Scalable Filtering of Large Graph-Coupled Hidden Markov Models

We consider the online littering problem for a graph-coupled hidden Markov model (GHMM) with the Anonymous Influence property. Large-scale spatial processes such as forest fires, social networks, disease epidemics, and robot swarms are often modeled by GHMMs with this property. We derive a scalable online recursive algorithm to produce a belief over states for each HMM node in the GHMM at each time step, given a history of noisy observations. In contrast to prior work, our algorithm is tractable for the high-dimensional discrete state spaces of GHMMs with arbitrary graph structure, and our method scales linearly with the total number of HMMs, i.e., nodes in the graph. We demonstrate the accuracy and scaling of our method using simulation experiments of a wildfire model containing 10(298) total states and a disease epidemic model containing 10(18) states.