Relation To Free Energy
The sum-product algorithm is related to the calculation of free energy in thermodynamics. Let Z be the partition function. A probability distribution
(as per the factor graph representation) can be viewed as a measure of the internal energy present in a system, computed as
The free energy of the system is then
It can then be shown that the points of convergence of the sum-product algorithm represent the points where the free energy in such a system is minimized. Similarly, it can be shown that a fixed point of the iterative belief propagation algorithm in graphs with cycles is a stationary point of a free energy approximation.
Read more about this topic: Belief Propagation
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