Soft Constraints for Inference with Declarative Knowledge
  We develop a likelihood free inference procedure for conditioning a
probabilistic model on a predicate. A predicate is a Boolean valued function
which expresses a yes/no question about a domain. Our contribution, which we
call predicate exchange, constructs a softened predicate which takes value in
the unit interval [0, 1] as opposed to a simply true or false. Intuitively, 1
corresponds to true, and a high value (such as 0.999) corresponds to "nearly
true" as determined by a distance metric. We define Boolean algebra for soft
predicates, such that they can be negated, conjoined and disjoined arbitrarily.
A softened predicate can serve as a tractable proxy to a likelihood function
for approximate posterior inference. However, to target exact inference, we
temper the relaxation by a temperature parameter, and add a accept/reject phase
use to replica exchange Markov Chain Mont Carlo, which exchanges states between
a sequence of models conditioned on predicates at varying temperatures. We
describe a lightweight implementation of predicate exchange that it provides a
language independent layer that can be implemented on top of existingn modeling
formalisms.
