Medoid splits for efficient random forests in metric spaces

2023/06/29 by Matthieu Bulté, Bulté, Matthieu, Helle Sørensen +1 · 3 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Machine Learning (stat.ML) #Methodology (stat.ME) #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2306.17031

openalex publication_date 2023/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper revisits an adaptation of the random forest algorithm for Fréchet 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 Fréchet means by substituting with a medoid-based approach. We validate this approach by demonstrating its asymptotic equivalence to Fréchet 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 Fréchet regression, broadening its application to non-standard data types and complex use cases.

Cited by

• Out-of-bag prediction balls for random forests in metric spaces
• End-to-End Deep Learning for Predicting Metric Space-Valued Outputs
• Conformal and kNN Predictive Uncertainty Quantification Algorithms in Metric Spaces

Related

• Fréchet random forests for metric space valued regression with non euclidean predictors
• Dimension Reduction for Fréchet Regression
• Fréchet Regression for Random Objects with Euclidean Predictors
• Out-of-bag prediction balls for random forests in metric spaces
• Total Variation Regularized Fréchet Regression for Metric-Space Valued Data