CAREER: Computational and Theoretical Investigations of Variational Inference

职业：变分推理的计算和理论研究

• 批准号: 1847590
• 负责人: Chao Gao
• 金额: $ 40万
• 依托单位: University of Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-03-01 至 2025-02-28
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1847590&HistoricalAwards=false
• 关键词: CAREER; Computational; Theoretical; Investigations; Variational

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.

复杂和大数据的新时代对我们对统计的计算和理论理解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有效地处理大量数据集，同时最大限度地减少信息损失，以帮助科学发现和决策。 这使得科学界采用近似的统计程序，实现计算效率和统计效率之间的最佳权衡。 一方面，近似应该易于处理以获得计算益处。另一方面，近似需要是紧密的，以便在原始问题的统计最优性方面不妥协太多。该项目旨在弥合复杂和非标准设置下各种统计问题的计算和理论差距。拟议研究的结果将对常规应用计算密集型方法的领域产生重大影响。 这些领域包括人口遗传学、天文学、计算机视觉、政治学、社会科学和动物科学。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。 变分推理是一种通过寻求对原始问题的变分近似来解决这两个挑战的技术，该变分近似不仅易于处理，而且也是紧密的。 然而，文献缺乏系统的调查变分推理从计算和统计的角度。 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的计算和理论差距，并导致变分推理的重大理论和计算进步。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。

项目成果

Testing equivalence of clustering

测试聚类的等价性

• DOI: 10.1214/21-aos2113
• 发表时间: 2022
• 期刊: The Annals of Statistics
• 作者: Gao, Chao;Ma, Zongming
• 通讯作者: Ma, Zongming

Robust regression via mutivariate regression depth

• DOI: 10.3150/19-bej1144
• 发表时间: 2017-02
• 期刊: Bernoulli
• 影响因子: 1.5
• 作者: Chao Gao

Minimax Rates in Network Analysis: Graphon Estimation, Community Detection and Hypothesis Testing

网络分析中的极小极大率：图估计、社区检测和假设检验

• DOI: 10.1214/19-sts736
• 发表时间: 2021
• 期刊: Statistical Science
• 影响因子: 5.7
• 作者: Gao, Chao;Ma, Zongming
• 通讯作者: Ma, Zongming

Optimal estimation of variance in nonparametric regression with random design

• DOI: 10.1214/20-aos1944
• 发表时间: 2019-02
• 期刊: The Annals of Statistics
• 作者: Yandi Shen;Chao Gao;D. Witten;Fang Han

Exact Minimax Estimation for Phase Synchronization

• DOI: 10.1109/tit.2021.3112712
• 发表时间: 2020-10
• 期刊: IEEE Transactions on Information Theory
• 影响因子: 2.5
• 作者: Chao Gao;A. Zhang