CAREER: Computational and Theoretical Investigations of Variational Inference

复杂和大数据的新时代对我们对统计学的计算和理论理解都提出了前所未有的挑战。现代数据科学中的一个基本问题是如何以最小的信息损失有效地处理海量数据集，以帮助科学发现和决策。这导致科学界采用近似的统计程序，在计算效率和统计效率之间实现最佳的权衡。一方面，近似应该是易于处理的，以获得计算优势。另一方面，近似需要是紧的，以便在原始问题的统计最优性方面不会有太大的妥协。该项目旨在弥合复杂和非标准环境下各种统计问题在计算和理论上的差距。拟议的研究结果将对以常规方式应用计算密集型方法而闻名的领域产生重大影响。这些学科包括种群遗传学、天文学、计算机视觉、政治学、社会科学和动物学。高维统计学和机器学习的最新发展集中在探索问题的内在低维结构。这在统计最优性和计算效率方面都提出了新的挑战。变分推理是一种技术，它通过寻求对原始问题的变分近似来解决这两个挑战，不仅容易处理，而且紧凑。然而，文献缺乏从计算和统计的角度对变分推理进行系统的研究。该项目的目标包括：(1)变分贝叶斯过程的理论研究；(2)稳健估计中的变分优化策略。该项目的成功将有助于弥合现代数据科学中计算和理论的差距，并在变分推理方面带来重大的理论和计算进步。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。

The new era of complex and big data poses unprecedented challenges in terms of both our computational and theoretical understanding of Statistics. One of the fundamental questions in modern data science is how to efficiently process massive data sets with minimal information loss to aid scientific discovery and decision making. This has led the scientific community to adopt approximate statistical procedures that achieve the optimal trade-off between computational efficiency and statistical efficiency. On the one hand, the approximation should be tractable to gain computational benefits. On the other hand, the approximation needs to be tight, so as to not compromise much in terms of the statistical optimality of the original problem. This project aims to bridge the computational and theoretical gaps in various statistical problems under complex and nonstandard settings. The results of the proposed research will significantly impact areas known for applying computationally intensive methods on a routine basis. These include population genetics, astronomy, computer vision, political science, social science, and animal science.Recent developments in high-dimensional statistics and machine learning focus on exploring the intrinsic low-dimensional structure of the problem. This poses new challenges in terms of both statistical optimality and computational efficiency. Variational inference is a technique that addresses both challenges by seeking a variational approximation to the original problem that is not only tractable, but also tight. However, the literature lacks a systematic investigation of variational inference from both the computational and statistical perspective. The goals of the project include: (1) theoretical investigations of variational Bayesian procedures; and (2) variational optimization strategies in robust estimation. The project's success will help bridge the computational and theoretical gaps in modern data science and lead to significant theoretical and computational advances in variational inference.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.