Mean Field Asymptotics in Statistical Inference: Variational Approach, Multiple Testing, and Predictive Inference

统计推断中的平均场渐进：变分方法、多重测试和预测推断

• 批准号: 2210827
• 负责人: Song Mei
• 金额: $ 20万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-07-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2210827&HistoricalAwards=false
• 关键词: Mean; Field; Asymptotics; Statistical; Inference

The era of big data poses unprecedented statistical and computational challenges in high-dimensional statistical inference. One challenge is the “dual objective” nature of various statistical inference tasks: statisticians hope to design procedures that achieve near-optimal statistical efficiency and satisfy desired validity guarantees even under model misspecification. Furthermore, many statistical inference procedures involve a Bayesian component, and performing exact Bayesian inference on large-scale datasets is computationally challenging. This project will address these challenges in some high dimensional statistical inference tasks. The techniques and methods developed in the project will further advance the interplay between a broad range of areas including high-dimensional statistics, statistical physics, optimization, information theory, and statistical machine learning. Results from this project are anticipated to have applicability in computational biology, computer vision, neuroscience, natural language processing, and multiple testing. Graduate and undergraduate students will be exposed to these results through involvement in the project, and the results will be incorporated in courses.This project aims to resolve statistical and computational challenges in multiple testing and predictive inference, using the mean field asymptotic theory of statistical inference. Focusing on a few stylized problems, the program consists of three major research thrusts: 1) analyze the non-convex landscape of Thouless-Anderson-Palmer (TAP) variational inference objective functions and design efficient algorithms for optimizing these functions; 2) in the task of false discovery rate (FDR) control, design procedures that maximize the number of discoveries when models are correctly specified while controlling the frequentist FDR even under model misspecification; and 3) in the task of predictive inference, design procedures that give reasonably small prediction sets while maintaining the frequentist validity of coverage in the presence of model misspecification. This research will develop new techniques for studying the mean field asymptotics of high-dimensional statistical models, which will likely be applicable beyond the specific statistical models and will be relevant in other areas of science and engineering.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.

大数据时代对高维统计推断提出了前所未有的统计和计算挑战。一个挑战是各种统计推断任务的“双重目标”性质：统计学家希望设计出实现接近最佳统计效率的程序，即使在模型错误指定的情况下也能满足所需的有效性保证。此外，许多统计推断过程涉及贝叶斯组件，并且在大规模数据集上执行精确的贝叶斯推断在计算上具有挑战性。这个项目将解决这些挑战，在一些高维统计推断任务。该项目中开发的技术和方法将进一步推动包括高维统计、统计物理、优化、信息论和统计机器学习在内的广泛领域之间的相互作用。该项目的结果预计将适用于计算生物学，计算机视觉，神经科学，自然语言处理和多重测试。研究生和本科生将通过参与该项目来接触这些结果，并且结果将纳入课程中。该项目旨在使用统计推断的平均场渐近理论来解决多重测试和预测推断中的统计和计算挑战。该计划围绕几个典型问题，主要包括三个研究方向：1）分析Thouless-Anderson-Palmer（TAP）变分推理目标函数的非凸性，并设计优化这些函数的有效算法; 2）在错误发现率（FDR）控制任务中，设计程序，当模型被正确指定时，最大化发现的数量，同时即使在模型错误指定的情况下也控制频率论FDR; 3）在预测推理任务中，设计程序，给出合理小的预测集，同时在存在模型误指定的情况下保持覆盖的频率论有效性。这项研究将开发用于研究高维统计模型的平均场渐近性的新技术，这将可能适用于特定统计模型之外，并将在科学和工程的其他领域相关。该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。