Inference for Belief Networks Using Coupling From the Past

Inference for belief networks using Gibbs sampling produces a distribution for unob­ served variables that differs from the correct distribution by a (usually) unknown error, since convergence to the right distribution occurs only asymptotically. The method of "coupling from the past" samples from ex­ actly the correct distribution by ( conceptu­ ally) running dependent Gibbs sampling sim­ ulations from every possible starting state from a time far enough in the past that all runs reach the same state at time t = 0. Ex­ plicitly considering every possible state is in­ tractable for large networks, however. We propose a method for layered noisy-or net­ works that uses a compact, but often impre­ cise, summary of a set of states. This method samples from exactly the correct distribution, and requires only about twice the time per step as ordinary Gibbs sampling, but it may require more simulation steps than would be needed if chains were tracked exactly.