CIF: Small: Learning on Graphs

University Of Colorado At Boulder, Boulder CO

Investigators

Abstract

Not unlike road networks, significant disruptions in the pattern of connections between brain regions have profound effect on brain function. International projects, such as the Human Connectome Project and the Autism Brain Imaging Data Exchange initiative, provide open access to massive datasets that can be used to learn the association between brain connectivity and psychiatric or neurological diseases. This award responds to the current lack of analytical and computational methods to quantify changes in the organization of brain functional networks. This project proposes to design novel machine learning algorithms that will lead the way toward precision medicine in psychiatry and neurology. The award will train several graduate students to work on big-data challenges in precision medicine. The source code that will implement the algorithms will be made publicly available in the form of open source toolboxes. The availability of large datasets composed of graphs creates an unprecedented need to invent tools in statistical learning to study "graph-valued random variables". The first goal of this project is to develop theory and algorithms to estimate the mean and variance of a set of graphs. This basic problem is at the core of several statistical inference problems about population of graph ensembles. The second aim is to develop statistical methods that can detect significant structural changes (e.g., alteration of the topology and connectivity, etc.) in a time series of graphs. The third aim is concerned with the question of learning functions defined on a graph ensemble. The proposed approach relies on the ability to equip a graph ensemble with a metric, effectively turning the learning problem into the question of extending functions defined on a metric space. 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.