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就我们对统计的计算和理论理解而言，提出了前所未有的挑战。 现代数据科学中的基本问题之一是如何有效地处理大规模数据集，并以最小的信息损失来帮助科学发现和决策。 这导致科学界采用了近似统计程序，以实现计算效率和统计效率之间的最佳权衡。 一方面，近似值应该是可访问的，以获得计算益处。另一方面，近似值需要紧密，以免在原始问题的统计最佳性方面妥协。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。拟议研究的结果将显着影响常规应用计算密集型方法已知的领域。 其中包括人口遗传学，天文学，计算机视觉，政治科学，社会科学和动物科学。高维统计和机器学习的截止性发展集中在探索问题的内在低维结构上。这在统计最佳和计算效率方面提出了新的挑战。 变分推断是一种通过寻求与原始问题的变异近似来解决这两种挑战的技术，不仅可以拖延，而且还紧密。 但是，文献从计算和统计角度都缺乏对变异推断的系统研究。 该项目的目标包括：（1）变异贝叶斯程序的理论研究； （2）可靠估计中的变异优化策略。 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，并在变分推理方面带来重大理论和计算进步。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的智力优点和更广泛影响的审查标准通过评估来获得支持的。

项目成果

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

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

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