Subgroup Analysis for High‐Dimensional Latent Factor Regression

ABSTRACT High‐dimensional heterogeneous learning has become a popular approach to uncover important scientific insights by effectively synthesizing subgroup‐specific information, as exemplified by numerous contemporary applications including precision medicine and customized marketing. However, naively applying existing methods when high collinearity exists among covariates can lead to misleading outcomes. Motivated by this challenge, this paper develops a two‐phase framework that integrates subgroup identification with latent factor analysis to simultaneously estimate heterogeneous effects alongside high‐dimensional coefficients in the existence of high collinearity. With the proper factor estimation through principal component analysis, it is demonstrated that an oracle estimator informed by the true grouping structures attains desirable statistical performance. Moreover, we establish rigorous theoretical guarantees for the proposed methodology by deriving joint estimation error bounds for heterogeneous effects and high‐dimensional coefficients. The validity of the developed approach is supported by numerical experiments and a real‐data analysis.