Medoid splits for efficient random forests in metric spaces

TL;DR

This paper introduces a medoid-based splitting rule for random forests in metric spaces, offering a more computationally efficient method for Fréchet regression while maintaining theoretical consistency.

Contribution

It proposes a novel medoid-based splitting rule that replaces Fréchet mean calculations, enabling efficient and consistent random forest regression in metric spaces.

Findings

The medoid-based approach is asymptotically equivalent to Fréchet mean methods.

The regression estimator is proven to be consistent.

The method broadens the applicability of Fréchet regression to complex data types.

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.