Learning Latent Graphs from Stationary Signals

University Of California-Davis, Davis CA

Investigators

Abstract

In recent years, data with many features and complicated interactions among these features and/or across time and space have become ubiquitous. How to extract meaningful information from such large complex data is one of the most pressing questions with significant scientific and societal implications. This research will generate new tools for modeling and analyzing such data through graph- or network-based representations of the data. The analytical and computational tools derived from this research can be applied to many fields including economics, finance, neuroscience, and various sub-fields within the social and biological sciences. This project will also provide training opportunities for a new generation of researchers empowering them to contribute to the rapid development of statistics, data science and related fields. Results of this research will be disseminated through publications, conference presentations, lectures, and open source software. This project will develop a novel Spectral Graph Models (SGM) framework which models multivariate data as graph-referenced stationary signals. The SGM framework provides new tools for network inference from a signal processing perspective and for modeling multivariate observations with complicated dependencies, including possible temporal or spatial dependence. It also provides new tools for covariance estimation through efficient graph-based representations. The SGM framework combines four key aspects - spectral representation of covariances, spectral graph theory, semiparametric modeling, and sparse parameterization. It allows for temporal dependency in graphs or parameters and can be used to model both independent and dependent multivariate observations. The SGM framework has a wide range of applications, and methods developed through this research will be applied to various types of data including brain activity and international trade data. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.