CAREER: New methods for multivariate analysis in high dimensions

来自成像、基因微阵列实验和许多其他领域的数据集通常比受试者具有更多的测量特征。 用标准的统计方法分析这些数据要么是不可能的，要么是不充分的。 研究人员通过开发适合于此类数据集的新统计方法来解决这一问题。 研究者为这些新方法和快速计算算法的应用开发理论依据。 实现这些算法的软件将向公众提供。 这些新产品将帮助行业从业者创建更好的预测模型，并有助于推进许多其他领域的研究。 研究人员还将开发新的课程，包括创建本科统计计算课程，本科统计机器学习课程，博士学位-水平的主题课程，并在本科统计学专业的一个新的轨道。当解释变量的数量超过样本大小时，建立统计模型是多变量分析的前沿一个令人兴奋的领域。 用经典技术拟合这些模型通常是不可能的，必须施加一些约束或惩罚。 鼓励参数估计为零的惩罚受到了极大的关注。 这些惩罚是有用的，因为它们导致可解释的参数估计，但假设这些零存在可能是不适当的，在某些应用程序。 研究人员开发和分析新的方法，以适应模型的高维度，不需要零存在于感兴趣的参数，但仍然允许从业者作出简单的解释，适合的测量变量。 这包括开发新方法来拟合多响应回归模型和多项logistic回归模型，以及开发新方法来缩小拟合预测模型所需的逆协方差估计值的特征。 研究人员将开发新的课程，并涉及博士。学生在研究。

Datasets from imaging, gene microarray experiments, and many other fields often have more measured characteristics than subjects. Analyzing these data with standard statistical methods is either impossible or inadequate. The investigator addresses this problem by developing new statistical methods that are appropriate for such datasets. The investigator develops theoretical justifications for these new methods and fast computational algorithms for their application. Software that implements these algorithms will be made available to the public. These new products will help practitioners in industry create better predictive models and will also help advance research in many other fields. The investigator will also develop new curricula, including the creation of an undergraduate statistical computing course, an undergraduate statistical machine learning course, a Ph.D.-level topics course, and a new track within the undergraduate statistics major.Building statistical models when the number of explanatory variables exceeds the sample size is an exciting area at the forefront of multivariate analysis. Fitting these models with classical techniques is typically impossible and some constraints or penalties must be imposed. Penalties that encourage zeros in parameter estimates have received substantial attention. These penalties are useful because they lead to interpretable parameter estimates, but assuming that these zeros exist may be inappropriate in some applications. The investigator develops and analyzes new methods to fit models in high dimensions that do not require that zeros are present in the parameters of interest, but still allow the practitioner to make simple interpretations of the fit in terms of the measured variables. This includes the development of new methods to fit multiple response regression models and multinomial logistic regression models, as well as the development of new methods to shrink characteristics of inverse covariance estimates that are needed to fit predictive models. The investigator will develop new curricula and involve Ph.D. students in the research.