Approximate Variational Message Propagation For Gmrf

Variational inference is an important deterministic approximate inference method, which computes the approximate expectation of random variables through variational iterations. However, with variational iteration increasing, variational inference pro-cess involve more and more information, and the new variables have weak influence. Therefore, approximate variational inference methods under incomplete iteration are proposed. This thesis proposes approximate variational message propagation (AVMP) that computes the lower expectation bounds of random variables for GMRF. Our main work is:1. We define the concept of Gaussian Ring-Split Tree to represent the iteration com-putation process of GMRF.2. We design the AVMP on the tree, which propagates belief message from bottom to top and then get the expectation bounds of random variables in root node.3. By the numerical simulation experiments we verify the validity of the algorithm, and compare the tightness and the complexity of the algorithm for different GMRF models.