UAlberta PIMS Mathematics and Statistics Colloquium: Peter Song

Abstract: We develop an ensemble inference framework for valid post-fusion inference in the context of supervised homogeneity pursuit (SHoP). This methodology allows to fuse numerous micro-level weak signals into a few macro-level strong predictors in regression analysis. Mixed integer optimization (MIO) supports the optimization involving simultaneously selecting important weak signals and estimating model parameters. 

We carry out post-fusion uncertainty quantification by the means of adversarial noise perturbations, through which we ensemble multiple solutions, each being generated from one set of synthetic errors, to construct valid confidence intervals. We establish theoretical guarantees for inclusion consistency and valid confidence coverage under both Gaussian and sub-Gaussian error distributions. Extensive simulations and a real-world data analysis demonstrate robust empirical performance across diverse error structures and sparsity levels.