Nonuniform Dynamic Discretization in Hybrid Networks
  We consider probabilistic inference in general hybrid networks, which include
continuous and discrete variables in an arbitrary topology. We reexamine the
question of variable discretization in a hybrid network aiming at minimizing
the information loss induced by the discretization. We show that a nonuniform
partition across all variables as opposed to uniform partition of each variable
separately reduces the size of the data structures needed to represent a
continuous function. We also provide a simple but efficient procedure for
nonuniform partition. To represent a nonuniform discretization in the computer
memory, we introduce a new data structure, which we call a Binary Split
Partition (BSP) tree. We show that BSP trees can be an exponential factor
smaller than the data structures in the standard uniform discretization in
multiple dimensions and show how the BSP trees can be used in the standard join
tree algorithm. We show that the accuracy of the inference process can be
significantly improved by adjusting discretization with evidence. We construct
an iterative anytime algorithm that gradually improves the quality of the
discretization and the accuracy of the answer on a query. We provide empirical
evidence that the algorithm converges.
