Nonuniform Dynamic Discretization in Hybrid Networks
This work addresses the challenge of efficient and accurate inference in hybrid probabilistic networks, which is incremental as it builds on existing discretization methods by optimizing partitions and data structures.
The paper tackles the problem of probabilistic inference in hybrid networks with continuous and discrete variables by introducing a nonuniform discretization method that reduces data structure size and improves inference accuracy, showing that Binary Split Partition trees can be exponentially smaller than standard uniform discretizations and that the algorithm converges empirically.
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.