sum-product algorithm

The sum-product algorithm is a computational method used in probabilistic models to efficiently determine the likelihood of certain outcomes. It works on a network of interconnected variables, passing and updating information called "messages" between nodes. Each message combines local information with messages received from neighboring nodes, enabling the algorithm to compute marginal probabilities—how likely each variable is to take particular values—without examining every possible combination. This approach is widely used in decoding error-correcting codes and inference tasks, providing accurate results efficiently in complex systems with many interdependent variables.