Revamped Bayesian Inference

改进的贝叶斯推理

• 批准号: 2051246
• 负责人: Benjamin Goodrich
• 金额: $ 30万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-09-01 至 2024-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2051246&HistoricalAwards=false
• 关键词: Revamped; Bayesian; Inference

This research project will make Bayesian statistical computation much faster. Bayesian methods have not gained much traction in the social sciences, in part because the approach is so computationally intensive. Many researchers who could usefully apply these techniques choose not to do so because the analysis is too costly. This project will improve the computational efficiency of Bayesian methods by harnessing a critical theorem that has long been overlooked by statisticians but proven by one of the twentieth century's greatest mathematicians. Some pieces will need to be put into place for this approach to work on today's computers. However, once implemented and with a little bit of additional training, scientists will be able to apply state-of-the-art statistical methods regardless of the amount of data. The beauty of the theorem underlying the modified calculation is that it is almost universally applicable and can be leveraged by all scientists. By lowering and flattening the cost function, this project will have a broad and deep impact in the social sciences and elsewhere. The results of this research will facilitate the analysis of large data sets that recently have become prevalent across scientific fields. Graduate students will be involved in the conduct of the project and trained in the use of this approach. The investigators will implement their findings in an existing free and open-source software program.This research project will leverage the Kolmogorov Superposition Theorem (KST) to increase the speed of computations for projects using Bayesian methods. Most statistical models of scientific phenomena ask: What was the probability, under the model, of observing this collection of data and how would that probability change depending on the values of unknown quantities that are to be estimated? To answer those questions, computers calculate that probability for many possible values of the unknowns and determine what ranges of the estimates are more probable than others. Each observation in a data set affects this probability, so when data sets are large, the calculation is slow and often infeasible. However, the KST demonstrates that there is an alternative way to exactly perform the calculation using only the addition of mathematical functions that each take in just one unknown and output one link in the chain. The number of links in the alternative chain depends only on the number of unknowns, rather than the number of observations in the data set, and thus the calculation can be dramatically accelerated in large data sets. To use this technique, scientists will need to think a little differently about how they build models and estimate the model's unknown quantities, but the investigators will provide a coherent theoretical framework and open-source software tools that will make this process not only faster, but simpler.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.

该研究项目将使贝叶斯统计计算变得更快。贝叶斯方法在社会科学领域并未获得太多关注，部分原因是该方法的计算量太大。许多可以有效应用这些技术的研究人员选择不这样做，因为分析成本太高。该项目将通过利用一个长期被统计学家忽视但已被二十世纪最伟大的数学家之一证明的关键定理来提高贝叶斯方法的计算效率。为了使这种方法在当今的计算机上发挥作用，需要将一些部分落实到位。然而，一旦实施并进行一些额外的培训，无论数据量有多少，科学家都将能够应用最先进的统计方法。修改后的计算所依据的定理的优点在于它几乎普遍适用并且可以被所有科学家利用。通过降低和扁平化成本函数，该项目将对社会科学和其他领域产生广泛而深刻的影响。这项研究的结果将有助于对最近在科学领域流行的大型数据集进行分析。研究生将参与该项目的实施，并接受使用这种方法的培训。研究人员将在现有的免费开源软件程序中实施他们的发现。该研究项目将利用柯尔莫哥洛夫叠加定理（KST）来提高使用贝叶斯方法的项目的计算速度。大多数科学现象的统计模型都会问：在该模型下，观察这组数据的概率是多少？该概率将如何根据要估计的未知量的值而变化？为了回答这些问题，计算机计算未知数的许多可能值的概率，并确定哪些估计范围比其他范围更有可能。数据集中的每个观察都会影响此概率，因此当数据集很大时，计算速度很慢并且通常不可行。然而，KST 表明，有一种替代方法可以仅使用添加数学函数来精确执行计算，每个数学函数仅接受一个未知数并输出链中的一个链接。替代链中的链接数量仅取决于未知数的数量，而不是数据集中观测的数量，因此在大数据集中可以显着加速计算。要使用这种技术，科学家们需要对如何构建模型和估计模型的未知量进行一些不同的思考，但研究人员将提供一个连贯的理论框架和开源软件工具，这将使这个过程不仅更快，而且该奖项反映了 NSF 的法定使命，并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，被认为值得支持。