Invited Session 1: Subsampling from Big Data

In the era of Big Data, analyzing entire datasets is often infeasible due to high computational costs and the risks of overfitting. Subsampling techniques have emerged as a cost-effective alternative, enabling researchers to extract informative subsets of data. This study investigates the performance of design-based subsampling methods under conditions of model misspecification and the presence of outliers. A comparative analysis of model-based approaches, such as D-optimal and LowCon, and model-free techniques, including MRSS, Twinning, and PDDS, is conducted. Simulation studies offer insights into the trade-offs between inferential robustness and computational efficiency, guiding the selection of optimal subsampling strategies for various applications.

The impact of the distribution of explanatory variables on parameter estimation and subsampling is studied. A simple linear regression model is considered, where a parameter is shared between the marginal distribution of the covariate and the conditional distribution of the response given the covariate. Joint likelihood estimation is shown to consistently outperform conditional likelihood estimation, especially when the variance of the conditional distribution is large relative to the explanatory variable. A two-step subsampling method is proposed to improve estimation, combining random sampling with targeted selection. Simulation results are presented to demonstrate the method’s performance. These results highlight the importance of the explanatory variable distribution in estimation and subsampling strategies.

Subdata selection is a crucial strategy when the size of large datasets exceed available computing resources, or when observing the response variable is costly. The challenge is to select a subset of n data points from N available datapoints, retaining a maximum amount of information. Since this is an NP hard problem, any solution is an approximation of the optimal solution. For various methods that have been proposed, little is known about the efficiency of selected subdata relative to the optimal solution. Based on continuous optimal design theory, we propose a method to bridge this gap.We obtain a lower and upper bound for the relative efficiency of any given subdata. We also develop a novel algorithm for subdata selection, show its convergence, and demonstrate its superior performance.