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

因果关系的发现是科学中的一个基本概念。要找到这种因果关系，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。因果发现的目的是从纯粹的观测数据中找到潜在的因果结构或模型，在各个学科中有许多应用。尽管它在许多真实的问题上取得了成功，但观测数据中存在的测量误差会在各种因果发现方法的输出中产生严重的错误。由于在测量过程中使用的仪器或替代物造成的测量误差无处不在，这个问题已被公认为可靠的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仍然是未知的，更不用说如何开发实用的算法来解决这个问题了。该项目旨在填补空白。它将研究可以从观察到的数据中恢复感兴趣的因果模型的哪些信息，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估计程序。 该项目将为潜在的、真实的因果结构建立理论上的可识别性结果，并根据这些结果开发实用的因果发现算法。初步结果从理论上表明了测量误差如何改变数据中的（条件）独立性和依赖关系，即，观察变量之间的（条件）独立性和独立关系与无测量误差变量之间的独立性和独立关系有何不同。在初步成果的基础上，将开展几项研究任务。首先，经典的因果发现通常假设数据的线性高斯模型，其中因果关系是线性的，变量是联合高斯的。这个项目将建立条件下，基本的因果模型是可识别的等价类或仅部分可识别。其次，本研究将探讨如何识别潜在的因果结构的测量误差的存在下，实际上可以受益于非高斯噪声假设。第三，本研究将开发统计上更有效的估计程序，通过扩展GES方法，通过利用适当的稀疏约束，或通过扩展的A* 贝叶斯网络学习过程。最后，将上述思想扩展到处理因果或统计学中的相关模型，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NSF的法定使命，并通过使用基金会的智力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.