Approximation by Quantization
  Inference in graphical models consists of repeatedly multiplying and summing
out potentials. It is generally intractable because the derived potentials
obtained in this way can be exponentially large. Approximate inference
techniques such as belief propagation and variational methods combat this by
simplifying the derived potentials, typically by dropping variables from them.
We propose an alternate method for simplifying potentials: quantizing their
values. Quantization causes different states of a potential to have the same
value, and therefore introduces context-specific independencies that can be
exploited to represent the potential more compactly. We use algebraic decision
diagrams (ADDs) to do this efficiently. We apply quantization and ADD reduction
to variable elimination and junction tree propagation, yielding a family of
bounded approximate inference schemes. Our experimental tests show that our new
schemes significantly outperform state-of-the-art approaches on many benchmark
instances.
