Advancing High-Dimensional Bayesian Asymptotics and Computation

大数据革命使统计学和机器学习成为高度活跃和快节奏的研究领域，在过去的几十年里取得了巨大的进步。然而，大数据和复杂模型的不确定性量化仍然是该领域的一个挑战。理论上，贝叶斯统计学优雅而直接地解决了不确定性量化问题。因此，需要一些思想和方法来构建有用的、计算上可扩展的贝叶斯过程。这项研究项目有助于实现这一目标。开发的方法可以改善自动驾驶、医疗诊断、保释决定、信用价值、刑事判决等领域的决策。这项研究还将包括对研究生的培训。该项目有助于发展理论上合理的，计算上可扩展的贝叶斯方法，用于恢复高维参数。为了实现这一目标，PI将开发一种新颖且广泛适用的准贝叶斯（半参数）框架来学习高维参数。该项目还将有助于贝叶斯渐近理论的发展，分析高维，不可识别的模型。在应用中广泛使用的一些高调模型（如神经网络模型）是不可识别的。通过将新框架应用于典型相关分析，本项目还将有助于开发用于高维稀疏典型相关分析的灵活贝叶斯解，在生物医学研究中具有广泛的适用性。该研究项目还将有助于高维贝叶斯统计的计算方面与几个新的MCMC和VA算法的发展。最后，随着贝叶斯生成对抗网络（GAN）的发展，该研究项目还将对统计学和机器学习做出更广泛的贡献。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。

The big data revolution has turned statistics and machine learning into highly active and fast-pace research areas that have seen great progress over the last few decades. However uncertainly quantification with big data and complex models remains a challenge in the field. In theory, Bayesian statistics solves -- elegantly and straightforwardly -- the uncertainty quantification problem. There is therefore a need for ideas and methods for constructing useful and computationally scalable Bayesian procedures. This research project contributes towards that goal. The developed methodology can improve decision making in areas such as autonomous driving, medical diagnostics, bail decision, credit worthiness, criminal sentencing, to list a few. This research will also include training for graduate students. This project contributes to the development of theoretically sound, and computationally scalable Bayesian methodologies for the recovery of high-dimensional parameters. Toward that goal, the PI will develop a novel and widely applicable quasi-Bayesian (semi-parametric) framework for learning high-dimensional parameters. The project will also contribute to the development of Bayesian asymptotic theory with the analysis of high-dimensional, non-identifiable models. Several high-profile models (e.g. neural network models) widely used in the applications are non-identifiable. By applying the new framework to canonical correlation analysis, this project will also contribute to the development of flexible Bayesian solutions for high-dimensional sparse canonical correlation analysis, with wide applicability in bio-medical research. This research project will also contribute to the computational aspects of high-dimensional Bayesian statistics with the development of several novel MCMC and VA algorithms. Finally, this research project will also contribute more broadly to statistics and machine learning with the development of Bayesian generative adversarial networks (GAN).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.