fr'echet regression has emerged as a promising approach for regression analysis involving non-Euclidean response variables. However, its practical applicability has been hindered by its reliance on ideal scenarios with abundant and noiseless covariate data. In this paper, we present a novel estimation method that tackles these limitations by leveraging the low-rank structure inherent in the covariate matrix. Our proposed framework combines the concepts of global Fr'echet regression and principal component regression, aiming to improve the efficiency and accuracy of the regression estimator. By incorporating the low-rank structure, our method enables more effective modeling and estimation, particularly in high-dimensional and errors-in-variables regression settings. We provide a theoretical analysis of the proposed estimator's large-sample properties, including a comprehensive rate analysis of bias, variance, and additional variations due to measurement errors. Furthermore, our numerical experiments provide empirical evidence that supports the theoretical findings, demonstrating the superior performance of our approach. Overall, this work introduces a promising framework for regression analysis of non-Euclidean variables, effectively addressing the challenges associated with limited and noisy covariate data, with potential applications in diverse fields.