Semantic Message Passing for TablesSemantic Message Passing. Factor nodes allow the joint inference process to operate. Typical inference algorithms such as belief propagation and message passing rely on pre-computed joint probability distribution tables (PDTs) stored at the factor nodes. For example, the factor node ψ3 for column header variable C1 would store a PDT over the variables C1, R11, R12, R13; i.e. ψ3 would precompute and store a PDT over the column header and all row cell values. As the size of the candidate set of values that Ci and Rij can be mapped to increases, the size of the PDT will rapidly grow. Assuming that the size of the candidate set for a variable is 25, ψ3 associated with the variables C1, R11, R12, R13 would have 390,625 entries in the joint PDT!