G-Lasso Network Analysis for Functional Data

Network analytical tools are becoming increasingly popular in analysing interdependent and interacting data entities. Statistical modelling of network data seeks to recover the underlying relational structure of the data capturing relevant characteristics and regularities in the pattern of interactions. This framework is widely adopted in multivariate data setting. However, in many applications, data are naturally regarded as random functions rather than multivariate vectors. In this work, we propose a simple approach to extend network analytical tools to the functional data setting. Specifically, we show that the graph representation of a set of functions can be retrieved through the precision matrix of a Gaussian Process, which encodes the conditional dependence structure among functional data. By using the standard graphical Lasso algorithm, preliminary results of the proposed methodology are shown for a benchmark dataset of daily average temperatures.