Properties of Approximate Inference for Complex High-Dimensional Models

复杂高维模型的近似推理的性质

• 批准号: 1811614
• 负责人: Iain Johnstone
• 金额: $ 60万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-07-01 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1811614&HistoricalAwards=false
• 关键词: Properties; Approximate; Inference; Complex; Dimensional

Modern scientific data acquisition often creates datasets with many measurements on a large sample size of individuals. The structure of interest in the data may be low dimensional or sparse. Examples arise in scientific domains from econometrics to genomics and image and signal processing and beyond. The project explores approximate methods of statistical inference for such structure in a representative set of contemporary settings: high dimensional estimation, generalized linear mixed models and low rank multivariate models. It aims to develop approximate methods backed by an optimality theory and/or performance guarantees. The work is expected to provide new theoretical insights into current problems in specific application domains such as Magnetic Resonance Imaging and quantitative genetics.The project will bring ideas from classical decision theory to compressed sensing and robust linear modeling, rigorously solving nonconvex optimization problems and obtaining reconstruction performance rigorously better than traditional convex optimization methods. It will exploit decision theoretic ideas in the proposer's previous work to provide new theoretical insights into a pressing practical problem in compressed sensing -- deriving optimal variable-density sampling schedules applicable to Magnetic Resonance Imaging and NMR spectroscopy. The project will also study theoretically the statistical performance of some methods for deterministic approximate inference popular in machine learning, but for which little attention has been given to properties such as consistency, asymptotic normality and efficiency. The study will begin with concrete examples in the realm of generalized linear mixed models, from a frequentist perspective, and seek to establish first-of-kind results for asymptotic efficiency of Expectation Propagation. Finally, the project will study approximate inference for the eigenstructure of highly multivariate models with low dimensional structure. It will adapt James' classical framework for multivariate analysis to a broad class of multispike models. Through collaboration with quantitative geneticists, it will develop methods for inference for low dimensional structure in high dimensional genetic covariance matrices. In both cases, methods from random matrix theory will be essential.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.

现代科学数据采集经常在大量个体样本上创建具有许多测量值的数据集。数据中感兴趣的结构可能是低维的或稀疏的。从计量经济学到基因组学、图像和信号处理等科学领域都有这样的例子。该项目探讨了在一组具有代表性的当代设置中这种结构的统计推断的近似方法：高维估计，广义线性混合模型和低秩多元模型。它旨在开发由最优性理论和/或性能保证支持的近似方法。这项工作有望为磁共振成像和定量遗传学等特定应用领域的当前问题提供新的理论见解。该项目将经典决策理论的思想引入压缩感知和鲁棒线性建模，严格解决非凸优化问题，并获得严格优于传统凸优化方法的重构性能。它将利用提议者以前工作中的决策理论思想，为压缩感知中的一个紧迫的实际问题提供新的理论见解-推导适用于磁共振成像和核磁共振波谱的最佳可变密度采样计划。该项目还将从理论上研究机器学习中流行的一些确定性近似推理方法的统计性能，但很少关注一致性，渐近正态性和效率等性质。本研究将从广义线性混合模型领域的具体例子开始，从频率论的角度出发，寻求建立期望传播的渐近效率的第一类结果。最后，本课题将研究具有低维结构的高多元模型的特征结构的近似推理。它将把詹姆斯的经典多变量分析框架应用于广泛的多尖峰模型。通过与定量遗传学家的合作，它将开发高维遗传协方差矩阵中低维结构的推理方法。在这两种情况下，随机矩阵理论的方法将是必不可少的。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。

项目成果

Larry Brown’s Work on Admissibility

拉里·布朗 (Larry Brown) 关于可受理性的著作

• DOI: 10.1214/19-sts744
• 发表时间: 2019
• 期刊: Statistical Science
• 影响因子: 5.7
• 作者: Johnstone, Iain M.

On minimax optimality of sparse Bayes predictive density estimates

稀疏贝叶斯预测密度估计的极小极大最优性

• DOI: 10.1214/21-aos2086
• 发表时间: 2022
• 期刊: The Annals of Statistics
• 作者: Mukherjee, Gourab;Johnstone, Iain M.
• 通讯作者: Johnstone, Iain M.

Fast and Accurate Binary Response Mixed Model Analysis Via Expectation Propagation.

通过期望传播的快速准确的二元响应混合模型分析。

• DOI: 10.1080/01621459.2019.1665529
• 发表时间: 2020
• 期刊: Journal of the American Statistical Association
• 影响因子: 3.7

Tracy–Widom at each edge of real covariance and MANOVA estimators

Tracy-Widom 在真实协方差和多元方差分析估计量的每个边缘

• DOI: 10.1214/21-aap1754
• 发表时间: 2022
• 期刊: The Annals of Applied Probability
• 作者: Fan, Zhou;Johnstone, Iain M.
• 通讯作者: Johnstone, Iain M.