BIGDATA: F: Reliable Inference with Big Data: Reproducibility, Data Sharing, Heterogeneity

BIGDATA：F：大数据的可靠推理：再现性、数据共享、异构性

• 批准号: 1741162
• 负责人: Andrea Montanari
• 金额: $ 65万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-09-01 至 2021-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1741162&HistoricalAwards=false
• 关键词: BIGDATA; Reliable; Inference; Big; Data

Over the last decade, 'big data' technologies have allowed the acquisition of vast amount of data (e.g. through smartphones) and their accumulation into large scale databases. Powerful hardware and software systems have been developed to crunch these data and extract statistical models. For instance, the outcome of a certain medical procedure can be modeled in terms of the features of the patient, thus in principle providing a personalized risk score for that procedure. Unfortunately, the increasing complexity of these data and of the algorithms used has made statistical models significantly less transparent. How certain are we of these statistical predictions? What is their limit of validity? How biased is the resulting model?This project focuses on four main challenges that are ubiquitous in big-data, and are crucial to extract reliable insights: reproducibility; data sharing; missing data; data heterogeneity. (1) Reproducibility requires being able to compare two models extracted from different data sets (e.g. after additional data have been accumulated). This is in turn impossible unless we have reliable procedures to quantify uncertainty and confidence in complex high-dimensional models. Recently proposed ideas in this direction are still insufficient to cope with realistic large-scale applications.(2) Data sharing is a key feature of modern data analysis, whereby a single massive data set is being studied by hundreds of independent researchers. Unguarded statistical inference by such a population of researchers unavoidably leads to large numbers of false discoveries. The project builds on false discovery rate-controlling methods to propose safe approaches for decentralized data analysis.(3) Missing data are ubiquitous in big data. While several methods have been developed in the past to deal with missing data, it is unclear to what extent they are applicable to modern scenarios. The project aims at developing principled guidelines based on a rigorous comparison of various approaches, and developing new algorithms based on maximum likelihood.(4) Data heterogeneity. Big data are often produced by the aggregation of multiple data sources. How can we prevent standard statistical procedures to be critically affected by such heterogeneities? The project uses new regularization schemes to fusion information across multiple sources.

在过去的十年中，“大数据”技术允许获取大量数据（例如通过智能手机）及其积累到大型数据库中。已经开发了强大的硬件和软件系统来处理这些数据并提取统计模型。例如，可以根据患者的特征对某个医疗程序的结果进行建模，因此原则上为该程序提供个性化的风险评分。不幸的是，这些数据和所使用的算法的复杂性日益增加，使统计模型显着透明。我们如何确定这些统计预测？他们的有效性限制是什么？由此产生的模型有多偏见？该项目着重于大数据中无处不在的四个主要挑战，对于提取可靠的见解至关重要：可重复性；数据共享；缺少数据；数据异质性。 （1）可重复性需要能够比较从不同数据集提取的两个模型（例如，在累积了其他数据之后）。反过来，除非我们有可靠的程序来量化对复杂的高维模型的不确定性和信心，否则这是不可能的。最近在这个方向上提出的想法仍然不足以应对现实的大规模应用。（2）数据共享是现代数据分析的关键特征，因此，数百名独立研究人员正在研究一个大规模的数据集。这样的研究人员不可避免地会导致大量错误发现。该项目建立在错误的发现率控制方法的基础上，以提出用于分散数据分析的安全方法。（3）丢失的数据在大数据中无处不在。尽管过去已经开发了几种方法来处理丢失的数据，但尚不清楚它们在多大程度上适用于现代方案。该项目旨在基于对各种方法的严格比较制定原则指南，并根据最大可能性开发新算法。（4）数据异质性。大数据通常是由多个数据源的汇总产生的。我们如何防止标准统计程序受到这种异质性的严重影响？该项目使用新的正规化方案来跨多个来源融合信息。

项目成果

Discussion of: “Nonparametric regression using deep neural networks with ReLU activation function”

• DOI: 10.1214/19-aos1910
• 发表时间: 2020-08
• 期刊: The Annals of Statistics
• 作者: B. Ghorbani;Song Mei;Theodor Misiakiewicz;A. Montanari

Learning with invariances in random features and kernel models

• 发表时间: 2021-02
• 期刊: ArXiv
• 作者: Song Mei;Theodor Misiakiewicz;A. Montanari

When do neural networks outperform kernel methods?

• DOI: 10.1088/1742-5468/ac3a81
• 发表时间: 2020-06
• 期刊: Journal of Statistical Mechanics: Theory and Experiment
• 作者: B. Ghorbani;Song Mei;Theodor Misiakiewicz;A. Montanari

Optimization of the Sherrington--Kirkpatrick Hamiltonian

Sherrington--Kirkpatrick 哈密顿量的优化

• DOI: 10.1137/20m132016x
• 发表时间: 2021
• 期刊: SIAM Journal on Computing
• 影响因子: 1.6
• 作者: Montanari, Andrea

The threshold for SDP-refutation of random regular NAE-3SAT

• DOI: 10.1137/1.9781611975482.140
• 发表时间: 2018-04
• 期刊: ArXiv
• 作者: Y. Deshpande;A. Montanari;R. O'Donnell;T. Schramm;S. Sen