Predictor-Assisted Nonparametric Graphical Models With Multivariate Error-Prone Data

Glioblastoma multiforme (GBM) is a highly aggressive and heterogeneous brain cancer. Emerging evidence suggests that microRNA expression profiles, together with auxiliary gene expression data, are closely associated with GBM and may provide insights into its underlying biological mechanisms. To explore these relationships, we aim to infer the network structure among microRNAs while incorporating gene expressions as auxiliary covariates. While traditional multivariate regression models are intuitive approaches, they are often inadequate in applications due to potential nonlinear relationships and measurement errors inherent in biological data. To address these challenges, we propose a novel model-free framework for joint network inference and variable selection with multivariate responses subject to measurement error. Our method integrates random forests to model marginal response-covariate relationships with built-in error correction, and extends the graphical lasso to recover the conditional dependency structure among microRNAs. This approach is easy for the implementation and offers robustness and flexibility in complex, error-prone biological datasets. Simulation studies and GBM data analysis demonstrate that the proposed method outperforms existing techniques in accurately identifying network structures and selecting informative covariates, offering new insights into the molecular architecture of GBM.