通过谱分析重构潜在处理效应，突破传统方法的高阶反演瓶颈。
The Spectral Structure of Latent Treatment Effects
- 构建可观测算子的谱结构，直接提取潜在处理效应的特征值。
- 在未观测混杂下实现高概率第一阶扰动界，稳定估计效应与混合比例。
- 适用于过完备代理变量系统，适合因果推断与高维数据建模者。
在存在未观测混杂的观测因果推断中，识别异质处理效应至关重要。针对具有离散潜变量混杂的代理模型，先前的合成潜在结果（SPO）方法通过递归构造标量矩来恢复处理效应的混合。本文揭示，该矩序列仅为一个更基础对象的投影。在相同总体因子分解假设下，存在一个精确压缩的可观测算子：将处理组商算子差投影至共享代理信号子空间后，其相似于潜变量处理效应的对角矩阵。其特征值即为潜变量效应；提升后的左特征向量经锚定归一化后可恢复目标-代理特征矩阵，并进一步获得潜变量混合比例。所有标量SPO矩均为该算子幂次的双线性泛函。新估计器能处理过完备代理系统，以有限维谱分析替代高阶标量反演，并对处理效应、特征行及单纯形投影的混合权重提供高概率一阶扰动界。
原文摘要 · Abstract (English)
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.
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