CIF: Medium: Collaborative Research: Information Theory and Statistical Inference from Large-Alphabet Data

统计分析是许多具有挑战性的应用程序的关键，如文本分类，语音识别和DNA分析。然而，可用的数据量通常与构成数据的符号集（字母表）相当或甚至更小。不幸的是，在这个所谓的大字母表域中，对最优推理知之甚少。近年来，不同的科学团体开发了一些有前途的方法，包括统计学和机器学习中的贝叶斯非参数，信息论中的通用压缩，数学和计算机科学中的图极限理论。研究人员从这些多个角度研究问题，但特别关注发展信息论方法。该研究研究了“模式最大似然”估计量的分析性质，该估计量在实践中表现良好，但理论上并不理解，并且还探索了计算加速。此外，它试图划定哪些问题类是更好地处理贝叶斯非参数技术和模式的方法，并探讨这些方法之间的联系。研究人员将由此产生的理论用于自动文档分类，从而在存储，检索和分析数据方面实现更多的自动化。此外，研究人员使用该理论来研究遗传变异，其与疾病诊断的联系是生物学系统量化的关键一步，在医学进步中发挥着越来越重要的作用。这项研究还为课堂带来了新的课程，并通过夏威夷土著科学和工程导师计划等方式，特别努力让妇女和代表性不足的少数民族参与进来。

Statistical analysis is key to many challenging applications such as text classification, speech recognition, and DNA analysis. However, often the amount of data available is comparable or even smaller than the set of symbols (alphabet) constituting the data. Unfortunately, not much is known about optimal inference in this so-called large-alphabet domain. Recently, several promising approaches have been developed by different scientific communities, including Bayesian nonparametrics in statistics and machine learning, universal compression in information theory, and the theory of graph limits in mathematics and computer science.The investigators study the problem drawing from these multiple perspectives, but with a particular focus on developing the information theoretic approach. The research studies analytical properties of the "pattern maximum likelihood'' estimator, which performs well in practice but is not understood theoretically, and also explores computational speedups. Moreover, it attempts to delineate which problem classes are better handled by Bayesian nonparametric techniques and which by the pattern approach, and explores links between these approaches. The investigators use the resulting theory for automatic document classification, allowing for more automation in storing, retrieving, and analyzing data. Furthermore, the investigators use the theory to study genetic variations, whose link with disease diagnosis is a crucial step in the systematic quantification of biology that is playing an increasingly important role in medical advancement. The research also brings new courses to the classroom, with a special outreach effort to involve women and under-represented minorities, including through the Native Hawaiian Science and Engineering Mentorship Program.