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更快。贝叶斯方法在社会科学方面并没有得到太多的吸引力，部分原因是该方法在计算上是如此之大。许多可以使用这些技术的研究人员选择不这样做，因为分析太昂贵。该项目将通过利用长期以来一直被统计学家忽视的关键定理来提高贝叶斯方法的计算效率，但被20世纪最伟大的数学家之一证明。为了在当今的计算机上使用这种方法，需要将一些作品放置在适当的位置。但是，一旦实施并进行了一些额外的培训，科学家将能够应用最先进的统计方法，无论数据量如何。修改后的计算基础定理的美丽是，它几乎是普遍适用的，所有科学家都可以利用。通过降低和平坦的成本功能，该项目将对社会科学和其他地方产生广泛而深远的影响。这项研究的结果将促进对最近在科学领域中普遍存在的大型数据集的分析。研究生将参与该项目的行为，并接受了这种方法的使用。研究人员将在现有的免费和开源软件程序中实施他们的发现。本研究项目将利用Kolmogorov叠加定理（KST）来提高使用贝叶斯方法的项目的计算速度。科学现象的大多数统计模型都要求：在模型下观察数据集合的概率是什么，以及该概率会如何根据要估计的未知数量的值而变化？为了回答这些问题，计算机计算了许多未知数可能值的概率，并确定估计值的范围比其他范围更有可能。数据集中的每个观察结果都会影响这一概率，因此当数据集很大时，计算很慢且通常不可行。但是，KST表明，只有使用数学函数添加每种数学函数，而每个函数仅在一个未知中输入并输出链中的一个链接，就有另一种方法可以精确地执行计算。替代链中的链接数仅取决于未知数的数量，而不是数据集中的观察次数，因此可以在大型数据集中显着加速计算。要使用这项技术，科学家将需要对他们如何构建模型并估算模型未知数量的方式有所不同，但是研究人员将提供一个连贯的理论框架和开源软件工具，这些工艺将不仅使该过程更快，而且更简单。该奖项反映了NSF的法定任务，并通过评估范围来反映出众所周知的支持者，该奖项是通过评估范围的范围的。