Sublinear time methods with statistical guarantees

点击翻译按钮获取中文摘要

In the era of big data the fundamental paradigm of statistical efficiency in mathematical statistics has shifted towards the development of computationally feasible methods for complex models. Well known statistically efficient methods (e.g. likelihood based) are no longer applicable as the computational costs play a major role in data analysis. In this project we will develop computationally tractable statistical methodology, which is able to deal with large scale data while still satisfying statistical risk guarantees. In the common linear model we study two prototypical problems in this context, namely data reduction by optimal subsampling strategies to identify the ``most informative data'' and optimal detection of possible change points in parameters with sublinear computational costs. For the first task we will use optimal design principles to develop subsampling strategies providing sublinear estimates and investigate their statistical properties. For the second task we aim to develop variants of binary segmentation which allow for sublinear change point detection.