A0467
Title: Confidence sets for high-dimensional variable selection
Authors: Davide Ferrari - Free University of Bozen/Bolzano (Italy) [presenting]
Abstract: The aim is to present a methodology for constructing variable selection confidence sets for high-dimensional regression models. Unlike traditional variable selection approaches, the new methodology goes beyond relying on a singular model obtained through a specific model selection criterion. Instead, it constructs a set of regression models encompassing the true model with a user-specified level of confidence. In noisy high-dimensional datasets, discriminating competing models is more challenging and generally results in broader confidence sets; conversely, in informative datasets, the confidence set contains relatively few valuable models. Within the confidence set methodology, the characteristics of lower boundary models are examined, defined as the set of most parsimonious models included in the confidence sets. Leveraging insights from the confidence set and lower boundary models, natural measures are explored to characterize overall model uncertainty and the importance of individual variables.
