论文标题
通过比例分数编程，部分识别潜在混杂的代理
Partial Identification with Proxy of Latent Confoundings via Sum-of-ratios Fractional Programming
论文作者
论文摘要
由于混淆的不可观念性，人们普遍关注如何定量地计算因果关系。为了应对这一挑战，通常采用了基于代理的负面控制方法，其中辅助结果变量$ \ bm {w} $作为混杂的代理$ \ bm {u} $。但是，这些方法依赖于强大的假设，例如可逆性，完整性或桥梁功能。这些假设缺乏直观的经验解释和扎实的验证技术，因此它们在现实世界中的应用是有限的。例如，当过渡矩阵$ p（\ bm {w} \ mid \ bm {u}）$不可逆时，这些方法是不适用的。在本文中，我们专注于一个较弱的假设，称为$ p（\ bm {w} \ mid \ bm {u}）$的部分可观察性。我们开发了一种更通用的单核阴性对照方法，称为“部分识别”，通过比率分数编程（PI-SFP）。它是基于分支机构策略的全球优化算法，旨在提供因果效应的有效界限。在模拟中，PI-SFP提供了有希望的数值结果，并填充了以前文献中无法处理的空白点，例如我们的部分信息为$ p（\ bm {w} \ mid \ mid \ bm {u}）$。
Due to the unobservability of confoundings, there has been widespread concern about how to compute causality quantitatively. To address this challenge, proxy-based negative control approaches have been commonly adopted, where auxiliary outcome variables $\bm{W}$ are introduced as the proxy of confoundings $\bm{U}$. However, these approaches rely on strong assumptions such as reversibility, completeness, or bridge functions. These assumptions lack intuitive empirical interpretation and solid verification techniques, hence their applications in the real world are limited. For instance, these approaches are inapplicable when the transition matrix $P(\bm{W} \mid \bm{U})$ is irreversible. In this paper, we focus on a weaker assumption called the partial observability of $P(\bm{W} \mid \bm{U})$. We develop a more general single-proxy negative control method called Partial Identification via Sum-of-ratios Fractional Programming (PI-SFP). It is a global optimization algorithm based on the branch-and-bound strategy, aiming to provide the valid bound of the causal effect. In the simulation, PI-SFP provides promising numerical results and fills in the blank spots that can not be handled in the previous literature, such as we have partial information of $P(\bm{W} \mid \bm{U})$.
