Administration/Data Management

在不同科学的交界处，统计学面临的一个基本挑战是开发分析海量数据集、复杂数据结构和高维预测指标的方法。这个德国-瑞士研究小组的目标是具体开发和分析复杂数据结构的统计正则化方法，因为它们在不同的应用领域中存在。在前景中，有一些方法是通过对数据模型的结构或几何的定性约束来给出正则化的。我们的基本假设是，通过定性约束进行的统计正则化为数据结构的建模提供了一种一致的方法，这种方法一方面足够灵活，可以识别和科学地利用数据的主要结构特征，但另一方面，足够具体，可以控制预测和分类错误。研究小组的目标和范围。我们在这个研究组的主要目标是从统计角度以统一的方式开发和分析复杂数据结构的正则化方法。特别强调基于定性约束的正则化方法，即考虑到关于某些模型参数的几何形状或结构假设(如可加性或单调性)的先验信息。一方面，我们将重点放在不同应用领域的不同数据模型上，其中我们将根据这些主题的需要开发专门定制的正则化方法。另一方面，我们的基本主张是，通过定性约束的统计正则化揭示了建模过程的统一原则，该原则足够灵活地解释重要的数据特征，并且足够具体地控制高度复杂的数据结构中的预测或分类错误。我们的目标是在更广泛的范围内理解它们在方法上的共性。我们的小组由长期从不同角度和不同学科处理正则化技术的研究人员组成，特别是从统计学、数值分析、机器学习、模式识别和计量经济学的角度。我们所有人都已经与这个小组的一些成员合作了一段时间，2008年4月，我们开始在这个雄心勃勃的项目中共同努力。在第二个筹资提案中，三名新同事(Gerard van den Berg、Tatana Krivobokova和Ulrike Schneider)已被整合。每个项目都是由一个真正的实质性应用程序问题驱动的。在许多情况下，同一数据集在不同项目中从不同角度处理(例如，B.Fitzenberger小组提供的劳动力市场数据或S.Hell小组提供的显微镜数据)。来自不同应用领域的相关研究小组的各种数据项目，如生物物理学、计量经济学、医学成像或分子生物学，显著增强了该研究小组的实用优势。我们声称，具有结构或质量限制的统计正规化程序允许在处理这些主题领域时采用一致的方法论观点和解决战略。

A basic challenge for statistics at the interface of different sciences is the developmentof methods for the analysis of massive data sets, complex data structures and highdimensionalpredictors. The objectives of this German-Swiss research group are specific developmentand analysis of statistical regularization methods for complex data structures as they mayoccur in different fields of application. In the foreground, there are methods in which regularization is given by qualitative constraints on the structure or geometry of data models. Our basic hypothesis is that statistical regularization by qualitative constraints produces a consistent methodology for modeling of data structures which, on the one hand, is flexible enough to identify and scientifically utilize main structural features of data, but, on the other hand, specific enough to control prediction and classification error. Aims and scope of the research group. Our primary goal in this research group is to develop and analyze regularization methods for complex data structures in a unifying way from a statistical perspective. Particular emphasis is on regularization methods based on qualitative constraints, i.e. taking into account prior information about the geometric shape of certain model parameters or structural assumptions such as additivity or monotonicity. On the one hand we focus on different data models in various fields of application where we will develop specifically tailored regularization methods according to the needs in these subject matters. On the other hand, our fundamental claim is that statistical regularization via qualitative constraints reveals a unifying principle for a modeling process which is flexible enough to explain important data features but also specific enough to control the prediction or classification error in highly complex data structures. We aim at understanding their methodological commonalities on a broader scale. Our group consists of researchers having dealt with regularization techniques from various perspectives and in various disciplines for a long time, in particular from the perspective of statistics, numerical analysis, machine learning, pattern recognition, and econometrics. All of us cooperated already with some members of this group for a certain time, and in April 2008 we have been started to work all together at this ambitious project. In this second funding proposal three new colleagues (Gerard van den Berg, Tatyana Krivobokova, Ulrike Schneider) have been integrated. Each project is driven by a real substantial application problem. In many cases the same data set is tackled from various perspectives within different projects (e.g. the labor market data provided by B. Fitzenberger’s group or the microscopy data by S. Hell’s group). Various data projects from associated research groups from various fields of applications, such as biophysics, econometrics, medical imaging or molecular biology significantly enhance the practical merits of this Research group. We claim that statistical regularization procedures with structural or qualitative constraints allow a consistent methodical perspective and solution strategy while dealing with those subject fields.