Sparse-Matrix Belief Propagation

We propose sparse-matrix belief propagation, which executes loopy belief propagation in pairwise Markov random fields by replacing indexing over graph neighborhoods with sparse-matrix operations. This abstraction allows for seamless integration with optimized sparse linear algebra libraries, including those that perform matrix and tensor operations on modern hardware such as graphical processing units (GPUs). The sparse-matrix abstraction allows the implementation of belief propagation in a high-level language (e.g., Python) that is also able to leverage the power of GPU parallelization. We demonstrate sparse-matrix belief propagation by implementing it in a modern deep learning framework (PyTorch), measuring the resulting massive improvement in running time, and facilitating future integration into deep learning models.