Collaborative Research: Causal Discovery in the Presence of Measurement Error Theory and Practical Algorithms

发现因果关系是科学的一个基本概念。为了找到这样的因果关系，基于干预或随机实验的传统方法通常是昂贵的，甚至是不可能的。因果发现旨在从纯粹的观测数据中找到潜在的因果结构或模型，在各个学科中都有许多应用。尽管它在许多实际问题上取得了成功，但观测数据中测量误差的存在会在各种因果发现方法的输出中产生严重错误。由于测量过程中使用的仪器或代理引起的测量误差无处不在，这一问题已被认为是可靠因果发现的主要障碍之一。在存在测量误差的情况下，相关变量的因果结构在多大程度上可以被识别，更不用说如何开发实用的算法来解决这一问题了。该项目旨在填补这一空白。它将调查兴趣因果模型的哪些信息可以从观察数据中恢复，以及必须做出哪些假设才能成功恢复因果信息。基于这些理论结果，该项目将研究有效的评估程序。该项目将为潜在的、真实的因果结构建立理论可识别性结果，并根据这些结果，开发实用的因果发现算法。初步结果从理论上说明了测量误差如何改变数据中的（条件）独立和依赖关系，即观测变量之间的（条件）独立和独立关系与无测量误差变量之间的（条件）独立和独立关系是如何不同的。在初步结果的基础上，将开展若干研究任务。首先，经典的因果发现通常假设数据为线性-高斯模型，其中因果关系是线性的，变量是联合高斯的。这个项目将建立一个条件，在这个条件下，潜在的因果模型是可识别的，直到一个等价类或只是部分可识别的。其次，本研究将探讨在存在测量误差的情况下，潜在因果结构的可识别性如何实际上受益于非高斯噪声假设。第三，本研究将通过扩展GES方法，利用适当的稀疏性约束，或扩展A*贝叶斯网络学习过程，开发统计上更有效的估计过程。最后，上述思想将扩展到处理因果关系或统计中的相关模型，包括其他污染模型，非线性因果模型和马尔可夫网络。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The discovery of cause-and-effect relationships is a fundamental notion in science. To find such causal relationships, traditional methods based on interventions or randomized experiments are usually expensive or even impossible. Causal discovery aims to find the underlying causal structure or model from purely observational data and has many applications in various disciplines. Despite its successes on a number of real problems, the presence of measurement error in the observed data can produce serious mistakes in the output of various causal discovery methods. Given the ubiquity of measurement error caused by instruments or proxies used in the measuring process, this problem has been recognized as one of the main obstacles to reliable causal discovery. It is still unknown to what extent the causal structure for relevant variables can be identified in the presence of measurement error, let alone how to develop practical algorithms to solve this problem. This project aims to fill the void. It will investigate what information of the causal model of interest can be recovered from observed data and what assumptions one has to make to achieve successful recovery of the causal information. Based on such theoretical results, the project will then investigate efficient estimation procedures. The project will establish theoretical identifiability results for the underlying, true causal structure and, in light of such results, develop practical causal discovery algorithms. Preliminary results show theoretically how measurement error changes the (conditional) independence and dependence relationships in the data, i.e., how the (conditional) independence and independence relations between the observed variables are different from those between the measurement-error-free variables. Based on the preliminary results, several research tasks will be carried out. First, classical causal discovery often assumes a linear-Gaussian model for the data, in which the causal relations are linear and the variables are jointly Gaussian. This project will establish the conditions under which the underlying causal model is identifiable up to an equivalence class or only partially identifiable. Second, this study will investigate how the identifiability of underlying causal structure in the presence of measurement error can actually benefit from the non-Gaussian noise assumption. Third, this study will develop statistically more efficient estimation procedures, by extending the GES method, by exploiting suitable sparsity constraints, or by extending the A* Bayesian network learning procedure. Finally, the above ideas will be extended to deal with related models in causality or statistics, including other contamination models, nonlinear causal models, and Markov networks.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.