A1151
Title: Analytical inclusion probabilities for optimal subsampling under misspecification
Authors: Alvaro Cia-Mina - University of Navarra (Spain)
Laura Deldossi - Universita Cattolica del Sacro Cuore di Milano (Italy)
Jesus Lopez-Fidalgo - University of Navarra (Spain)
Chiara Tommasi - University of Milan (Italy) [presenting]
Abstract: The rapid expansion of digital technologies and the internet has enabled the massive collection of Big Data. These large-scale datasets, often noisy or heterogeneous, challenge the feasibility of traditional analytical methods and motivate the development of new strategies for efficient Data processing. Optimal subsampling offers a promising solution by selecting a representative subset of the Data that preserves predictive performance while significantly reducing computational and labeling costs. However, when the sampling strategy relies on an assumed statistical model, model misspecification becomes a critical concern. A theoretical framework for optimal subsampling under model misspecification is introduced, with the objective of minimizing a prediction error metric integrated over the marginal distribution of the explanatory variables. A central contribution is a theorem that provides a closed-form expression for the optimal inclusion probabilities in a Poisson sampling design, establishing a novel connection between sampling theory and optimal experimental design for probability sub-measures. Theoretical findings are validated through simulation studies, focusing in particular on simple linear regression where explicit solutions are available.
