Anytime Belief Propagation Using Sparse Domains
This work addresses the need for efficient and anytime-consistent inference in probabilistic graphical models, particularly for applications like natural language processing, though it is incremental as it builds on existing approximations.
The paper tackles the problem of slow belief propagation for marginal inference on large-domain variables and high-order factors by proposing a message passing algorithm using sparse domains with dynamic scheduling, achieving speedups of up to 25 times on grid models and 6 times on a natural language processing task.
Belief Propagation has been widely used for marginal inference, however it is slow on problems with large-domain variables and high-order factors. Previous work provides useful approximations to facilitate inference on such models, but lacks important anytime properties such as: 1) providing accurate and consistent marginals when stopped early, 2) improving the approximation when run longer, and 3) converging to the fixed point of BP. To this end, we propose a message passing algorithm that works on sparse (partially instantiated) domains, and converges to consistent marginals using dynamic message scheduling. The algorithm grows the sparse domains incrementally, selecting the next value to add using prioritization schemes based on the gradients of the marginal inference objective. Our experiments demonstrate local anytime consistency and fast convergence, providing significant speedups over BP to obtain low-error marginals: up to 25 times on grid models, and up to 6 times on a real-world natural language processing task.