Distributed Relational State Representations for Complex Stochastic Processes

Several promising variants of hidden Markov models (HMMs) have recently been developed to efficiently deal with large state and observation spaces and relational structure. Many application domains, however, have an apriori componential structure such as parts in musical scores. In this case, exact inference within relational HMMs still grows exponentially in the number of components. In this paper, we propose to approximate the complex joint relational HMM with a simpler, distributed one: k relational hidden chains over n states, one for each component. Then, we iteratively perform inference for each chain given fixed values for the other chains until convergence. Due to this structured mean field approximation, the effective size of the hidden state space collapses from O(n) to O(n).