- M. T. Bahadori, Yan Liu, E. Xing. 2013. Fast structure learning in generalized stochastic processes with latent factors. Abstract: Understanding and quantifying the impact of unobserved processes is one of the major challenges of analyzing multivariate time series data. In this paper, we analyze a flexible stochastic process model, the generalized linear auto-regressive process (GLARP) and identify the conditions under which the impact of hidden variables appears as an additive term to the evolution matrix estimated with the maximum likelihood. In particular, we examine three examples, including two popular models for count data, i.e, Poisson and Conwey-Maxwell Poisson vector auto-regressive processes, and one powerful model for extreme value data, i.e., Gumbel vector auto-regressive processes. We demonstrate that the impact of hidden factors can be separated out via convex optimization in these three models. We also propose a fast greedy algorithm based on the selection of composite atoms in each iteration and provide a performance guarantee for it. Experiments on two synthetic datasets, one social network dataset and one climatology dataset demonstrate the the superior performance of our proposed models.
