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
Famous quotes containing the words relation to, relation, free and/or energy:
“We must get back into relation, vivid and nourishing relation to the cosmos and the universe. The way is through daily ritual, and is an affair of the individual and the household, a ritual of dawn and noon and sunset, the ritual of the kindling fire and pouring water, the ritual of the first breath, and the last.”
—D.H. (David Herbert)
“The difference between objective and subjective extension is one of relation to a context solely.”
—William James (1842–1910)
“... that phrase of mischievous sophistry, “all men are born free and equal.” This false and futile axiom, which has done, is doing, and will do so much harm to this fine country ...”
—Frances Trollope (1780–1863)
“While the State becomes inflated and hypertrophied in order to obtain a firm enough grip upon individuals, but without succeeding, the latter, without mutual relationships, tumble over one another like so many liquid molecules, encountering no central energy to retain, fix and organize them.”
—Emile Durkheim (1858–1917)