Medoid splits for efficient random forests in metric spaces

• URL: http://arxiv.org/abs/2306.17031v1
• Date: Thu, 29 Jun 2023 15:32:11 GMT
• Title: Medoid splits for efficient random forests in metric spaces
• Authors: Matthieu Bult\'e and Helle S{\o}rensen
• Abstract summary: This paper revisits an adaptation of the random forest for Fr'echet regression, addressing the challenge of regression in metric spaces. We introduce a new splitting rule that circumvents the computationally expensive operation of Fr'echet means by substituting with a medoid-based approach.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper revisits an adaptation of the random forest algorithm for Fr\'echet regression, addressing the challenge of regression in the context of random objects in metric spaces. Recognizing the limitations of previous approaches, we introduce a new splitting rule that circumvents the computationally expensive operation of Fr\'echet means by substituting with a medoid-based approach. We validate this approach by demonstrating its asymptotic equivalence to Fr\'echet mean-based procedures and establish the consistency of the associated regression estimator. The paper provides a sound theoretical framework and a more efficient computational approach to Fr\'echet regression, broadening its application to non-standard data types and complex use cases.

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