How does Random Forest relate to kernel density estimation in feature space?

Random Forest implicitly performs adaptive partition-based density estimation rather than smooth kernel smoothing.

Kernel density estimation (KDE) uses smooth kernels centered at data points, while Random Forest defines adaptive hyper-rectangular partitions where density is approximated by sample frequency in leaves. The proximity matrix in RF can be interpreted as an adaptive similarity kernel, making RF a data-dependent, non-smooth alternative to KDE.