How data heterogeneity affects innovating knowledge and information in gene identification: A statistical learning perspective

Data heterogeneity, particularly noted in fields such as genetics, has been identified as a key feature of big data, posing significant challenges to innovation in knowledge and information. This paper focuses on characterizing and understanding the so-called "curse of heterogeneity" in gene identification for low infant birth weight from a statistical learning perspective. Owing to the computational and analytical advantages of expectile regression in handling heterogeneity, this paper proposes a flexible, regularized, partially linear additive expectile regression model for high-dimensional heterogeneous data. Unlike most existing works that assume Gaussian or sub-Gaussian error distributions, we adopt a more realistic, less stringent assumption that the errors have only finite moments. Additionally, we derive a two-step algorithm to address the reduced optimization problem and demonstrate that our method, with a probability approaching one, achieves optimal estimation accuracy. Furthermore, we demonstrate that the proposed algorithm converges at least linearly, ensuring the practical applicability of our method. Monte Carlo simulations reveal that our method's resulting estimator performs well in terms of estimation accuracy, model selection, and heterogeneity identification. Empirical analysis in gene trait expression further underscores the potential for guiding public health interventions.