Sublinear time methods with statistical guarantees

在大数据时代，数理统计中统计效率的基本范式已经转向为复杂模型开发计算上可行的方法。 众所周知的统计学上有效的方法（例如基于似然的方法）不再适用，因为计算成本在数据分析中起着重要作用。在这个项目中，我们将开发计算上易于处理的统计方法，它能够处理大规模数据，同时仍然满足统计风险保证。在普通线性模型中，我们研究了两个典型的 这方面的问题，即通过最佳二次抽样战略减少数据，以确定“最具信息性的数据”，并以次线性计算成本最佳检测参数中可能的变化点。对于第一个任务，我们将使用最优设计原理来开发提供次线性估计的子采样策略，并研究其统计特性。第二项任务，我们的目标是开发 二进制分割的变体，其允许次线性变化点检测。

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 Well known statistically efficient methods (e.g. likelihood based) are no longer applicable as the computational costs play a major role in data analysis.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.