Accelerating Generalized Random Forests with Fixed-Point Trees

Generalized random forests arXiv:1610.01271 build upon the well-established success of conventional forests (Breiman, 2001) to offer a flexible and powerful non-parametric method for estimating local solutions of heterogeneous estimating equations. Estimators are constructed by leveraging random forests as an adaptive kernel weighting algorithm and implemented through a gradient-based tree-growing procedure. By expressing this gradient-based approximation as being induced from a single Newton-Raphson root-finding iteration, and drawing upon the connection between estimating equations and fixed-point problems arXiv:2110.11074, we propose a new tree-growing rule for generalized random forests induced from a fixed-point iteration type of approximation, enabling gradient-free optimization, and yielding substantial time savings for tasks involving even modest dimensionality of the target quantity (e.g. multiple/multi-level treatment effects). We develop an asymptotic theory for estimators obtained from forests whose trees are grown through the fixed-point splitting rule, and provide numerical simulations demonstrating that the estimators obtained from such forests are comparable to those obtained from the more costly gradient-based rule.