Medoid splits for efficient random forests in metric spaces
针对度量空间中随机对象的回归问题，提出一种用中心点替代弗雷歇均值的分裂规则，在保证渐近等价和估计一致性的同时大幅提升计算效率，适用于非标准数据类型。
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.