Data-Guided Model Combination by Decomposition and Aggregation

Model selection and model combination is a general problem in many areas. Especially, when we have several different candidate models and also have gathered a new data set, we want to construct a more accurate and precise model in order to help predict future events. In this paper, we propose a new data-guided model combination method by decomposition and aggregation. With the aid of influence diagrams, we analyze the dependence among candidate models and apply latent factors to characterize such dependence. After analyzing model structures in this framework, we derive an optimal composite model. Two widely used data analysis tools, namely, Principal Component Analysis (PCA) and Independent Component Analysis (ICA) are applied for the purpose of factor extraction from the class of candidate models. Once factors are ready, they are sorted and aggregated in order to produce composite models. During the course of factor aggregation, another important issue, namely factor selection, is also touched on. Finally, a numerical study shows how this method works and an application using physical data is also presented