MILFM: Multiple index latent factor model based on high-dimensional features

The aim of this article is to develop a multiple-index latent factor modeling (MILFM) framework to build an accurate prediction model for clinical outcomes based on a massive number of features. We develop a three-stage estimation procedure to build the prediction model. MILFM uses an independent screening method to select a set of informative features, which may have a complex nonlinear relationship with the outcome variables. Moreover, we develop a latent factor model to project all informative predictors onto a small number of local subspaces, which lead to a few key features that capture reliable and informative covariate information. Finally, we fit the regularized empirical estimate to those key features in order to accurately predict clinical outcomes. We systematically investigate the theoretical properties of MILFM, such as risk bounds and selection consistency. Our simulation results and real data analysis show that MILFM outperforms many state-of-the-art methods in terms of prediction accuracy.