CIF: Small: Collaborative Research:Algorithms and Information-Theoretic Limits for Data-Limited Inference

CIF：小型：协作研究：数据有限推理的算法和信息论限制

• 批准号: 1117128
• 负责人: Aaron Wagner
• 金额: $ 24万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-08-01 至 2014-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1117128&HistoricalAwards=false
• 关键词: CIF; Small; Collaborative; Research; Algorithms

It is an irony of our time that despite living in the 'information age' we are often data-limited. After decades of research, scientists still debate the causes and effects of climate change, and recent work has shown that a significant fraction of the most influential medical studies over the past 13 years have been subsequently found to be inaccurate, largely due to insufficient data. One reason for this apparent paradox is that modeling complex, real-world information sources requires rich probabilistic models that cannot be accurately learned even from very large data sets. On a deeper level, research inherently resides at the edge of the possible, and seeks to address questions that available data can only partially answer. It is therefore reasonable to expect that we will always be data-limited.This research involves developing new algorithms and performance bounds for data-limited inference. Prior work of the PIs has shown that, by taking an information-theoretic approach, one can develop new algorithms that are tailored specifically to the data-limited regime and perform better than was previously known, and in some cases are provably optimal. This project advances the goal of developing a general theory for data-limited inference by considering a suite of problems spanning multiple application areas, such as classification; determining whether two data sets were generated by the same distribution or by different distributions; distribution estimation from event timings; entropy estimation; and communication over complex and unknown channels. Whereas these problems have all been studied before in isolation, prior work of the PIs has shown it is fruitful to view them as instances of the same underlying problem: data-limited inference.

尽管我们生活在“信息时代”，但我们经常受到数据的限制，这是我们这个时代的一个讽刺。经过几十年的研究，科学家们仍在争论气候变化的原因和影响，最近的工作表明，在过去13年里，有很大一部分最具影响力的医学研究后来被发现是不准确的，主要原因是数据不足。造成这种明显矛盾的一个原因是，对复杂的现实世界信息源进行建模需要丰富的概率模型，即使从非常大的数据集中也无法准确地学习到这些模型。在更深的层次上，研究本质上停留在可能的边缘，并寻求解决现有数据只能部分回答的问题。因此，有理由期望我们将永远受到数据的限制。这项研究涉及开发新的算法和性能界限的数据有限的推理。pi的先前工作表明，通过采用信息理论方法，可以开发专门针对数据有限的制度量身定制的新算法，并且比以前已知的性能更好，并且在某些情况下可以证明是最佳的。该项目通过考虑跨越多个应用领域的一系列问题，例如分类，推进了为数据有限推理开发通用理论的目标；确定两个数据集是由相同分布生成的还是由不同分布生成的；基于事件时间的分布估计；熵估计;通过复杂和未知的渠道进行交流。尽管这些问题之前都是单独研究过的，但先前对pi的研究表明，将它们视为同一个潜在问题的实例是富有成效的：数据有限的推理。