Accelerating Generalized Random Forests with Fixed-Point Trees
David Fleischer David A. Stephens Archer Yang
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.