A value such that a*1 = a
Product of two entries, as defined by the particular inference problem.
Sum of two entries, as defined by the particular inference problem.
Sum of two entries, as defined by the particular inference problem. E.g., for computing conditional probabilities, sum is ordinary addition; for most probable explanation, it is max.
A value such that a + 0 = a
Sum of many entries.
Sum of many entries. Typically, this would be implemented by the ordinary sum, but there may be more efficient implementations.
Operations in factored algorithms are defined by a semiring algebraic structure. Each semiring defines a product and sum operation, and a value for zero and one which satisfy a set of properties. Different semirings are appropriate for certain algorithms and data types.