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，这些算法可以从大量数据集中学习复杂的关系和理解复杂的现象。这些算法已成功应用于各种应用，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，但它们仍然存在安全性、透明性、公平性和可解释性问题。这些实际挑战中的许多可以追溯到众所周知的可解释性，因果关系和错误发现方面的限制。与此同时，近年来，我们在只有几个因素和相对简单的模型的相对简单的环境中对这些实际挑战的理解取得了重大进展。本研究旨在整合这些努力，以提供一个灵活的框架，灵活的，可解释的，因果建模从高维，复杂的数据集。所研究的方法专门寻求避免通常出现在复杂数据集中的虚假相关性，同时保留现代机器学习算法的灵活性，着眼于医学，生物学和金融领域的应用。虽然机器学习的许多应用都受到复杂预测模型令人印象深刻的进步的推动，但同时也出现了对模型的需求，这些模型可以从大量，未标记的数据集图形模型提供了一种原则性的和有效的方法来发现这种类型的知识从未标记的数据。虽然学习无向图的问题在过去十年中已经取得了一系列显着的进展，但编码有向的潜在因果信息的有向无环图（DAG）并没有从这些进展中受益。因此，迫切需要一种新的、理论上合理的方法来学习DAG，这些方法可以捕捉复杂的、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，为迄今为止缺乏的一般统计和计算框架提供了基础。技术目标可分为沿着三个主轴：1）开发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设置中的优化方案的行为的新工具，和3）非参数因果模型及其统计特性的理论进展。该奖项反映了NSF的法定使命，并被认为是值得的。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来提供支持。

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.