Predicting graphical models based on functional data

Abstract

Graphical models are widely used to model complex relationships between variables in various fields. However, existing analysis methods focus primarily on scalar data and give little attention to addressing the challenges posed by nonscalar data, e.g., functional data, which are prevalent in many real-world applications. Additionally, most methods assume a static graphical model within the observed period, neglecting the dynamic changes that may occur over time. In this paper, we propose a novel method for predicting graphical models based on functional data. Our approach transforms functional data into finite-dimensional vectors via basis function expansion and cross-validation. We then establish a sequential prediction model for determining the correlation coefficient matrix of the decomposed data, thus accounting for the constraints imposed on the matrix via a transformation technique. Finally, we employ conditional independence tests to identify the edges of the predicted graphical model. We demonstrate the effectiveness of our method through extensive simulations and real data analyses. The results show that our method performs better than the competing methods in terms of prediction accuracy and provides valuable insights into the dynamic changes exhibited by a network. This work opens new possibilities for conducting graphical model analyses in various domains, particularly in terms of handling functional data and predicting dynamic relationships.