CAREER: Flexible Statistical Learning for Complex Data

统计学习被广泛认为是一个非常活跃的跨学科研究领域，它介于统计学、计算机科学和优化之间。这项研究为解决复杂的学习问题，特别是高维和噪声数据的学习问题提供了一系列新的统计学习技术。特别是，研究者开发了(1)几个新的大边际分类器，这些分类器有望产生高度竞争的分类精度，类概率估计以及变量选择；(2)一类非平稳空间自回归模型协方差矩阵估计的正则化新方法；(3)一种评估高维数据聚类统计显著性的新技术。随着科技的飞速发展，许多不同的科学领域正在产生大量复杂的数据。分析这类数据变得越来越具有挑战性。本研究的一个主要目标是提供一套灵活的统计学习技术。这些工具将对癌症研究、医学成像、微阵列数据分析和时空建模产生有益的影响。研究者与统计学以外的许多领域的科学家合作，如生物学、计算机科学、药学和遗传学。新的发展使科学家能够以高预测精度和更高的可解释性分析复杂的数据。高效的算法和软件被开发出来供公众使用。研究目标与教育活动的整合旨在帮助研究生，本科生和高中水平的学生以及来自不同学科的研究人员获得最先进的统计学习方法和工具。

Statistical learning is widely recognized as a very active area of interdisciplinary research, which lives between statistics, computer science, and optimization. This research offers a host of new statistical learning techniques for solving complicated learning problems, especially for high dimensional and noisy data. In particular, the investigator develops (1). several novel large-margin classifiers which are expected to yield highly competitive classification accuracy, class probability estimation, as well as variable selection; (2). a new regularization approach to estimate the covariance matrix for a class of nonstationary spatial autoregressive model; (3). a novel technique to assess statistical significance of clustering for high dimensional data.With the rapid advance of technology, massive and complex data are being generated across many different scientific fields. Analyzing such data becomes more and more challenging. A major goal of this research is to provide a set of flexible statistical learning techniques. These tools should have beneficial impact on cancer research, medical imaging, microarray data analysis and spatial-temporal modeling. The investigator collaborates with a number of scientists in various fields outside of statistics such as biology, computer science, pharmacy, and genetics. The new developments allow scientists to analyze complex data with high prediction accuracy and increased interpretability. Efficient algorithms and software are developed for public use. The integration of the research goals with educational activities aims to help students at graduate, undergraduate, and high school levels and researchers from various disciplines to acquire state-of-the-art statistical learning methods and tools.