In an attempt to better understand the behavior of the sum-product algorithm in richly-connected graphical models, we study its application in Gaussian networks with cycles. Experimentally, we find that the algorithm occasionally diverges and sometimes reaches a dynamic equilibrium. However, in most cases the algorithm converges and it turns out that the fixed point of the means coincides with the exact solution. Each of us will present a different approach to analyzing this problem and reveal theorems on fixed points, the exactness of inference and convergence to the fixed point.

Slides used during the talk

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