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

科学研究通常旨在回答各种领域的因果关系问题，如公共卫生、医学、经济或教育政策、监管政策、商业决策等。然而，正是因为这些问题中有很多是利害攸关的，科学家们经常被伦理或其他限制因素排除在随机对照试验（RCT）之外，这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。因果网络框架是一种相对较新的科学方法，它使人们能够编纂假设，即系统的某些部分对其他部分没有直接影响（不排除间接影响）。当某些假设成立时，原则上可以使用纯观察数据代替随机对照试验来确定因果关系。然而，现有的方法只能在一个狭窄的假设范围内被证明是合理的，而且往往不能很好地扩展到大型网络。该项目将由研究者、学生、博士后和合作者共同开展，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强度界限，来增加这些方法的适用性范围。在基本层面上，严格的因果推理存在两个障碍：潜在混淆和选择偏差。发生潜在混淆是因为系统的重要方面不能（或没有）被观察到。如果只在与感兴趣的数量相关的特殊情况下记录数据，则会发生选择偏差。全局混杂因素（影响所有可观测值的因素）的存在排除了因果识别——除非引入额外的假设。其中一种是全局混杂值范围上的基数边界；然而，现有的方法还需要一个统计分离假设。本项目的工作旨在放宽这一假设，有利于在Wasserstein距离下的模型识别。该项目还寻求超越单一全球混杂因素，以有效治疗多个全球混杂因素。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，这是一个具有当前独特方法的主题。该项目的一个关键目标是提供强信息不平等：一个特殊的情况，强数据处理不平等，已经研究了噪声通道的连接，因果网络的最简单的例子；但是，对于具有潜在混淆和选择偏差的网络来说，这种类型的情况并不为人所知。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），尽管存在基数有限的全局混杂，但这些方法工作效率高，对噪声具有鲁棒性。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。

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.