Discovery of Influence between Processes Represented by Hidden Markov Models

Learning the underlying structure between processes is a common problem found in the sciences, however not much work is dedicated towards this problem. In this paper, we attempt to use the language of structure learning to address learning the dynamic influence network between partially observable processes represented as hidden Markov models (HMMs). The importance of learning an influence network is for knowledge discovery and to improve density estimation in temporal distributions. We learn the dynamic influence network, defined by this paper, by first learning the optimal distribution for each process using hidden Markov models, and thereafter apply redefined structure learning algorithms for temporal models to reveal influence relationships. This paper provides the following contributions: we (a) provide a definition of influence between stochastic processes represented by HMMs; and (b) expand on the conventional structure learning literature by providing a structure score and learning procedure to learn influence relationships between HMMs. We provide empirical evidence of the effectiveness of our method over several baselines.