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的关键，例如文本分类、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，甚至更小。不幸的是，在这个所谓的大字母表领域，人们对最佳推理知之甚少。最近，不同的科学界发展了几种很有前途的方法，包括统计学和机器学习中的贝叶斯非参数方法，信息论中的普遍压缩方法，以及数学和计算机科学中的图形极限理论。这项研究研究了“模式最大似然”估计器的分析性质，它在实践中表现良好，但在理论上还没有被理解，并探索了计算加速比。此外，它试图描述哪些问题类更好地由贝叶斯非参数技术处理，哪些问题类由模式方法处理，并探索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，允许在存储、检索和分析数据方面实现更多自动化。此外，研究人员还利用这一理论来研究基因变异，它与疾病诊断的联系是生物学系统量化的关键一步，生物学在医学进步中发挥着越来越重要的作用。这项研究还将新课程引入课堂，特别是通过夏威夷原住民科学和工程导师计划，努力让妇女和代表性不足的少数族裔参与进来。

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.