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

协作研究：测量误差理论和实用算法存在下的因果发现

• 批准号: 1829681
• 负责人: Kun Zhang
• 金额: $ 6万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-08-01 至 2019-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1829681&HistoricalAwards=false
• 关键词: Collaborative; Research; Causal; Discovery; Presence

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.

因果关系的发现是科学中的基本观念。为了找到这种因果关系，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。因果发现旨在从纯观察数据中找到基本的因果结构或模型，并在各种学科中具有许多应用。尽管在许多实际问题上取得了成功，但观察到的数据中的测量误差的存在可能会在各种因果发现方法的输出中造成严重的错误。鉴于由测量过程中使用的工具或代理引起的测量误差无处不在，因此该问题被认为是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，可以确定相关变量的因果结构在多大程度上仍然未知，更不用说如何开发实用算法来解决此问题了。该项目旨在填补空隙。它将调查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，以及人们必须做出哪些假设才能成功恢复因果信息。基于这样的理论结果，该项目将研究有效的估计程序。 该项目将为基本的，真正的因果结构建立理论可识别性结果，并鉴于这种结果，会发展实际的因果发现算法。初步结果表明，从理论上讲，测量误差如何改变数据中（条件）独立性和依赖关系，即（条件）独立性和独立性之间的独立性和独立性与无测量变量之间的变量不同。根据初步结果，将执行几项研究任务。首先，经典因果发现通常假设数据线性高斯模型，其中因果关系是线性的，变量是共同的高斯。该项目将确定基本因果模型可识别为等效类或仅部分可识别的条件。其次，这项研究将研究在存在测量误差的情况下基本因果结构的可识别性实际上可以从非高斯噪声假设中受益。第三，这项研究将通过扩展GES方法，利用合适的稀疏性约束或扩展A* Bayesian网络学习程序来制定统计上更有效的估计程序。最后，上述想法将扩展到应对因果关系或统计数据中的相关模型，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的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的影响来评估的。

项目成果

On Learning Invariant Representations for Domain Adaptation

• 发表时间: 2019-05
• 期刊: Journal of biomechanics
• 影响因子: 2.4
• 作者: H. Zhao;Rémi Tachet des Combes;Kun Zhang;Geoffrey J. Gordon

Causal discovery in the presence of missing data

存在缺失数据时的因果发现

• 发表时间: 2019
• 期刊: Proceedings of Machine Learning Research
• 作者: Ruibo Tu, Cheng Zhang

Low-Dimensional Density Ratio Estimation for Covariate Shift Correction

• 发表时间: 2019-04
• 期刊: Proceedings of machine learning research
• 作者: P. Stojanov;Mingming Gong;J. Carbonell;Kun Zhang

Likelihood-Free Overcomplete ICA and Applications in Causal Discovery

• 发表时间: 2019-09
• 作者: Chenwei Ding;Mingming Gong;Kun Zhang;D. Tao

Triad Constraints for Learning Causal Structure of Latent Variables

• 发表时间: 2019
• 作者: Ruichu Cai;Feng Xie;C. Glymour;Z. Hao;Kun Zhang