Medoid splits for efficient random forests in metric spaces

Matthieu Bulté and Helle Sørensen

Computational Statistics & Data Analysis, 2024, vol. 198, issue C

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.

Keywords: Least squares regression; Medoid; Metric spaces; Random forest; Random objects (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:198:y:2024:i:c:s0167947324000793

DOI: 10.1016/j.csda.2024.107995

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