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.

翻译：广义随机森林（arXiv:1610.01271）建立在传统随机森林（Breiman, 2001）已获广泛验证的成功基础上，提供了一种灵活而强大的非参数方法，用于估计异质估计方程中的局部解。该类估计量通过利用随机森林作为自适应核加权算法构建，并借助基于梯度的树生长过程实现。通过将该梯度近似表达为单次牛顿-拉夫森寻根迭代的诱导结果，并利用估计方程与不动点问题（arXiv:2110.11074）之间的关联，我们提出了一种新的树生长规则——由不动点迭代型近似导出的广义随机森林规则。该规则实现了无需梯度的优化，并且即使目标量维度适中（如多重/多层次处理效应），也能显著节省计算时间。我们为通过不动点分裂规则生长的树所构成的森林估计量建立了渐近理论，并通过数值模拟表明，此类森林获得的估计量与成本更高的基于梯度规则所获估计量性能相当。