Learning Linear Dependency Trees from Multivariate Time-series Data

Representing interactions between variables in large data sets in an understandable way is usually important and hard task. This article presents a methodology how a linear dependency structure between variables can be constructed from multivariate data. The dependencies between the variables are specified by multiple linear regression models. A sparse regression algorithm and bootstrap based resampling are used in the estimation of models and in construction of a belief graph. The belief graph highlights the most important mutual dependencies between the variables. Thresholding and graph operations may be applied to the belief graph to obtain a final dependency structure, which is a tree or a forest. In the experimental section results of the proposed method using real-world data set were realistic and convincing.