Message Passing On Factor Graphs
A popular message passing algorithm on factor graphs is the sum-product algorithm, which efficiently computes all the marginals of the individual variables of the function. In particular, the marginal of variable is defined as
where the notation means that the summation goes over all the variables, except . The messages of the sum-product algorithm are conceptually computed in the vertices and passed along the edges. A message from or to a variable vertex is always a function of that particular variable. For instance, when a variable is binary, the messages over the edges incident to the corresponding vertex can be represented as vectors of length 2: the first entry is the message evaluated in 0, the second entry is the message evaluated in 1. When a variable belongs to the field of real numbers, messages can be arbitrary functions, and special care needs to be taken in their representation.
In practice, the sum-product algorithm is used for statistical inference, whereby is a joint distribution or a joint likelihood function, and the factorization depends on the conditional independencies among the variables.
The Hammersley–Clifford theorem shows that other probabilistic models such as Markov networks and Bayesian networks can be represented as factor graphs; the latter representation is frequently used when performing inference over such networks using belief propagation. On the other hand, Bayesian networks are more naturally suited for generative models, as they can directly represent the causalities of the model.
Read more about this topic: Factor Graph
Famous quotes containing the words message, passing and/or factor:
“Television does not dominate or insist, as movies do. It is not sensational, but taken for granted. Insistence would destroy it, for its message is so dire that it relies on being the background drone that counters silence. For most of us, it is something turned on and off as we would the light. It is a service, not a luxury or a thing of choice.”
—David Thomson, U.S. film historian. America in the Dark: The Impact of Hollywood Films on American Culture, ch. 8, William Morrow (1977)
“There is, indeed, nothing that so much seduces reason from vigilance, as the thought of passing life with an amiable woman.”
—Samuel Johnson (1709–1784)
“You factor in racism as a reality and you keep moving.”
—Jewell Jackson McCabe (b. 1945)