On Factor Graphs And Electrical Networks

Factor graphs are graphical models with origins in coding theory. The sum-product and the max-product algorithms, which operate by message passing in a factor graph, subsume a great variety of algorithms in coding, signal processing, and artificial intelligence. In this paper, factor graphs are used to express a one-to-one correspondence (based on results by Dennis) between a class of static electrical circuits andmulti-variable probability distributions; these factor graphs may also be viewed as variational representations of the electrical networks. For the classical linear state space models, both the sum-product algorithm and the max-product algorithm coincide with Kalman filtering. By the mentioned correspondence, these algorithms have a circuit theory interpretation that was discovered by Carter