Guaranteed Weighted Counting for Affinity Computation: Beyond Determinism and Structure

Computing the constant Z that normalizes an arbitrary distribution into a probability distribution is a difficult problem that has applications in statistics, biophysics and probabilistic reasoning. In biophysics, it is a prerequisite for the computation of the binding affinity between two molecules, a central question for protein design. In the case of a discrete stochastic Graphical Model, the problem of computing Z is equivalent to weighted model counting in SAT or CSP, known to be #P-complete [38]. SAT solvers have been used to accelerate guaranteed normalizing constant computation, leading to exact tools such as cachet [33], ace [8] or minic2d [28]. They exploit determinism in the stochastic model to prune during counting and the dependency structure of the model (partially captured by tree-width) to cache intermediary counts, trading time for space. When determinism or structure are not sufficient, we consider the idea of discarding sufficiently negligible contributions to Z to speedup counting. We test and compare this approach with other solvers providing deterministic guarantees on various benchmarks, including protein binding affinity computations, and show that it can provide important speedups.