High Dimensional Point Process System Identification: PCA and Dynamic Index Models

In a number of areas of application, system identification problems are being transformed by the unprecedented amounts of data now becoming available. Hundreds or even thousands of signals may be recorded and in areas such as communication networks and systems neuroscience this data takes the form of point processes (spike trains). These huge data dimensions are forcing a renewed interest in dimension reduction methods as traditional approaches predicated on small data dimensions fail. Here we develop for the first time a true principal components analysis for multivariate point processes as well as a dynamic index model