Description
Random forests are a popular method in supervised learning and can be
used for regression and classification problems. For a regression problem
a random forest averages the results of several randomized decision trees
that are constructed on different subsamples of the dataset. In practice
random forests appear to be very successful and are therefore a commonly
used algorithm. Contrary to this there is little known about the
mathematical properties of classic random forests that use data dependent
partitions. Most results in the literature cover simpler versions of random
forests often with partitions that are independent of the dataset. One
example of these simpler algorithms are centered purely random forests.
Moreover the majority of the results in the literature are consistency theorems
and there are noticeably less central limit theorems. In our work
we prove a central limit theorem for centered purely random forests. The
proof uses results by Peng et al. (2022) which are based on an interpretation
of random forests as generalized U-Statistics.
References
Wei Peng, Tim Coleman, and Lucas Mentch. Rates of convergence for random
forests via generalized u-statistics. Electronic Journal of Statistics,
16(1):232–292, 2022.
