潜在治疗效果的谱结构

中文摘要 AI 辅助

在未观察到混杂因素的情况下识别异质治疗效果是观察性因果推断的核心。在具有离散潜在混杂因素的代理模型中，先前的合成潜在结果（SPO）通过递归构造的标量矩恢复治疗效果的混合。我们表明这个序列是一个更基本对象的一个投影。在相同的总体分解假设下，存在一个精确的压缩可观测算子：投影到共享代理信号子空间后，两个治疗臂商算子的差类似于潜在治疗效果的对角矩阵。其特征值是潜在效果；其提升的左特征向量在锚定归一化后恢复目标 - 代理特征矩阵，进而恢复潜在混合比例。每个标量 SPO 矩是该算子幂的双线性泛函。所得估计器处理过完备代理系统，用有限维谱分析取代高阶标量求逆，并允许对治疗效果、特征行和单纯形投影混合权重进行高概率一阶扰动界估计。

英文摘要

Identifying heterogeneous treatment effects under unobserved confounding is central in observational causal inference. In proxy models with a discrete latent confounder, prior Synthetic Potential Outcomes (SPO) [Mazaheri-Squires-Uhler '25] recover the mixture of treatment effects through recursively constructed scalar moments. We show that this sequence is one projection of a more fundamental object. Under the same population factorization assumptions, there is an exact compressed observable operator: after projecting onto the shared proxy signal subspace, the difference of two treatment-arm quotient operators is similar to the diagonal matrix of latent treatment effects. Its eigenvalues are the latent effects; its lifted left eigenvectors, after anchor normalization, recover the target-proxy feature matrix and then the latent mixture proportions. Every scalar SPO moment is a bilinear functional of a power of this operator. The resulting estimator handles overcomplete proxy systems, replaces high-order scalar inversion with finite-dimensional spectral analysis, and admits high-probability first-order perturbation bounds for treatment effects, feature rows, and simplex-projected mixture weights.

发表机构

• Dartmouth College（达特茅斯学院）
• Broad Institute of MIT and Harvard（麻省理工学院和哈佛大学布罗德研究所）
• Hofstra University（霍夫斯特拉大学）

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