A Collaborative Learning Framework for Estimating Many Individualized Regression Models in a Heterogeneous Population
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2017 IEEE. Mixed-effect models (MEMs) have been found very useful for modeling complex dataset where many similar individualized regression models should be estimated. Like many statistical models, the success of these models builds on the assumption that a central tendency can effectively establish the population-level characteristics and covariates are sufficient to characterize the individual variation as derivation from the center. In many real-world problems, however, the dataset is collected from a rather heterogeneous population, where each individual has a distinct model. To fill in this gap, we propose a collaborative learning framework that provides a generic methodology for estimating a heterogeneous population of individualized regression models by exploiting the idea of 'canonical models' and model regularization. By using a set of canonical models to represent the heterogeneous population characteristics, the canonical models span the modeling space for the individuals' models, e.g., although each individual model is distinct, its model parameter vector can be represented by the parameter vectors of the canonical models. Theoretical analysis is also conducted to reveal a connection between the proposed method and the MEMs. Both simulation studies and applications on Alzheimer's disease and degradation modeling of turbofan engines demonstrate the efficacy of the proposed method.
