A0901
Title: Prediction balls for random forests with response in metric spaces
Authors: Diego Serrano - Universidad Carlos III de Madrid (Spain) [presenting]
Eduardo Garcia-Portugues - Universidad Carlos III de Madrid (Spain)
Abstract: Random forests have recently been generalized for variables taking values in a general metric space. The most relevant methods in this sense are Frechet random forests and random forest weighted local constant Frechet regression (RFWLCFR). A new methodology to quantify the uncertainty in the prediction of FRF/RFWLCFR is proposed. The confidence regions are based on the out-of-bag errors obtained from a single forest training, allowing the use of the entire dataset for both prediction and uncertainty estimation. This results in more precise and computationally efficient estimations when compared to generic split-conformal approaches. Asymptotic coverage theory is presented in four different scenarios for the type of coverage. The proposed prediction regions are illustrated through simulations using RFWLCFR in different metric spaces, including the Euclidean space, unit sphere, unit hyperboloid, and the space of symmetric positive definite matrices. The methodology is also applied to create prediction regions for the estimated death location of sunspot groups.
