On sparse approximations for time-series networks

Christopher J. Quinn

Abstract: Learning the full structure of large networks of interacting time-series can be computationally and statistically challenging. In such cases, sparse approximations, which preserve only a few edges in the network, might be sought instead. Sparse networks are easier to visually analyze and potentially more tractable to identify. The quality of an approximation can be measured using the Kullback-Leibler divergence between the full joint distribution and the approximating distributions. Given the challenge of learning the full (dense) network, a natural question is how statistically and computationally difficult it is to learn the best approximations for classes of sparse graphs. We will investigate bounds on the sample complexity, which characterizes the amount of data needed to find an optimal approximation with high probability, for certain classes of sparse approximations.