Relational Dynamic Bayesian Networks
  Stochastic processes that involve the creation of objects and relations over
time are widespread, but relatively poorly studied. For example, accurate fault
diagnosis in factory assembly processes requires inferring the probabilities of
erroneous assembly operations, but doing this efficiently and accurately is
difficult. Modeled as dynamic Bayesian networks, these processes have discrete
variables with very large domains and extremely high dimensionality. In this
paper, we introduce relational dynamic Bayesian networks (RDBNs), which are an
extension of dynamic Bayesian networks (DBNs) to first-order logic. RDBNs are a
generalization of dynamic probabilistic relational models (DPRMs), which we had
proposed in our previous work to model dynamic uncertain domains. We first
extend the Rao-Blackwellised particle filtering described in our earlier work
to RDBNs. Next, we lift the assumptions associated with Rao-Blackwellization in
RDBNs and propose two new forms of particle filtering. The first one uses
abstraction hierarchies over the predicates to smooth the particle filters
estimates. The second employs kernel density estimation with a kernel function
specifically designed for relational domains. Experiments show these two
methods greatly outperform standard particle filtering on the task of assembly
plan execution monitoring.
