Subsampling is commonly used to overcome computational and economical bottlenecks in the analysis of finite populations and massive datasets. Existing methods are often limited in scope and use optimality criteria (e.g., A-optimality) with well-known deficiencies, such as lack of invariance to the measurement-scale of the data and parameterisation of the model. A unified theory of optimal subsampling design is still lacking. We present a theory of optimal design for general data subsampling problems, including finite population inference, parametric density estimation, and regression modelling. Our theory encompasses and generalises most existing methods in the field of optimal subdata selection based on unequal probability sampling and inverse probability weighting. We derive optimality conditions for a general class of optimality criteria, and present corresponding algorithms for finding optimal sampling schemes under Poisson and multinomial sampling designs. We present a novel class of transformation- and parameterisation-invariant linear optimality criteria which enjoy the best of two worlds: the computational tractability of A-optimality and invariance properties similar to D-optimality. The methodology is illustrated on an application in the traffic safety domain. In our experiments, the proposed invariant linear optimality criteria achieve 92-99% D-efficiency with 90-95% lower computational demand. In contrast, the A-optimality criterion has only 46% and 60% D-efficiency on two of the examples.

翻译：子抽样常用于克服有限总体分析与海量数据集分析中的计算与经济瓶颈。现有方法在适用范围内存在局限，且使用的优化准则（如A-优化准则）存在已知缺陷，例如对数据测量尺度与模型参数化缺乏不变性。目前尚缺乏统一的最优子抽样设计理论。本文提出适用于一般数据子抽样问题的最优设计理论，涵盖有限总体推断、参数密度估计及回归建模等领域。该理论囊括并推广了现有基于不等概率抽样与逆概率加权的最优子数据选择领域中的多数方法。我们推导出一类一般性优化准则的最优性条件，并给出了在泊松抽样与多项抽样设计下寻找最优抽样方案的相应算法。提出了一类兼具两者优势的新型变换与参数化不变的线性优化准则：既具备A-优化准则的计算可行性，又拥有类似于D-优化准则的不变性特征。以交通安域应用为例验证方法有效性。实验表明，所提出的不变性线性优化准则在计算需求降低90-95%的条件下，达到了92-99%的D-效率；而A-优化准则在两个实例中仅分别获得46%与60%的D-效率。