NSF-BSF: AF: Small: Algorithmic and Information-Theoretic Challenges in Causal Inference

科学研究通常旨在回答公共卫生、医学、经济或教育政策、监管政策、商业决策等不同领域的因果关系问题。然而，正是由于其中许多问题事关重大，科学家往往因伦理或其他限制而无法通过随机对照试验(RCT)解决这些问题，随机对照试验是实验研究的黄金标准。这往往是在公共利益问题上确定因果关系的最大障碍之一。因果网络的框架是对科学方法的相对较新的阐述，它使人们能够编纂假设，即一个系统的某些部分对其他部分没有直接影响(而不排除间接影响)。当某些假设被证明是合理的时，人们原则上可以使用纯粹的观测数据来代替随机对照试验来确定因果效应。然而，现有的方法仅在很小的假设范围内被证明是合理的，并且通常不能很好地扩展到大型网络。这个项目将由研究人员、学生、博士后和合作者共同完成，致力于通过新的算法和样本复杂性界限以及在大型稀疏因果网络中可能出现的相关性的强度界限来扩大这种方法的适用范围。在根本层面上，严格的因果推理存在两个障碍：潜在的混淆和选择偏差。潜在的混淆发生是因为系统的重要方面不能(或没有)被观察到。如果只有在与感兴趣的数量相关的特殊情况下才记录数据，就会出现选择偏差。全局混杂的存在(影响所有可观测对象的混杂)排除了因果识别的可能性-除非引入额外的假设。其中之一是全局混乱器范围上的基数界限；然而，现有方法还需要统计分离假设。这个项目的工作旨在放松这一假设，有利于在Wasserstein距离下进行模型识别。该项目还寻求超越单一的全球混杂因素，转向对多个全球混杂因素的有效治疗。该项目的另一个目标是将因果网络应用于时间序列数据的分析，这是一个目前具有独特方法的主题。该项目的一个关键目标是提供强信息不平等：已经研究了噪声信道级联的一种特殊情况-强数据处理不平等，这是因果网络的最简单例子；但对于具有潜在混杂和选择偏差的网络，这类情况尚不为人所知。该项目的另一个目标是给出因果发现的方法(使用统计数据而不是领域知识来确定网络结构)，这些方法有效地工作并对噪声具有健壮性，尽管存在基数限制的全球混淆。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。

Scientific research is often intended to answer questions of causal effect in various domains such as public health, medicine, economic or educational policy, regulatory policy, business decisions, etc. However, precisely because so much is at stake in many of these questions, scientists are frequently precluded by ethical or other constraints from addressing them with a randomized controlled trial (RCT), the gold standard for experimental research. This has often been one of the greatest barriers to establishing cause and effect in matters of public interest. The framework of causal networks is a relatively recent elaboration of the scientific method which enables one to codify assumptions that some parts of a system have no direct effect on some others (without ruling out indirect effects). When certain assumptions are justified, one can in principle use purely observational data in lieu of RCTs to determine causal effects. However, existing methods are justified only within a narrow range of assumptions and often do not scale well to large networks. This project, to be carried out by the investigator, students, postdocs and collaborators, is dedicated to increasing the range of applicability of such methods with new algorithms and sample complexity bounds, as well as bounds on the strength of correlations that can occur in large, sparse causal networks.At a fundamental level, there are two obstacles to rigorous causal inference: latent confounding and selection bias. Latent confounding occurs because significant aspects of the system cannot (or have not) been observed. Selection bias occurs if data is recorded only under special circumstances that are correlated with the quantities of interest. The presence of a global confounder (one which affects all observables) rules out causal identification---unless additional assumptions are introduced. One such is a cardinality bound on the range of the global confounder; however, existing methods require in addition a statistical separation assumption. Work in this project aims to relax this assumption in favor of model identification in Wasserstein distance. The project also seeks to move beyond a single global confounder to efficient treatment of multiple global confounders. Another goal of the project is to apply causal networks to the analysis of time series data, a topic with a currently distinct methodology. A key goal of the project is to provide strong information inequalities: a special case, strong data processing inequalities, have been studied for concatenations of noisy channels, the simplest example of a causal network; but nothing of this type is known for networks with latent confounding and selection bias. A further goal of the project is to give methods for causal discovery (the use of statistical data rather than domain knowledge to determine network structure) that work efficiently and are robust to noise despite a cardinality-bounded global confounder.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.