Gaussian belief propagation code

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Gaussian belief propagation code

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Gaussian belief propagation (GaBP) is an efficient algorithm for performing inference on probabilistic graphical models, particularly those involving Gaussian distributions. It operates by passing messages between nodes in a factor graph to iteratively refine estimates of marginal distributions.

In MATLAB, implementing GaBP typically involves representing the graph structure and defining the message update rules. The algorithm is well-suited for problems like linear systems, Gaussian processes, and sensor networks where exact inference is computationally expensive.

The core idea revolves around nodes exchanging Gaussian messages characterized by mean and precision parameters. Each node updates its belief based on incoming messages and propagates new messages to neighbors. The process continues until convergence, yielding marginal distributions for all variables.

MATLAB's matrix operations make it convenient to implement the precision matrix updates central to GaBP. The algorithm's distributed nature allows handling large-scale problems by decomposing them into local computations. Convergence properties depend on the graph topology, with tree-structured graphs guaranteeing exact solutions in finite iterations.

Key considerations include message scheduling strategies (synchronous/asynchronous) and handling numerical stability when dealing with high-dimensional systems. GaBP's simplicity and scalability have made it popular for applications ranging from wireless communications to image processing.