Title: Supervised Homogeneity Pursuit via Mixed Integer Optimization

Abstract: Stratification is one statistical principle in data processing to mitigate the underlying population heterogeneity, which is typically handled by clustering when stratum labels are unknown.  Many practical problems require post-clustering statistical learning that is challenged by the issue of “double data dipping”, leading to the difficulty of uncertainty quantification.  One solution to address this challenge is to perform a simultaneous operation of clustering and estimation in data analyses.  Recently we developed a new paradigm of supervised homogeneity pursuit via mixed integer optimization, which provides a conceptually simple and computationally straightforward machinery with the use of suitable constraints in optimization.  In addition, we develop a self-conformal inference to quantify post-fusion uncertainty.  This novel toolbox has been then applied to solve several real-world problems arising from infectious disease surveillance, influence of environmental exposure to health, and risk factors for aging.  Some algorithmic limitations worth future research will be discussed.