While random forests are commonly used for regression problems, existing methods often lack adaptability in complex situations or lose optimality under simple, smooth scenarios. In this study, we introduce the adaptive split balancing forest (ASBF), capable of learning tree representations from data while simultaneously achieving minimax optimality under the Lipschitz class. To exploit higher-order smoothness levels, we further propose a localized version that attains the minimax rate under the H\"older class $\mathcal{H}^{q,\beta}$ for any $q\in\mathbb{N}$ and $\beta\in(0,1]$. Rather than relying on the widely-used random feature selection, we consider a balanced modification to existing approaches. Our results indicate that an over-reliance on auxiliary randomness may compromise the approximation power of tree models, leading to suboptimal results. Conversely, a less random, more balanced approach demonstrates optimality. Additionally, we establish uniform upper bounds and explore the application of random forests in average treatment effect estimation problems. Through simulation studies and real-data applications, we demonstrate the superior empirical performance of the proposed methods over existing random forests.

Statistical inference and estimation for causal relationships has a long tradition and has attracted significant attention as the emerging of large and complex datasets and the need for new statistical tools to handle such challenging datasets. In many applications, data is collected dynamically over time, and individuals are exposed to treatments at multiple stages. Typical examples include mobile health datasets, electronic health records, and many other biomedical studies and political science datasets. This work considers statistical inference of causal effects for longitudinal and observational data with high-dimensional covariates (confounders). We aim to establish valid statistical inference for dynamic treatment effects under possible model misspecifications. For the sake of simplicity, we consider dynamic settings with two exposure times. Suppose that we collect independent and identically distributed (i.i.d.) samples S: (W

This paper proposes a confidence interval construction for heterogeneous treatment effects in the context of multi-stage experiments with $N$ samples and high-dimensional, $d$, confounders. Our focus is on the case of $d\gg N$, but the results obtained also apply to low-dimensional cases. We showcase that the bias of regularized estimation, unavoidable in high-dimensional covariate spaces, is mitigated with a simple double-robust score. In this way, no additional bias removal is necessary, and we obtain root-$N$ inference results while allowing multi-stage interdependency of the treatments and covariates. Memoryless property is also not assumed; treatment can possibly depend on all previous treatment assignments and all previous multi-stage confounders. Our results rely on certain sparsity assumptions of the underlying dependencies. We discover new product rate conditions necessary for robust inference with dynamic treatments.