Identifying the Network Structure of Stochastic Dynamical Systems

Christopher Quinn, University of Illinois at Urbana-Champaign

We are developing methods for researchers to take network time series data (such as biological recordings, Facebook activity or stock market data), apply our methods, and obtain a graphical representation of the causal influence structure – that is, not who is friends with whom on Facebook, but who is influencing whom.

The two major aspects of this problem are data modeling and graph identification. We want to apply our methods to large networks and we will use time series data. For both aspects, computation is an important issue. Data modeling often involves parameter fitting and model selection, which can be an expensive optimization problem. The graph identification involves computing statistics for each process to determine which edges should be present.

Our recent work has focused on developing a well-defined graphical model to represent the structure of stochastic dynamical systems. It is analogous to Markov and Bayesian networks, but for the context of processes. We also have shown that for the graph identification phase the full graph structure, as well as optimal, low-complexity approximations, can be identified in a distributed manner, often with low-order statistics. This greatly improves computational tractability and makes the problem more amenable to computing with HPC resources.

Abstract Author(s): Christopher Quinn, Todd Coleman, and Negar Kiyavash