Although understanding and characterizing causal effects have become essential in observational studies, it is challenging when the confounders are high-dimensional. In this article, we develop a general framework $\textit{CausalEGM}$ for estimating causal effects by encoding generative modeling, which can be applied in both binary and continuous treatment settings. Under the potential outcome framework with unconfoundedness, we establish a bidirectional transformation between the high-dimensional confounders space and a low-dimensional latent space where the density is known (e.g., multivariate normal distribution). Through this, CausalEGM simultaneously decouples the dependencies of confounders on both treatment and outcome and maps the confounders to the low-dimensional latent space. By conditioning on the low-dimensional latent features, CausalEGM can estimate the causal effect for each individual or the average causal effect within a population. Our theoretical analysis shows that the excess risk for CausalEGM can be bounded through empirical process theory. Under an assumption on encoder-decoder networks, the consistency of the estimate can be guaranteed. In a series of experiments, CausalEGM demonstrates superior performance over existing methods for both binary and continuous treatments. Specifically, we find CausalEGM to be substantially more powerful than competing methods in the presence of large sample sizes and high dimensional confounders. The software of CausalEGM is freely available at https://github.com/SUwonglab/CausalEGM.

翻译：尽管理解和定性因果关系在观察研究中变得至关重要,但当混凝土者具有高度的高度时,理解和定性因果关系就具有挑战性。在本篇文章中,我们开发了一个通用框架$\textit{CausalsalEGM}$,通过编码基因模型来估计因果关系,可以在二进制和连续的处理环境中应用。在潜在的成果框架中,在没有根据的情况下,我们在高维共者空间和已知密度(例如多变正常分布)的低维度潜伏空间之间建立了双向转变。通过这个框架,CausalEGM同时消除了混集体者对治疗和结果的依赖性,并将混集体模型绘制出与低维潜在空间的相容模型。CausEGM可以对每个个体的因果关系或平均因果关系进行估计。我们的理论分析表明,CausgibalEGM的过度风险可以通过实验过程理论来约束。根据对 encoder 网络的假设,Coder-decoder 网络,Cus consubuplement of condition of condustrual rodual rodual rodual rodual rogradual rodual rogrations regraphal laus laus be real 和BImals remacial deal exal exal exal deal exal exal exal exal exal exal exal exal exal suplodimals real exal laveal roduction extiduction laveal exaldaldaldaldals exal exaldaldaldal degraduls ex exaldals 和Bal 。在现有的软GM 方法中,可以从地面上, 和Bal 和Bal 25的大规模地展示,可以大大显示, 和高级的高级方法,可以大大上, 方法, 和高级地展示, 方法,可以大大显示,在高级的高级方法可以大大。