CAREER: Flexible Parsimonious Models for Complex Data

学术界、工业界和政府的研究人员正在生成规模和复杂程度远远超出以前想象的数据。复杂的数据需要足够灵活的统计模型来适应有意义的潜在信号，使科学家能够发现意想不到的模式。然而，随着社会越来越依赖统计算法来做出影响日常生活的决策，一种方法的输出能够被非专家解释就变得越来越重要。这要求简约：简单的解释比复杂的解释更受青睐。例如，互联网带来了前所未有的大量文本形式的数据（如文章、博客、网页、消费者评论和许多其他社交媒体产品）。这样的文本数据代表了洞察世界的潜在宝藏——人们在想什么，这是如何随时间变化的，这是如何随地点变化的，等等。研究者开发了新的统计方法，以克服从这些数据中收集有用信息的主要技术挑战。同样的方法可以应用于微生物组的研究，微生物组是生活在人类肠道等环境中的巨大微生物群落。需要更好的统计方法来识别肠道中对人类健康和疾病起关键作用的微生物类型。这个项目要解决的另一个问题涉及到长期收集的数据建模（比如风速数据和野生动物监测）。所开发的方法允许更准确的预测，这在许多领域至关重要，包括卫生和医药以及开发成本较低的能源系统。这个项目的最后一个主要领域是致力于使统计研究过程更有效，其软件质量更高，更容易在统计研究人员社区中共享。最后，所有三个研究目标都与教育成果紧密结合，包括研究生的监督和教学，向非统计学家和非科学家的推广，以及发布本科生可访问的描述研究者新研究成果的迷你论文。这个项目的重点是设计新的统计方法，以平衡两种重要的、经常对立的需求：灵活性和节俭性。(1)当特征高度稀疏时，很难建立预测回归和分类模型。虽然许多方法都关注高维的挑战，但相对较少的方法考虑到非零特征所带来的障碍。当特征高度稀疏时，研究者开发了一个新的特征选择框架，在现有方法失败的情况下成功。这从理论和计算的角度进行了研究。(2)高维协方差估计和时间序列建模是统计学中两个丰富但又截然不同的领域，研究者将这两个领域结合起来，开发了局部平稳时间序列建模的新方法。从平稳性到局部平稳性所增加的灵活性必须谨慎地与节俭相平衡。(3)将在研究者的新平台上免费在线发布一系列特定区域的软件模块，以简化进行模拟研究的过程。每个模块将实现一些最常见的模型，方法，并在统计研究的给定区域使用的指标。目标是通过创建易于适应的标准化格式，促进统计研究社区中高质量、可重复的模拟代码的共享。

Researchers throughout academia, industry, and government are generating data at scales and levels of complexity far beyond what could previously have been imagined. Complex data demand statistical models that are sufficiently flexible to adapt to meaningful, underlying signals, allowing scientists to discover unexpected patterns. Yet as society relies more heavily on statistical algorithms to make decisions impacting everyday life, it becomes increasingly important for a method's output to be interpretable by non-experts. This demands parsimony: that simpler explanations be favored over more complicated ones. For example, the Internet has led to unprecedented quantities of data in the form of text (such as articles, blogs, webpages, consumer reviews, and many other social media products). Such text data represent a potential treasure trove of insights into the world -- what people are thinking, how this is changing over time, how this varies by location, etc. The investigator develops new statistical methods for overcoming major technical challenges to gleaning useful information from this data. This same methodology can be applied to the study of the microbiome, the vast community of microbes living in an environment such as the human gut. Better statistical methods are needed to identify types of microbes in the gut that play a crucial role in human health and disease. Another problem that is tackled in this project involves modeling data collected over time (such as wind-speed data and wildlife monitoring). The methods that are developed allow for more accurate forecasting, which is crucial in many areas including health and medicine and the development of lower cost energy systems. The last major area in this project is devoted to making the process of statistical research more efficient and its software of higher quality and easier to share across the community of statistical researchers. Finally, all three research objectives are closely integrated with educational outcomes, including the supervision and teaching of graduate students, outreach to non-statisticians and non-scientists, and the release of undergraduate-accessible mini-papers describing the investigator's new research findings.This project focuses on the design of new statistical methods that balance two important and often opposing needs: flexibility and parsimony. (1) Building predictive regression and classification models is difficult when the features are highly sparse. While many methods focus on the challenge of high dimensionality, relatively few have considered the obstacle posed by features that are rarely nonzero. The investigator develops a new framework for feature selection when the features are highly sparse that succeeds where preexisting methods fail. This is studied both from theoretical and computational standpoints. (2) High-dimensional covariance estimation and time series modeling are two rich, but largely distinct, areas in statistics, which the investigator combines to develop new methods for modeling locally stationary time series. The added flexibility in going from stationarity to local stationarity must be carefully balanced with parsimony. (3) A series of area-specific software modules will be distributed freely online building on the investigator's new platform for streamlining the process of performing simulation studies. Each module will implement some of the most common models, methods, and metrics used in a given area of statistics research. The goal is to facilitate the sharing of high-quality, reproducible simulation code in the statistics research community by creating an easily-adaptable standardized format.