Sequential Dependence Decomposition and Feature Learning

In this paper, we introduce an approach to decompose statistical dependence and learn informative features from sequential data. We first present a sequential decomposition of dependence, which extends the chain rule of mutual information. To learn this decomposition from data, we investigate the optimal feature representations associated with decomposed dependence modes and develop corresponding learning algorithms. Specifically, for stationary processes, we demonstrate applications of the learned features in computing optimal Markov approximation and testing the order of Markov processes.