2019/06/04 by Louis Capitaine, Jérémie Bigot, Capitaine, Louis +5 · 6 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Advanced Clustering Algorithms Research #FOS: Computer and information sciences #Face and Expression Recognition #Gene expression and cancer classification #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Methodology (stat.ME) #Morphological variations and asymmetry #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1906.01741
openalex publication_date 2019/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Random forests are a statistical learning method widely used in many areas of scientific research because of its ability to learn complex relationships between input and output variables and also its capacity to handle high-dimensional data. However, current random forest approaches are not flexible enough to handle heterogeneous data such as curves, images and shapes. In this paper, we introduce Fréchet trees and Fréchet random forests, which allow to handle data for which input and output variables take values in general metric spaces. To this end, a new way of splitting the nodes of trees is introduced and the prediction procedures of trees and forests are generalized. Then, random forests out-of-bag error and variable importance score are naturally adapted. A consistency theorem for Fréchet regressogram predictor using data-driven partitions is given and applied to Fréchet purely uniformly random trees. The method is studied through several simulation scenarios on heterogeneous data combining longitudinal, image and scalar data. Finally, one real dataset about air quality is used to illustrate the use of the proposed method in practice.