mlsanityData to 14 Oct 2026

Metric space valued Fr'echet regression

arXiv 2602.05225 ↗First posted 5 Feb 2026math.ST stat.ML stat.THcited by 0

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Abstract (arXiv)

We consider the problem of estimating the Fr'echet and conditional Fr'echet mean from data taking values in separable metric spaces. Unlike Euclidean spaces, where well-established methods are available, there is no practical estimator that works universally for all metric spaces. Therefore, we introduce a computable estimator for the Fr'echet mean based on random quantization techniques and establish its universal consistency across any separable metric spaces. Additionally, we propose another estimator for the conditional Fr'echet mean, leveraging data-driven partitioning and quantization, and demonstrate its universal consistency when the output space is any Banach space.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 15 of its 43 references that are in the map. First posted on arXiv 5 Feb 2026.

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References · 15

  1. 2016Fr'echet Regression for Random Objects with Euclidean Predictorscited by 57
  2. 2013Loss minimization and parameter estimation with heavy tailscited by 50
  3. 2019Universal Bayes consistency in metric spacescited by 33
  4. 2014Hypothesis Testing For Network Data in Functional Neuroimagingcited by 20
  5. 2020Universal consistency and rates of convergence of multiclass prototype algorithms in metric spacescited by 18
  6. 2021Network Regression with Graph Laplacianscited by 15
  7. 2019Modeling Network Populations via Graph Distancescited by 13
  8. 2019Fr'echet random forests for metric space valued regression with non euclidean predictorscited by 13
  9. 2022Random Forest Weighted Local Fr'echet Regression with Random Objectscited by 12
  10. 2019Manifold valued data analysis of samples of networks, with applications in corpus linguisticscited by 8
  11. 2020Uniform convergence of local Fr'echet regression, with applications to locating extrema and time warping for metric space valued trajectoriescited by 8
  12. 2020Universal consistency of the k-NN rule in metric spaces and Nagata dimensioncited by 4
3 more
  1. 2023Universal consistency of the k-NN rule in metric spaces and Nagata dimension. IIcited by 2
  2. 2025Robust Estimation in metric spaces: Achieving Exponential Concentration with a Fr'echet Mediancited by 1
  3. 2026Bayesian Multiple Multivariate Density-Density Regressioncited by 1

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