Statistical Pattern Recognition in Massive Brain-Graphs

Statistical pattern recognition is a field of inquiry devoted to developing theory and methods to facilitate classifying a data point X into one of a finite number of data classes, Y \in {Y_1, Y_2, …}. Historically, work proceeds by first assuming (X,Y) are jointly sampled from some true but unknown distribution. Then, we strive to derive estimators with desirable properties, including consistency, robustness, and computational tractability. Despite much progress, the vast majority of effort has been devoted to a very special case; specifically, the case in which X is a finite dimensional Euclidean vector. Our interests, however, lie in situations in which X is a graph. Such scenarios arise in myriad domains of interest, ranging from chemistry to molecular biology to neuroscience to social/communication networks. Our motivating application is neuroscience, in which it is becoming widely popular to represent neurodata by a "connectome' or brain-graph. We extend the theory and practice of statistical pattern recognition to graph-valued random variables, developing and analyzing non-parametric, semi-parametric, parametric, and hacko-metric classifiers. Via synthetic and real data experiments, we demonstrate that "graph-inspired' methods dominate their graph-ambivalent counterparts.
Joshua Vogelstein is a Visiting Assistant Research Professor in the Department of Mathematics at Duke University and an Assistant Research Scientist at the Human Language Technology Center of Excellence of Johns Hopkins University.