Medoid splits for efficient random forests in metric spaces

Matthieu Bulté*, Helle Sørensen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

An adaptation of the random forest algorithm for Fréchet regression is revisited, addressing the challenge of regression with random objects in metric spaces. To overcome the limitations of previous approaches, a new splitting rule is introduced, substituting the computationally expensive Fréchet means with a medoid-based approach. The asymptotic equivalence of this method to Fréchet mean-based procedures is demonstrated, along with the consistency of the associated regression estimator. This approach provides a sound theoretical framework and a more efficient computational solution to Fréchet regression, broadening its application to non-standard data types and complex use cases.

Original languageEnglish
Article number107995
JournalComputational Statistics and Data Analysis
Volume198
ISSN0167-9473
DOIs
Publication statusPublished - 2024

Bibliographical note

Publisher Copyright:
© 2024 The Authors

Keywords

  • Least squares regression
  • Medoid
  • Metric spaces
  • Random forest
  • Random objects

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