CDS&E-MSS: Causal Induction in Sequential Decision Processes

因果归纳，即从数据中学习一组变量之间的因果关系，是科学研究和工程中的一个基本问题。一种理想的因果归纳和推理方法是通过实验干预。在许多应用中，学者们经常感兴趣的是通过一组候选的实验干预来最大化某些结果变量，例如在所谓的因果盗贼问题中。在现有方法面临的几个紧迫挑战，即未知因果关系，数据异构性，以及如何设计自适应的实验干预的动机下，PI将发展基于有向无环图的因果关系和归纳的新的统计方法和理论，有向无环图是一类流行的表示因果关系的图形模型。将发布软件包，以提供这些方法和算法的有效实施。这项研究将纳入本科生和研究生的教育和研究培训。具有详细文档的开源软件将增加研究项目的可见性和实际应用。本课题研究序贯决策过程框架下的因果归纳问题。为了处理未知的因果关系，PI计划开发一种带有因果父母识别的强盗算法和一种贝叶斯后门强盗方法，该方法平均父母集的不确定性。这两种方法都有效地利用观测数据来补充在顺序干预过程中产生的实验数据。这将在很大程度上推广因果关系强盗的方法论和理论保证，使其适用于未知因果关系下的具有挑战性的背景。PI借用了面对不确定性时的乐观原则，进一步开发了新的数据自适应干预程序，直接针对因果归纳，以实现对潜在因果图形模型的主动学习。由于不同实验干预下产生的数据不服从相同的分布，PI将开发一种新的方法来学习此类异质实验数据的干预等价类。PI将发展理论结果，以建立因果强盗方法中累积后悔的上界和结构学习算法的一致性。主动因果学习的序贯干预设计适用于有限大小的数据，并可应用于一般潜在的因果图。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Causal induction, i.e. learning the causal relations among a set of variables from data, is a fundamental problem in scientific research and engineering. An ideal approach to causal induction and inference is through experimental interventions. In many applications, scholars are often interested in maximizing certain outcome variables over a set of candidate experimental interventions, as in the so-called causal bandit problem. Motivated by a few pressing challenges faced by existing methods, namely unknown causality, data heterogeneity, and how to design adaptive experimental interventions, the PI will develop novel statistical methodology and theory for causal bandit and induction based on directed acyclic graphs, a class of popular graphical models for representing causality. Software packages will be released to provide efficient implementation of these methods and algorithms. The research will be integrated into education and research training at both undergraduate and graduate levels. Open-source software with detailed documentation will increase the visibility and the practical application of the research project. This project investigates the causal induction problem under the framework of a sequential decision process. To handle unknown causality, the PI plans to develop a bandit algorithm with causal parent identification and a Bayesian backdoor bandit methodology that averages over parent set uncertainty. Both methods make efficient use of observational data to complement experimental data generated during sequential interventions. This will substantially generalize the causal bandit methodology and theoretical guarantees to the challenging setting under unknown causality. Borrowing the principle of optimism in the face of uncertainty, the PI further develops novel data-adaptive intervention procedures that directly target causal induction, to achieve active learning of the underlying causal graphical model. Since data generated under different experimental interventions do not follow an identical distribution, the PI will develop a new method to learn the interventional equivalence class on such heterogeneous experimental data. The PI will develop theoretical results to establish upper bounds on the cumulative regret in the causal bandit methods and the consistency of the structure learning algorithms. The sequential intervention design for active causal learning is adaptive to finite-size data and can be applied to a general underlying causal graph.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.