Predicate Exchange: Inference with Declarative Knowledge

We address the problem of conditioning probabilistic models on predicates, as a means to express declarative knowledge. Models conditioned on predicates rarely have a tractable likelihood; sampling from them requires likelihood-free inference. Existing likelihood-free inference methods focus on predicates which express observations. To address a broader class of predicates, we develop an inference procedure called predicate exchange, which \emph{softens} predicates. Soft predicates return values in a continuous Boolean algebra and can serve as a proxy likelihood function in inference. However, softening introduces an approximation error which depends on a temperature parameter. At zero-temperature predicates are identical, but are often intractable to condition on. At higher temperatures, soft predicates are easier to sample from, but introduce more error. To mitigate this trade-off, we simulate Markov chains at different temperatures and use replica exchange to swap between chains. We implement predicate exchange through a nonstandard execution of a simulation based model, and provide a light-weight tool that can be supplanted on top of existing probabilistic programming formalisms. We demonstrate the approach on sequence models of health and inverse rendering.