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

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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.