Ensemble Inference in Supervised Homogeneity Pursuit

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.

Host: Nan Lin

Dr. Song is Pharmacia Research Professor of Biostatistics at the University of Michigan School of Public Health, Ann Arbor. He received his PhD in Statistics from the University of British Columbia, Vancouver, Canada in 1996.  He has published over 250 peer-reviewed papers and graduated 29 PhD students and trained 7 postdoc research fellows.  Dr. Song's current research interests include data integration, distributed inference, high-dimensional data analysis, longitudinal data analysis, mediation analysis, and spatiotemporal modeling with applications in aging, nephrology, chronic disease epidemiology, environmental health sciences, and nutritional sciences. He is AAAS Fellow, IMS Fellow, ASA Fellow and Elected Member of the International Statistical Institute. Dr. Song now serves as Area Editor of the Annals of Applied Statistics (Medicine, EHR and Smart Health), Associate Editor of the Journal of American Statistical Association, Journal of the Royal Statistical Society Series B (Statistical Methodology) and the Journal of Multivariate Analysis.  His research programs have been supported by NIH and NSF grants.