Inference in Dynamic Probabilistic Relational Models

Stochastic processes that involve the creation and modifica- tion of objects and relations over time are widespread, but relatively poorly studied. For example, accurate fault diagno- sis in factory assembly processes requires inferring the prob- abilities 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. Recently, Sanghai et al. (2003) introduced dynamic proba- bilistic relational models (DPRMs) to model probabilistic re- lational domains that change with time. They also proposed a form of Rao-Blackwellized particle filtering which performs well on problems of this type, but relies on very restrictive as- sumptions. In this paper we lift these assumptions, develop- ing two forms of particle filtering that are in principle appli- cable to any relational stochastic process. The first one uses an abstraction lattice over relational variables to smooth the particle filter's estimates. The second employs kernel den- sity estimation using a kernel function specifically designed for relational domains. Experiments show these two methods greatly outperforms standard particle filtering on the task of assembly plan execution monitoring.