arXiv subjects

Louis Capitaine

Publications and source records attributed to Louis Capitaine.

2 recordsLinked to original sources

arXiv2019

Fr\'echet random forests for metric space valued regression with non euclidean predictors

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 Fr\'echet trees and Fr\'echet 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 Fr\'echet regressogram predictor using data-driven partitions is given and applied to Fr\'echet 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.

stat.ML↗

arXiv2019

Random forests for high-dimensional longitudinal data

Random forests is a state-of-the-art supervised machine learning method which behaves well in high-dimensional settings although some limitations may happen when $p$, the number of predictors, is much larger than the number of observations $n$. Repeated measurements can help by offering additional information but no approach has been proposed for high-dimensional longitudinal data. Random forests have been adapted to standard (i.e., $n > p$) longitudinal data by using a semi-parametric mixed-effects model, in which the non-parametric part is estimated using random forests. We first propose a stochastic extension of the model which allows the covariance structure to vary over time. Furthermore, we develop a new method which takes intra-individual covariance into consideration to build the forest. Simulations reveal the superiority of our approach compared to existing ones. The method has been applied to an HIV vaccine trial including 17 HIV infected patients with 10 repeated measurements of 20000 gene transcripts and the blood concentration of human immunodeficiency virus RNA at the time of antiretroviral interruption. The approach selected 21 gene transcripts for which the association with HIV viral load was fully relevant and consistent with results observed during primary infection.

stat.ME↗