Collaborative Research: RI: Medium: A Rigorous, General Framework for Tractable Learning of Large-Scale DAGs from Data

机器学习和人工智能的最新进展在很大程度上归功于算法的发展，这些算法可以学习复杂的关系，并从海量数据集中理解复杂的现象。这些算法已经成功地应用于各种应用，包括医学、遗传学、机器人、营销、金融，以及越来越多的社会应用。然而，尽管这些应用程序取得了许多成功，但它们仍然受到安全性、透明度、公平性和可解释性问题的困扰。这些实际挑战中的许多可以追溯到众所周知的关于可解释性、因果关系和错误发现的限制。与此同时，近年来，我们在相对简单的情况下，仅用几个因素和相对简单的模型，在理解这些实际挑战方面取得了实质性进展。这项研究试图整合这些努力，以便为从高维、复杂的数据集进行灵活的、可解释的、因果建模提供一个灵活的框架。所研究的方法特别寻求避免复杂数据集中常见的虚假相关性，同时保留现代机器学习算法的灵活性，着眼于在医学、生物和金融领域的应用。尽管机器学习的许多应用受到复杂预测模型令人印象深刻的进步的推动，但同时也出现了对能够从海量、未标记的数据集中提取因果信息的模型的需求。图形模型提供了一种从未标记数据中发现此类知识的有原则且有效的方法。尽管学习无向图的问题在过去的十年中取得了一系列显著的进展，但编码有向的、潜在的因果信息的有向无环图(DAG)并没有从这些进展中受益。因此，迫切需要新颖且理论上合理的方法来学习DAG，以捕获复杂的、不对称的关系，降低模型的复杂性，最重要的是，为人类决策者和利益相关者学习因果关系。该项目探索了一种从数据中学习DAG的新方法，该方法为迄今缺乏的一般统计和计算框架提供了基础。技术目标可以分为三个主要轴：1)开发在结构学习问题中出现的组合优化问题的新的连续松弛，2)开发用于分析高度非凸环境中优化方案的行为的新工具，以及3)非参数因果建模及其统计特性的理论进步。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。

Recent advances in machine learning and artificial intelligence owe much of their success to the development of algorithms that learn complicated relationships and understanding complex phenomena from massive datasets. These algorithms have been successfully applied on a diverse array of applications, including medicine, genetics, robotics, marketing, finance, and, increasingly, in societal applications. Despite their many successes, however, these applications continue to suffer from security, transparency, fairness, and interpretability problems. Many of these practical challenges can be traced back to well-known limitations with respect to interpretability, causality, and false discoveries. At the same time, substantial progress has been made in recent years in our understanding of these practical challenges in relatively simple settings with only a few factors and comparatively simple models. This research seeks to integrate these efforts, in order to provide a flexible framework for flexible, interpretable, causal modeling from high-dimensional, complex datasets. The investigated approach specifically seeks to avoid spurious correlations that commonly appear in complex datasets, while retaining the flexibility of modern machine learning algorithms with an eye towards applications in medicine, biology, and finance.While many applications of machine learning have been driven by impressive advances in complex predictive models, at the same time a need has emerged for models that can extract causal information from massive, unlabeled datasets. Graphical models provide a principled and effective way to uncover this type knowledge from unlabeled data. Although the problem of learning undirected graphs has witnessed a series of remarkable advances over the past decade, directed acyclic graphs (DAGs) that encode directed, potentially causal information, have not benefited from these advances. As a result, there is a pressing need for novel and theoretically sound methods for learning DAGs that can capture complex, asymmetric relationships, reduce model complexity, and most importantly, learn causal relationships for human decision-makers and stakeholders. This project explores a new approach for learning DAGs from data that provides the basis for a general statistical and computational framework, which has been lacking thus far. The technical aims can be divided along three major axes: 1) Developing novel continuous relaxations of the combinatorial optimization problems that arise in structure learning problems, 2) Developing new tools for analyzing the behavior of optimization schemes in highly nonconvex settings, and 3) Theoretical advances in nonparametric causal modeling and its statistical properties.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.